Syllabus to learn statistics

PHASE 0 - FOUNDATIONAL MATHEMATICS

Day 1: Functions: concept and notation - Foundations

• Objective: Build a solid conceptual understanding of functions: concept and notation.

• Theory: A function maps every input to exactly one output; domain and range define what is allowed in and out.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 2: Functions: concept and notation - Applied Practice

• Objective: Apply functions: concept and notation to solve concrete problems and solidify intuition.

• Theory (recap): A function maps every input to exactly one output; domain and range define what is allowed in and out.

• Practice: Write 3 examples of functions you use daily (e.g. price -> tax) and identify domain/range.

Day 3: Logarithms - Foundations

• Objective: Build a solid conceptual understanding of logarithms.

• Theory: Logarithms are the inverse of exponentiation; they compress large ranges and turn multiplication into addition. log rules: log(ab)=log a + log b, log(a/b)=log a - log b, log(a^n)=n log a.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 4: Logarithms - Applied Practice

• Objective: Apply logarithms to solve concrete problems and solidify intuition.

• Theory (recap): Logarithms are the inverse of exponentiation; they compress large ranges and turn multiplication into addition.

• Practice: Solve 10 log equations and explain why log-scale is used for skewed data like income.

Day 5: Exponential functions - Foundations

• Objective: Build a solid conceptual understanding of exponential functions.

• Theory: Exponential growth/decay: y = a * e^(kx); the rate of change is proportional to the current value. Connection to compound interest and to the exponential distribution.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 6: Exponential functions - Applied Practice

• Objective: Apply exponential functions to solve concrete problems and solidify intuition.

• Theory (recap): Exponential growth/decay: y = a * e^(kx); the rate of change is proportional to the current value.

• Practice: Plot exponential growth vs decay curves and identify the half-life/doubling time.

Day 7: Sigma notation (summation) - Foundations

• Objective: Build a solid conceptual understanding of sigma notation (summation).

• Theory: Sigma notation compactly represents repeated addition, e.g. sum of x_i from i=1 to n.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 8: Sigma notation (summation) - Applied Practice

• Objective: Apply sigma notation (summation) to solve concrete problems and solidify intuition.

• Theory (recap): Sigma notation compactly represents repeated addition, e.g. sum of x_i from i=1 to n.

• Practice: Rewrite 5 formulas (mean, variance) fully in sigma notation from scratch.

Day 9: Vectors: definition and operations - Introduction

• Objective: Grasp the core intuition behind vectors: definition and operations before the mechanics.

• Theory: A vector is an ordered list of numbers representing magnitude and direction; supports addition, scalar multiplication.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 10: Vectors: definition and operations - Deep Dive

• Objective: Understand the full mechanics/derivation behind vectors: definition and operations.

• Theory: A vector is an ordered list of numbers representing magnitude and direction; supports addition, scalar multiplication. Vector norm (length) and the dot product measure size and alignment between vectors.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 11: Vectors: definition and operations - Applied Practice

• Objective: Apply vectors: definition and operations to a concrete problem or dataset.

• Theory (recap): Vector norm (length) and the dot product measure size and alignment between vectors.

• Practice: Compute the norm and dot product of 5 vector pairs by hand, then verify with NumPy.

Day 12: Matrices: definition and notation - Foundations

• Objective: Build a solid conceptual understanding of matrices: definition and notation.

• Theory: A matrix is a rectangular array of numbers; rows/columns encode structured data (e.g. a dataset).

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 13: Matrices: definition and notation - Applied Practice

• Objective: Apply matrices: definition and notation to solve concrete problems and solidify intuition.

• Theory (recap): A matrix is a rectangular array of numbers; rows/columns encode structured data (e.g. a dataset).

• Practice: Represent a small dataset (5 rows, 3 features) as a matrix and label its dimensions.

Day 14: Matrix operations - Foundations

• Objective: Build a solid conceptual understanding of matrix operations.

• Theory: Matrix addition and multiplication follow strict dimension rules; multiplication is not commutative. The identity matrix and matrix inverse play the role of '1' and division in matrix algebra.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 15: Matrix operations - Applied Practice

• Objective: Apply matrix operations to solve concrete problems and solidify intuition.

• Theory (recap): Matrix addition and multiplication follow strict dimension rules; multiplication is not commutative.

• Practice: Multiply 3 matrix pairs by hand, then verify using NumPy; try one non-conformable pair and explain the error.

Day 16: Solving systems of linear equations - Foundations

• Objective: Build a solid conceptual understanding of solving systems of linear equations.

• Theory: A system of linear equations can be written as Ax = b and solved via elimination or matrix inversion. Systems can be consistent (unique/infinite solutions) or inconsistent (no solution).

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 17: Solving systems of linear equations - Applied Practice

• Objective: Apply solving systems of linear equations to solve concrete problems and solidify intuition.

• Theory (recap): A system of linear equations can be written as Ax = b and solved via elimination or matrix inversion.

• Practice: Solve 5 systems of equations by hand, then confirm each with numpy.linalg.solve.

Day 18: Eigenvalues and eigenvectors (intuition) - Introduction

• Objective: Grasp the core intuition behind eigenvalues and eigenvectors (intuition) before the mechanics.

• Theory: An eigenvector of a matrix points in a direction that the matrix only stretches, not rotates; the eigenvalue is the stretch factor.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 19: Eigenvalues and eigenvectors (intuition) - Deep Dive

• Objective: Understand the full mechanics/derivation behind eigenvalues and eigenvectors (intuition).

• Theory: An eigenvector of a matrix points in a direction that the matrix only stretches, not rotates; the eigenvalue is the stretch factor. Eigen-decomposition underlies PCA, covariance structure, and stability analysis.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 20: Eigenvalues and eigenvectors (intuition) - Applied Practice

• Objective: Apply eigenvalues and eigenvectors (intuition) to a concrete problem or dataset.

• Theory (recap): Eigen-decomposition underlies PCA, covariance structure, and stability analysis.

• Practice: Compute eigenvalues/eigenvectors of a 2x2 matrix by hand and visualize the transformation.

Day 21: Derivatives - Introduction

• Objective: Grasp the core intuition behind derivatives before the mechanics.

• Theory: A derivative measures the instantaneous rate of change of a function; it is the slope of the tangent line.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 22: Derivatives - Deep Dive

• Objective: Understand the full mechanics/derivation behind derivatives.

• Theory: A derivative measures the instantaneous rate of change of a function; it is the slope of the tangent line. Common rules: power rule, product rule, chain rule.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 23: Derivatives - Applied Practice

• Objective: Apply derivatives to a concrete problem or dataset.

• Theory (recap): Common rules: power rule, product rule, chain rule.

• Practice: Differentiate 10 functions by hand and verify symbolically with SymPy.

Day 24: Partial derivatives - Foundations

• Objective: Build a solid conceptual understanding of partial derivatives.

• Theory: A partial derivative measures how a multivariable function changes with respect to one variable, holding others fixed. Partial derivatives are the building block of gradients used in optimization (e.g. least squares, gradient descent).

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 25: Partial derivatives - Applied Practice

• Objective: Apply partial derivatives to solve concrete problems and solidify intuition.

• Theory (recap): A partial derivative measures how a multivariable function changes with respect to one variable, holding others fixed.

• Practice: Compute partial derivatives of a 2-variable loss function and find its minimum by hand.

Day 26: Integrals - Foundations

• Objective: Build a solid conceptual understanding of integrals.

• Theory: An integral accumulates area under a curve; it is the inverse operation of differentiation. Definite integrals compute exact accumulated quantities (e.g. probability over an interval).

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 27: Integrals - Applied Practice

• Objective: Apply integrals to solve concrete problems and solidify intuition.

• Theory (recap): An integral accumulates area under a curve; it is the inverse operation of differentiation.

• Practice: Compute 5 definite integrals by hand and confirm with SciPy's quad.

Day 28: Why a PDF must integrate to 1 - Introduction

• Objective: Grasp the core intuition behind why a pdf must integrate to 1 before the mechanics.

• Theory: A probability density function describes relative likelihood; total probability across all outcomes must equal 1 by the axioms of probability.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 29: Why a PDF must integrate to 1 - Deep Dive

• Objective: Understand the full mechanics/derivation behind why a pdf must integrate to 1.

• Theory: A probability density function describes relative likelihood; total probability across all outcomes must equal 1 by the axioms of probability. This constraint is what lets us normalize arbitrary non-negative functions into valid densities.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 30: Why a PDF must integrate to 1 - Applied Practice

• Objective: Apply why a pdf must integrate to 1 to a concrete problem or dataset.

• Theory (recap): This constraint is what lets us normalize arbitrary non-negative functions into valid densities.

• Practice: Verify by integration that the Normal and Exponential PDFs each integrate to 1 over their support.

Day 31: Multivariable calculus basics - Foundations

• Objective: Build a solid conceptual understanding of multivariable calculus basics.

• Theory: Gradients generalize the derivative to multiple dimensions and point in the direction of steepest increase. Multivariable calculus underlies optimization of loss functions with many parameters.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 32: Multivariable calculus basics - Applied Practice

• Objective: Apply multivariable calculus basics to solve concrete problems and solidify intuition.

• Theory (recap): Gradients generalize the derivative to multiple dimensions and point in the direction of steepest increase.

• Practice: Compute the gradient of a simple 2-parameter loss function and interpret its direction.

Day 33: Why expectation is an integral - Foundations

• Objective: Build a solid conceptual understanding of why expectation is an integral.

• Theory: Expectation is a probability-weighted average; for continuous variables this weighted sum becomes an integral of x * f(x). This connects calculus directly to the core statistical concept of the mean of a random variable.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 34: Why expectation is an integral - Applied Practice

• Objective: Apply why expectation is an integral to solve concrete problems and solidify intuition.

• Theory (recap): Expectation is a probability-weighted average; for continuous variables this weighted sum becomes an integral of x * f(x).

• Practice: Derive E[X] for the Uniform(0,1) distribution by hand using integration.

Day 35: Vector spaces - Introduction

• Objective: Grasp the core intuition behind vector spaces before the mechanics.

• Theory: A vector space is a set of vectors closed under addition and scalar multiplication, satisfying specific axioms.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 36: Vector spaces - Deep Dive

• Objective: Understand the full mechanics/derivation behind vector spaces.

• Theory: A vector space is a set of vectors closed under addition and scalar multiplication, satisfying specific axioms. Statistical models live inside vector spaces (e.g. the space of possible regression coefficients).

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 37: Vector spaces - Applied Practice

• Objective: Apply vector spaces to a concrete problem or dataset.

• Theory (recap): Statistical models live inside vector spaces (e.g. the space of possible regression coefficients).

• Practice: Check whether 3 given sets qualify as vector spaces by testing the axioms.

Day 38: Basis and dimension - Foundations

• Objective: Build a solid conceptual understanding of basis and dimension.

• Theory: A basis is a minimal set of vectors that spans a vector space; dimension is the number of vectors needed. Choosing a good basis (e.g. principal components) simplifies high-dimensional data.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 39: Basis and dimension - Applied Practice

• Objective: Apply basis and dimension to solve concrete problems and solidify intuition.

• Theory (recap): A basis is a minimal set of vectors that spans a vector space; dimension is the number of vectors needed.

• Practice: Find a basis for a given 2D and 3D subspace and confirm linear independence.

Day 40: Orthogonality - Foundations

• Objective: Build a solid conceptual understanding of orthogonality.

• Theory: Orthogonal vectors have a zero dot product and represent independent directions. Orthogonality underlies uncorrelated predictors in regression and independent components in PCA.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 41: Orthogonality - Applied Practice

• Objective: Apply orthogonality to solve concrete problems and solidify intuition.

• Theory (recap): Orthogonal vectors have a zero dot product and represent independent directions.

• Practice: Check orthogonality of vector pairs and orthogonalize a non-orthogonal pair via Gram-Schmidt.

Day 42: Projections - Introduction

• Objective: Grasp the core intuition behind projections before the mechanics.

• Theory: Projecting a vector onto another finds the closest point in that direction; this is the geometric basis of least-squares regression.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 43: Projections - Deep Dive

• Objective: Understand the full mechanics/derivation behind projections.

• Theory: Projecting a vector onto another finds the closest point in that direction; this is the geometric basis of least-squares regression. The residual in regression is exactly the part of y orthogonal to the projection onto predictor space.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 44: Projections - Applied Practice

• Objective: Apply projections to a concrete problem or dataset.

• Theory (recap): The residual in regression is exactly the part of y orthogonal to the projection onto predictor space.

• Practice: Project a vector onto another by hand and relate the result to fitting a simple regression line.

Day 45: Linear algebra foundations for Regression - Foundations

• Objective: Build a solid conceptual understanding of linear algebra foundations for regression.

• Theory: Regression coefficients solve a projection problem: finding the linear combination of predictors closest to y.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 46: Linear algebra foundations for Regression - Applied Practice

• Objective: Apply linear algebra foundations for regression to solve concrete problems and solidify intuition.

• Theory (recap): Regression coefficients solve a projection problem: finding the linear combination of predictors closest to y.

• Practice: Derive the normal equations (X^T X)b = X^T y from the projection viewpoint.

Day 47: Linear algebra foundations for PCA - Foundations

• Objective: Build a solid conceptual understanding of linear algebra foundations for pca.

• Theory: PCA finds the eigenvectors of the covariance matrix, i.e. the orthogonal directions of maximum variance.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 48: Linear algebra foundations for PCA - Applied Practice

• Objective: Apply linear algebra foundations for pca to solve concrete problems and solidify intuition.

• Theory (recap): PCA finds the eigenvectors of the covariance matrix, i.e. the orthogonal directions of maximum variance.

• Practice: Explain in your own words why PCA is an eigenvalue problem on the covariance matrix.

Day 49: Linear algebra foundations for Factor Analysis - Foundations

• Objective: Build a solid conceptual understanding of linear algebra foundations for factor analysis.

• Theory: Factor Analysis models observed variables as linear combinations of fewer latent (unobserved) factors plus noise.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 50: Linear algebra foundations for Factor Analysis - Applied Practice

• Objective: Apply linear algebra foundations for factor analysis to solve concrete problems and solidify intuition.

• Theory (recap): Factor Analysis models observed variables as linear combinations of fewer latent (unobserved) factors plus noise.

• Practice: Compare PCA and Factor Analysis conceptually: variance explained vs latent causal structure.

Day 51: Linear algebra foundations for Machine Learning - Foundations

• Objective: Build a solid conceptual understanding of linear algebra foundations for machine learning.

• Theory: Most ML models (linear/logistic regression, neural nets, SVMs) are fundamentally matrix and vector operations.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 52: Linear algebra foundations for Machine Learning - Applied Practice

• Objective: Apply linear algebra foundations for machine learning to solve concrete problems and solidify intuition.

• Theory (recap): Most ML models (linear/logistic regression, neural nets, SVMs) are fundamentally matrix and vector operations.

• Practice: Trace how a simple neural network layer (Wx + b) is pure linear algebra.

Day 53: Review: Foundational math recap

• Objective: Understand and internalize review: foundational math recap.

• Theory: Consolidate algebra, calculus, and linear algebra concepts learned so far before moving into probability.

• Practice: Take a 20-question mixed review quiz covering functions, derivatives, integrals, vectors, and matrices.

Day 54: Practice: comprehensive math foundations problem set

• Objective: Understand and internalize practice: comprehensive math foundations problem set.

• Theory: Apply all foundational math tools together on realistic mini-problems.

• Practice: Complete a problem set that combines calculus and linear algebra (e.g. derive least squares by hand).

PHASE 1 - DESCRIPTIVE STATISTICS

Day 55: Arithmetic mean - Foundations

• Objective: Build a solid conceptual understanding of arithmetic mean.

• Theory: The arithmetic mean sums all values and divides by the count; it represents the 'balance point' of the data.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 56: Arithmetic mean - Applied Practice

• Objective: Apply arithmetic mean to solve concrete problems and solidify intuition.

• Theory (recap): The arithmetic mean sums all values and divides by the count; it represents the 'balance point' of the data.

• Practice: Compute the mean of a small dataset by hand and verify with Python.

Day 57: Weighted mean - Foundations

• Objective: Build a solid conceptual understanding of weighted mean.

• Theory: A weighted mean gives different importance to each observation, useful when data points are not equally reliable.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 58: Weighted mean - Applied Practice

• Objective: Apply weighted mean to solve concrete problems and solidify intuition.

• Theory (recap): A weighted mean gives different importance to each observation, useful when data points are not equally reliable.

• Practice: Compute a GPA (weighted by credit hours) using the weighted mean formula.

Day 59: Geometric mean - Foundations

• Objective: Build a solid conceptual understanding of geometric mean.

• Theory: The geometric mean is the nth root of the product of n values; it is appropriate for multiplicative processes like growth rates.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 60: Geometric mean - Applied Practice

• Objective: Apply geometric mean to solve concrete problems and solidify intuition.

• Theory (recap): The geometric mean is the nth root of the product of n values; it is appropriate for multiplicative processes like growth rates.

• Practice: Compute the geometric mean of 5 years of investment returns and compare it to the arithmetic mean.

Day 61: Harmonic mean - Introduction

• Objective: Grasp the core intuition behind harmonic mean before the mechanics.

• Theory: The harmonic mean is the reciprocal of the average of reciprocals; it suits rates like speed or price-per-unit.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 62: Harmonic mean - Deep Dive

• Objective: Understand the full mechanics/derivation behind harmonic mean.

• Theory: The harmonic mean is the reciprocal of the average of reciprocals; it suits rates like speed or price-per-unit.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 63: Harmonic mean - Applied Practice

• Objective: Apply harmonic mean to a concrete problem or dataset.

• Theory (recap): The harmonic mean is the reciprocal of the average of reciprocals; it suits rates like speed or price-per-unit.

• Practice: Compute the harmonic mean of speeds for a trip with equal distances at different speeds.

Day 64: Why mean is sensitive to outliers - Foundations

• Objective: Build a solid conceptual understanding of why mean is sensitive to outliers.

• Theory: A single extreme value can shift the arithmetic mean drastically because every value contributes proportionally to the sum.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 65: Why mean is sensitive to outliers - Applied Practice

• Objective: Apply why mean is sensitive to outliers to solve concrete problems and solidify intuition.

• Theory (recap): A single extreme value can shift the arithmetic mean drastically because every value contributes proportionally to the sum.

• Practice: Add one extreme outlier to a dataset and observe how much the mean shifts vs the median.

Day 66: Median - Foundations

• Objective: Build a solid conceptual understanding of median.

• Theory: The median is the middle value of sorted data; it is robust to outliers because it depends only on rank, not magnitude.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 67: Median - Applied Practice

• Objective: Apply median to solve concrete problems and solidify intuition.

• Theory (recap): The median is the middle value of sorted data; it is robust to outliers because it depends only on rank, not magnitude.

• Practice: Compute the median of 3 datasets, one with a heavy outlier, and compare stability to the mean.

Day 68: Quantiles and percentiles - Foundations

• Objective: Build a solid conceptual understanding of quantiles and percentiles.

• Theory: Quantiles divide sorted data into equal-sized groups; percentiles are quantiles expressed out of 100. Common quantiles: quartiles (4 groups), deciles (10 groups).

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 69: Quantiles and percentiles - Applied Practice

• Objective: Apply quantiles and percentiles to solve concrete problems and solidify intuition.

• Theory (recap): Quantiles divide sorted data into equal-sized groups; percentiles are quantiles expressed out of 100.

• Practice: Compute the 25th, 50th, and 75th percentiles of a dataset by hand and with numpy.percentile.

Day 70: Interquartile range (IQR) - Foundations

• Objective: Build a solid conceptual understanding of interquartile range (iqr).

• Theory: IQR = Q3 - Q1 measures the spread of the middle 50% of data and is robust to outliers. IQR is used to define outlier thresholds (below Q1-1.5IQR or above Q3+1.5IQR).

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 71: Interquartile range (IQR) - Applied Practice

• Objective: Apply interquartile range (iqr) to solve concrete problems and solidify intuition.

• Theory (recap): IQR = Q3 - Q1 measures the spread of the middle 50% of data and is robust to outliers.

• Practice: Compute IQR for a dataset and flag any outliers using the 1.5*IQR rule.

Day 72: Median vs Mean: when to use each - Foundations

• Objective: Build a solid conceptual understanding of median vs mean: when to use each.

• Theory: Use the median for skewed data or data with outliers (e.g. income); use the mean for symmetric, well-behaved data.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 73: Median vs Mean: when to use each - Applied Practice

• Objective: Apply median vs mean: when to use each to solve concrete problems and solidify intuition.

• Theory (recap): Use the median for skewed data or data with outliers (e.g. income); use the mean for symmetric, well-behaved data.

• Practice: Given 3 real-world datasets, decide and justify whether mean or median better represents each.

Day 74: Variance - Introduction

• Objective: Grasp the core intuition behind variance before the mechanics.

• Theory: Variance measures the average squared deviation from the mean, capturing how spread out the data is.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 75: Variance - Deep Dive

• Objective: Understand the full mechanics/derivation behind variance.

• Theory: Variance measures the average squared deviation from the mean, capturing how spread out the data is. Population variance divides by n; sample variance divides by n-1 (Bessel's correction).

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 76: Variance - Applied Practice

• Objective: Apply variance to a concrete problem or dataset.

• Theory (recap): Population variance divides by n; sample variance divides by n-1 (Bessel's correction).

• Practice: Compute variance by hand for a small dataset, then explain why n-1 is used for sample variance.

Day 77: Standard deviation - Foundations

• Objective: Build a solid conceptual understanding of standard deviation.

• Theory: Standard deviation is the square root of variance, expressed in the same units as the original data. It quantifies typical distance of observations from the mean.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 78: Standard deviation - Applied Practice

• Objective: Apply standard deviation to solve concrete problems and solidify intuition.

• Theory (recap): Standard deviation is the square root of variance, expressed in the same units as the original data.

• Practice: Compute the standard deviation of 3 datasets and interpret what it means in context (e.g. exam scores).

Day 79: Coefficient of variation - Foundations

• Objective: Build a solid conceptual understanding of coefficient of variation.

• Theory: The coefficient of variation (SD/mean) allows comparing variability across datasets with different units or scales.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 80: Coefficient of variation - Applied Practice

• Objective: Apply coefficient of variation to solve concrete problems and solidify intuition.

• Theory (recap): The coefficient of variation (SD/mean) allows comparing variability across datasets with different units or scales.

• Practice: Compare the variability of two datasets with different units using the coefficient of variation.

Day 81: Spread, dispersion, and volatility - Foundations

• Objective: Build a solid conceptual understanding of spread, dispersion, and volatility.

• Theory: These terms all describe how scattered data is around a central value, used interchangeably across stats, finance, and engineering.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 82: Spread, dispersion, and volatility - Applied Practice

• Objective: Apply spread, dispersion, and volatility to solve concrete problems and solidify intuition.

• Theory (recap): These terms all describe how scattered data is around a central value, used interchangeably across stats, finance, and engineering.

• Practice: Match 5 real-world scenarios to the correct dispersion term (spread, dispersion, volatility).

Day 83: Distribution shape: symmetric distributions - Foundations

• Objective: Build a solid conceptual understanding of distribution shape: symmetric distributions.

• Theory: A symmetric distribution has matching shape on both sides of its center; mean, median, and mode coincide.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 84: Distribution shape: symmetric distributions - Applied Practice

• Objective: Apply distribution shape: symmetric distributions to solve concrete problems and solidify intuition.

• Theory (recap): A symmetric distribution has matching shape on both sides of its center; mean, median, and mode coincide.

• Practice: Identify 3 real datasets that appear approximately symmetric and plot histograms to confirm.

Day 85: Distribution shape: left skew - Foundations

• Objective: Build a solid conceptual understanding of distribution shape: left skew.

• Theory: Left (negative) skew has a longer tail on the left; the mean is pulled below the median.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 86: Distribution shape: left skew - Applied Practice

• Objective: Apply distribution shape: left skew to solve concrete problems and solidify intuition.

• Theory (recap): Left (negative) skew has a longer tail on the left; the mean is pulled below the median.

• Practice: Find a real dataset with left skew (e.g. age at retirement) and explain the tail's cause.

Day 87: Distribution shape: right skew - Foundations

• Objective: Build a solid conceptual understanding of distribution shape: right skew.

• Theory: Right (positive) skew has a longer tail on the right; the mean is pulled above the median (e.g. income).

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 88: Distribution shape: right skew - Applied Practice

• Objective: Apply distribution shape: right skew to solve concrete problems and solidify intuition.

• Theory (recap): Right (positive) skew has a longer tail on the right; the mean is pulled above the median (e.g. income).

• Practice: Find a real dataset with right skew and compare its mean and median numerically.

Day 89: Heavy-tailed distributions - Foundations

• Objective: Build a solid conceptual understanding of heavy-tailed distributions.

• Theory: Heavy tails mean extreme values occur more often than a Normal distribution would predict (e.g. stock returns, insurance claims).

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 90: Heavy-tailed distributions - Applied Practice

• Objective: Apply heavy-tailed distributions to solve concrete problems and solidify intuition.

• Theory (recap): Heavy tails mean extreme values occur more often than a Normal distribution would predict (e.g. stock returns, insurance claims).

• Practice: Compare a Normal-generated sample to a heavy-tailed sample (e.g. Student-t with low df) visually.

Day 91: Skewness (quantitative measure) - Introduction

• Objective: Grasp the core intuition behind skewness (quantitative measure) before the mechanics.

• Theory: Skewness is a numeric measure of asymmetry; positive skewness indicates a right tail, negative indicates a left tail.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 92: Skewness (quantitative measure) - Deep Dive

• Objective: Understand the full mechanics/derivation behind skewness (quantitative measure).

• Theory: Skewness is a numeric measure of asymmetry; positive skewness indicates a right tail, negative indicates a left tail.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 93: Skewness (quantitative measure) - Applied Practice

• Objective: Apply skewness (quantitative measure) to a concrete problem or dataset.

• Theory (recap): Skewness is a numeric measure of asymmetry; positive skewness indicates a right tail, negative indicates a left tail.

• Practice: Compute skewness for 3 datasets and match the sign/magnitude to the histogram shape.

Day 94: Kurtosis - Introduction

• Objective: Grasp the core intuition behind kurtosis before the mechanics.

• Theory: Kurtosis measures tail heaviness/peakedness relative to a Normal distribution; excess kurtosis of 0 means Normal-like tails.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 95: Kurtosis - Deep Dive

• Objective: Understand the full mechanics/derivation behind kurtosis.

• Theory: Kurtosis measures tail heaviness/peakedness relative to a Normal distribution; excess kurtosis of 0 means Normal-like tails.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 96: Kurtosis - Applied Practice

• Objective: Apply kurtosis to a concrete problem or dataset.

• Theory (recap): Kurtosis measures tail heaviness/peakedness relative to a Normal distribution; excess kurtosis of 0 means Normal-like tails.

• Practice: Compute kurtosis for a Normal sample and a heavy-tailed sample and compare.

Day 97: Practice: full descriptive statistics report

• Objective: Understand and internalize practice: full descriptive statistics report.

• Theory: Combine all descriptive measures into a single coherent summary of a dataset.

• Practice: Write a one-page descriptive statistics report (mean, median, SD, skew, kurtosis, plots) for a public dataset.

PHASE 2 - PROBABILITY

Day 98: Sample space and events - Foundations

• Objective: Build a solid conceptual understanding of sample space and events.

• Theory: The sample space is the set of all possible outcomes; an event is any subset of that sample space.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 99: Sample space and events - Applied Practice

• Objective: Apply sample space and events to solve concrete problems and solidify intuition.

• Theory (recap): The sample space is the set of all possible outcomes; an event is any subset of that sample space.

• Practice: Define the sample space and 3 events for rolling two dice.

Day 100: Probability axioms - Foundations

• Objective: Build a solid conceptual understanding of probability axioms.

• Theory: Kolmogorov's axioms: probabilities are non-negative, the sample space has probability 1, and probabilities of disjoint events add.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 101: Probability axioms - Applied Practice

• Objective: Apply probability axioms to solve concrete problems and solidify intuition.

• Theory (recap): Kolmogorov's axioms: probabilities are non-negative, the sample space has probability 1, and probabilities of disjoint events add.

• Practice: Verify the axioms hold for a simple dice/card example.

Day 102: Counting principles/combinatorics basics - Foundations

• Objective: Build a solid conceptual understanding of counting principles/combinatorics basics.

• Theory: The multiplication principle counts outcomes of sequential independent choices.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 103: Counting principles/combinatorics basics - Applied Practice

• Objective: Apply counting principles/combinatorics basics to solve concrete problems and solidify intuition.

• Theory (recap): The multiplication principle counts outcomes of sequential independent choices.

• Practice: Count the number of possible passwords under given length/character rules.

Day 104: Permutations - Foundations

• Objective: Build a solid conceptual understanding of permutations.

• Theory: Permutations count ordered arrangements of items; order matters (nPr = n!/(n-r)!).

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 105: Permutations - Applied Practice

• Objective: Apply permutations to solve concrete problems and solidify intuition.

• Theory (recap): Permutations count ordered arrangements of items; order matters (nPr = n!/(n-r)!).

• Practice: Compute the number of ways to arrange 5 books on a shelf, and 3 out of 5 books in order.

Day 106: Combinations - Introduction

• Objective: Grasp the core intuition behind combinations before the mechanics.

• Theory: Combinations count unordered selections of items; order does not matter (nCr = n!/(r!(n-r)!)).

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 107: Combinations - Deep Dive

• Objective: Understand the full mechanics/derivation behind combinations.

• Theory: Combinations count unordered selections of items; order does not matter (nCr = n!/(r!(n-r)!)).

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 108: Combinations - Applied Practice

• Objective: Apply combinations to a concrete problem or dataset.

• Theory (recap): Combinations count unordered selections of items; order does not matter (nCr = n!/(r!(n-r)!)).

• Practice: Compute the number of ways to choose 3 people from a group of 10 for a committee.

Day 109: Conditional probability - Introduction

• Objective: Grasp the core intuition behind conditional probability before the mechanics.

• Theory: Conditional probability P(A|B) = P(A and B)/P(B) updates the probability of A given that B has occurred.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 110: Conditional probability - Deep Dive

• Objective: Understand the full mechanics/derivation behind conditional probability.

• Theory: Conditional probability P(A|B) = P(A and B)/P(B) updates the probability of A given that B has occurred.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 111: Conditional probability - Applied Practice

• Objective: Apply conditional probability to a concrete problem or dataset.

• Theory (recap): Conditional probability P(A|B) = P(A and B)/P(B) updates the probability of A given that B has occurred.

• Practice: Compute conditional probabilities from a 2x2 contingency table of disease/test results.

Day 112: Law of total probability - Foundations

• Objective: Build a solid conceptual understanding of law of total probability.

• Theory: The law of total probability decomposes an event's probability across a partition of the sample space.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 113: Law of total probability - Applied Practice

• Objective: Apply law of total probability to solve concrete problems and solidify intuition.

• Theory (recap): The law of total probability decomposes an event's probability across a partition of the sample space.

• Practice: Use the law of total probability to compute the overall defect rate across 3 factories.

Day 114: Bayes' theorem: derivation - Introduction

• Objective: Grasp the core intuition behind bayes' theorem: derivation before the mechanics.

• Theory: Bayes' theorem inverts conditional probability: P(A|B) = P(B|A)P(A)/P(B), derived directly from the definition of conditional probability.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 115: Bayes' theorem: derivation - Deep Dive

• Objective: Understand the full mechanics/derivation behind bayes' theorem: derivation.

• Theory: Bayes' theorem inverts conditional probability: P(A|B) = P(B|A)P(A)/P(B), derived directly from the definition of conditional probability.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 116: Bayes' theorem: derivation - Applied Practice

• Objective: Apply bayes' theorem: derivation to a concrete problem or dataset.

• Theory (recap): Bayes' theorem inverts conditional probability: P(A|B) = P(B|A)P(A)/P(B), derived directly from the definition of conditional probability.

• Practice: Derive Bayes' theorem from scratch starting from the definition of conditional probability.

Day 117: Bayes' theorem: prior, likelihood, posterior - Introduction

• Objective: Grasp the core intuition behind bayes' theorem: prior, likelihood, posterior before the mechanics.

• Theory: Prior encodes belief before evidence, likelihood is how probable the evidence is given a hypothesis, posterior updates belief after evidence.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 118: Bayes' theorem: prior, likelihood, posterior - Deep Dive

• Objective: Understand the full mechanics/derivation behind bayes' theorem: prior, likelihood, posterior.

• Theory: Prior encodes belief before evidence, likelihood is how probable the evidence is given a hypothesis, posterior updates belief after evidence.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 119: Bayes' theorem: prior, likelihood, posterior - Applied Practice

• Objective: Apply bayes' theorem: prior, likelihood, posterior to a concrete problem or dataset.

• Theory (recap): Prior encodes belief before evidence, likelihood is how probable the evidence is given a hypothesis, posterior updates belief after evidence.

• Practice: Solve the classic medical-test Bayes problem and correctly interpret the counter-intuitive result.

Day 120: Independence of events - Foundations

• Objective: Build a solid conceptual understanding of independence of events.

• Theory: Two events are independent if P(A and B) = P(A)P(B); knowing one gives no information about the other.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 121: Independence of events - Applied Practice

• Objective: Apply independence of events to solve concrete problems and solidify intuition.

• Theory (recap): Two events are independent if P(A and B) = P(A)P(B); knowing one gives no information about the other.

• Practice: Test whether two events in a dataset (e.g. gender and product choice) are statistically independent.

Day 122: Mutually exclusive vs independent: common confusion - Foundations

• Objective: Build a solid conceptual understanding of mutually exclusive vs independent: common confusion.

• Theory: Mutually exclusive events cannot both happen (and are therefore strongly dependent); independent events can co-occur freely.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 123: Mutually exclusive vs independent: common confusion - Applied Practice

• Objective: Apply mutually exclusive vs independent: common confusion to solve concrete problems and solidify intuition.

• Theory (recap): Mutually exclusive events cannot both happen (and are therefore strongly dependent); independent events can co-occur freely.

• Practice: Give 2 examples each of mutually exclusive and independent events and explain the difference.

Day 124: Random variables: discrete - Foundations

• Objective: Build a solid conceptual understanding of random variables: discrete.

• Theory: A discrete random variable takes countable values, each with an associated probability mass.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 125: Random variables: discrete - Applied Practice

• Objective: Apply random variables: discrete to solve concrete problems and solidify intuition.

• Theory (recap): A discrete random variable takes countable values, each with an associated probability mass.

• Practice: Define a discrete random variable for the outcome of rolling a die and list its distribution.

Day 126: Random variables: continuous - Foundations

• Objective: Build a solid conceptual understanding of random variables: continuous.

• Theory: A continuous random variable takes uncountably many values; probability is described by a density, not a mass.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 127: Random variables: continuous - Applied Practice

• Objective: Apply random variables: continuous to solve concrete problems and solidify intuition.

• Theory (recap): A continuous random variable takes uncountably many values; probability is described by a density, not a mass.

• Practice: Explain why P(X = exact value) = 0 for a continuous random variable.

Day 128: Probability mass function (PMF) - Foundations

• Objective: Build a solid conceptual understanding of probability mass function (pmf).

• Theory: The PMF gives the probability of each specific value for a discrete random variable.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 129: Probability mass function (PMF) - Applied Practice

• Objective: Apply probability mass function (pmf) to solve concrete problems and solidify intuition.

• Theory (recap): The PMF gives the probability of each specific value for a discrete random variable.

• Practice: Plot the PMF of a Binomial(n=10, p=0.3) random variable.

Day 130: Probability density function (PDF) - Introduction

• Objective: Grasp the core intuition behind probability density function (pdf) before the mechanics.

• Theory: The PDF describes relative likelihood for continuous variables; probability over an interval is the area under the curve.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 131: Probability density function (PDF) - Deep Dive

• Objective: Understand the full mechanics/derivation behind probability density function (pdf).

• Theory: The PDF describes relative likelihood for continuous variables; probability over an interval is the area under the curve.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 132: Probability density function (PDF) - Applied Practice

• Objective: Apply probability density function (pdf) to a concrete problem or dataset.

• Theory (recap): The PDF describes relative likelihood for continuous variables; probability over an interval is the area under the curve.

• Practice: Plot the PDF of a Normal(0,1) and shade the area representing P(-1<X<1).

Day 133: Cumulative distribution function (CDF) - Foundations

• Objective: Build a solid conceptual understanding of cumulative distribution function (cdf).

• Theory: The CDF gives P(X <= x) for any x, and is the integral (or sum) of the PDF (or PMF) up to that point.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 134: Cumulative distribution function (CDF) - Applied Practice

• Objective: Apply cumulative distribution function (cdf) to solve concrete problems and solidify intuition.

• Theory (recap): The CDF gives P(X <= x) for any x, and is the integral (or sum) of the PDF (or PMF) up to that point.

• Practice: Plot the CDF corresponding to a Normal PDF and read off P(X<1) directly from the graph.

Day 135: Expectation: definition and intuition - Introduction

• Objective: Grasp the core intuition behind expectation: definition and intuition before the mechanics.

• Theory: Expectation is the long-run average value of a random variable if the experiment were repeated infinitely.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 136: Expectation: definition and intuition - Deep Dive

• Objective: Understand the full mechanics/derivation behind expectation: definition and intuition.

• Theory: Expectation is the long-run average value of a random variable if the experiment were repeated infinitely.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 137: Expectation: definition and intuition - Applied Practice

• Objective: Apply expectation: definition and intuition to a concrete problem or dataset.

• Theory (recap): Expectation is the long-run average value of a random variable if the experiment were repeated infinitely.

• Practice: Compute E[X] by hand for a simple dice game with payouts.

Day 138: Expectation as a weighted average - Foundations

• Objective: Build a solid conceptual understanding of expectation as a weighted average.

• Theory: E[X] = sum of x*P(x); each outcome is weighted by how likely it is.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 139: Expectation as a weighted average - Applied Practice

• Objective: Apply expectation as a weighted average to solve concrete problems and solidify intuition.

• Theory (recap): E[X] = sum of x*P(x); each outcome is weighted by how likely it is.

• Practice: Compute the expected value of a lottery ticket and interpret whether the game is fair.

Day 140: Variance of a random variable - Introduction

• Objective: Grasp the core intuition behind variance of a random variable before the mechanics.

• Theory: Var(X) = E[(X-E[X])^2] = E[X^2] - (E[X])^2 measures the spread of a random variable's distribution.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 141: Variance of a random variable - Deep Dive

• Objective: Understand the full mechanics/derivation behind variance of a random variable.

• Theory: Var(X) = E[(X-E[X])^2] = E[X^2] - (E[X])^2 measures the spread of a random variable's distribution.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 142: Variance of a random variable - Applied Practice

• Objective: Apply variance of a random variable to a concrete problem or dataset.

• Theory (recap): Var(X) = E[(X-E[X])^2] = E[X^2] - (E[X])^2 measures the spread of a random variable's distribution.

• Practice: Derive Var(X) for a Bernoulli random variable from the definition.

Day 143: Covariance - Introduction

• Objective: Grasp the core intuition behind covariance before the mechanics.

• Theory: Covariance measures how two random variables move together; positive covariance means they tend to increase together.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 144: Covariance - Deep Dive

• Objective: Understand the full mechanics/derivation behind covariance.

• Theory: Covariance measures how two random variables move together; positive covariance means they tend to increase together.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 145: Covariance - Applied Practice

• Objective: Apply covariance to a concrete problem or dataset.

• Theory (recap): Covariance measures how two random variables move together; positive covariance means they tend to increase together.

• Practice: Compute covariance between two variables in a small dataset and interpret the sign.

Day 146: Correlation (probabilistic definition) - Foundations

• Objective: Build a solid conceptual understanding of correlation (probabilistic definition).

• Theory: Correlation standardizes covariance to the range [-1,1], making it comparable across variable scales.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 147: Correlation (probabilistic definition) - Applied Practice

• Objective: Apply correlation (probabilistic definition) to solve concrete problems and solidify intuition.

• Theory (recap): Correlation standardizes covariance to the range [-1,1], making it comparable across variable scales.

• Practice: Compute correlation from covariance and variances for a dataset and confirm it matches numpy.corrcoef.

Day 148: Bernoulli distribution - Foundations

• Objective: Build a solid conceptual understanding of bernoulli distribution.

• Theory: The Bernoulli distribution models a single binary trial (success/failure) with probability p of success.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 149: Bernoulli distribution - Applied Practice

• Objective: Apply bernoulli distribution to solve concrete problems and solidify intuition.

• Theory (recap): The Bernoulli distribution models a single binary trial (success/failure) with probability p of success.

• Practice: Simulate 1000 Bernoulli(p=0.3) trials and confirm the empirical mean approaches p.

Day 150: Binomial distribution - Introduction

• Objective: Grasp the core intuition behind binomial distribution before the mechanics.

• Theory: The Binomial distribution models the number of successes in n independent Bernoulli trials.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 151: Binomial distribution - Deep Dive

• Objective: Understand the full mechanics/derivation behind binomial distribution.

• Theory: The Binomial distribution models the number of successes in n independent Bernoulli trials.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 152: Binomial distribution - Applied Practice

• Objective: Apply binomial distribution to a concrete problem or dataset.

• Theory (recap): The Binomial distribution models the number of successes in n independent Bernoulli trials.

• Practice: Simulate a Binomial(n=20,p=0.5) distribution and overlay the theoretical PMF.

Day 153: Geometric distribution - Foundations

• Objective: Build a solid conceptual understanding of geometric distribution.

• Theory: The Geometric distribution models the number of trials until the first success in repeated Bernoulli trials.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 154: Geometric distribution - Applied Practice

• Objective: Apply geometric distribution to solve concrete problems and solidify intuition.

• Theory (recap): The Geometric distribution models the number of trials until the first success in repeated Bernoulli trials.

• Practice: Simulate the number of coin flips until the first heads, 10,000 times, and plot the distribution.

Day 155: Poisson distribution - Introduction

• Objective: Grasp the core intuition behind poisson distribution before the mechanics.

• Theory: The Poisson distribution models the count of rare events in a fixed interval, characterized by rate lambda.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 156: Poisson distribution - Deep Dive

• Objective: Understand the full mechanics/derivation behind poisson distribution.

• Theory: The Poisson distribution models the count of rare events in a fixed interval, characterized by rate lambda.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 157: Poisson distribution - Applied Practice

• Objective: Apply poisson distribution to a concrete problem or dataset.

• Theory (recap): The Poisson distribution models the count of rare events in a fixed interval, characterized by rate lambda.

• Practice: Model the number of customer arrivals per hour at a shop using a Poisson distribution.

Day 158: Uniform distribution - Foundations

• Objective: Build a solid conceptual understanding of uniform distribution.

• Theory: The Uniform distribution assigns equal probability density across a fixed range.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 159: Uniform distribution - Applied Practice

• Objective: Apply uniform distribution to solve concrete problems and solidify intuition.

• Theory (recap): The Uniform distribution assigns equal probability density across a fixed range.

• Practice: Simulate Uniform(0,1) samples and verify the empirical mean and variance match theory.

Day 160: Normal distribution - Introduction

• Objective: Grasp the core intuition behind normal distribution before the mechanics.

• Theory: The Normal distribution is symmetric and bell-shaped, fully described by its mean and variance, and appears pervasively due to the Central Limit Theorem.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 161: Normal distribution - Deep Dive

• Objective: Understand the full mechanics/derivation behind normal distribution.

• Theory: The Normal distribution is symmetric and bell-shaped, fully described by its mean and variance, and appears pervasively due to the Central Limit Theorem.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 162: Normal distribution - Applied Practice

• Objective: Apply normal distribution to a concrete problem or dataset.

• Theory (recap): The Normal distribution is symmetric and bell-shaped, fully described by its mean and variance, and appears pervasively due to the Central Limit Theorem.

• Practice: Plot 3 Normal distributions with different means/variances on the same axes.

Day 163: Normal distribution: 68-95-99.7 rule - Foundations

• Objective: Build a solid conceptual understanding of normal distribution: 68-95-99.7 rule.

• Theory: Approximately 68%, 95%, and 99.7% of Normal data fall within 1, 2, and 3 standard deviations of the mean.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 164: Normal distribution: 68-95-99.7 rule - Applied Practice

• Objective: Apply normal distribution: 68-95-99.7 rule to solve concrete problems and solidify intuition.

• Theory (recap): Approximately 68%, 95%, and 99.7% of Normal data fall within 1, 2, and 3 standard deviations of the mean.

• Practice: Verify the 68-95-99.7 rule empirically by simulating a large Normal sample.

Day 165: Exponential distribution - Introduction

• Objective: Grasp the core intuition behind exponential distribution before the mechanics.

• Theory: The Exponential distribution models waiting time between independent Poisson events and has the memoryless property.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 166: Exponential distribution - Deep Dive

• Objective: Understand the full mechanics/derivation behind exponential distribution.

• Theory: The Exponential distribution models waiting time between independent Poisson events and has the memoryless property.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 167: Exponential distribution - Applied Practice

• Objective: Apply exponential distribution to a concrete problem or dataset.

• Theory (recap): The Exponential distribution models waiting time between independent Poisson events and has the memoryless property.

• Practice: Simulate waiting times between Poisson arrivals and confirm they follow an Exponential distribution.

Day 168: Gamma distribution - Foundations

• Objective: Build a solid conceptual understanding of gamma distribution.

• Theory: The Gamma distribution generalizes the Exponential distribution to model the sum of multiple waiting times.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 169: Gamma distribution - Applied Practice

• Objective: Apply gamma distribution to solve concrete problems and solidify intuition.

• Theory (recap): The Gamma distribution generalizes the Exponential distribution to model the sum of multiple waiting times.

• Practice: Show that summing several Exponential random variables produces a Gamma-distributed variable.

Day 170: Beta distribution - Foundations

• Objective: Build a solid conceptual understanding of beta distribution.

• Theory: The Beta distribution models probabilities/proportions themselves and is the natural conjugate prior for Binomial data.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 171: Beta distribution - Applied Practice

• Objective: Apply beta distribution to solve concrete problems and solidify intuition.

• Theory (recap): The Beta distribution models probabilities/proportions themselves and is the natural conjugate prior for Binomial data.

• Practice: Plot Beta distributions with different shape parameters and interpret them as beliefs about a probability.

Day 172: Chi-square distribution - Introduction

• Objective: Grasp the core intuition behind chi-square distribution before the mechanics.

• Theory: The Chi-square distribution arises as the sum of squared independent standard Normal variables; central to variance tests and goodness-of-fit.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 173: Chi-square distribution - Deep Dive

• Objective: Understand the full mechanics/derivation behind chi-square distribution.

• Theory: The Chi-square distribution arises as the sum of squared independent standard Normal variables; central to variance tests and goodness-of-fit.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 174: Chi-square distribution - Applied Practice

• Objective: Apply chi-square distribution to a concrete problem or dataset.

• Theory (recap): The Chi-square distribution arises as the sum of squared independent standard Normal variables; central to variance tests and goodness-of-fit.

• Practice: Simulate sums of squared standard Normal variables and confirm they follow a Chi-square distribution.

Day 175: Student t-distribution - Foundations

• Objective: Build a solid conceptual understanding of student t-distribution.

• Theory: The t-distribution resembles the Normal but with heavier tails, used when estimating the mean with unknown variance from small samples.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 176: Student t-distribution - Applied Practice

• Objective: Apply student t-distribution to solve concrete problems and solidify intuition.

• Theory (recap): The t-distribution resembles the Normal but with heavier tails, used when estimating the mean with unknown variance from small samples.

• Practice: Compare a t-distribution (low df) to a Normal distribution and observe the tail differences.

Day 177: Relationships between distributions - Foundations

• Objective: Build a solid conceptual understanding of relationships between distributions.

• Theory: Many distributions are special cases or limits of others (e.g. Binomial approaches Normal for large n; Poisson approaches Normal for large lambda).

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 178: Relationships between distributions - Applied Practice

• Objective: Apply relationships between distributions to solve concrete problems and solidify intuition.

• Theory (recap): Many distributions are special cases or limits of others (e.g. Binomial approaches Normal for large n; Poisson approaches Normal for large lambda).

• Practice: Demonstrate the Binomial-to-Normal approximation for large n using simulation.

Day 179: Joint distributions - Foundations

• Objective: Build a solid conceptual understanding of joint distributions.

• Theory: A joint distribution describes the probability behavior of two or more random variables together.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 180: Joint distributions - Applied Practice

• Objective: Apply joint distributions to solve concrete problems and solidify intuition.

• Theory (recap): A joint distribution describes the probability behavior of two or more random variables together.

• Practice: Construct a joint PMF table for two dependent discrete variables.

Day 181: Marginal distributions - Foundations

• Objective: Build a solid conceptual understanding of marginal distributions.

• Theory: A marginal distribution is obtained by summing/integrating a joint distribution over the other variable(s).

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 182: Marginal distributions - Applied Practice

• Objective: Apply marginal distributions to solve concrete problems and solidify intuition.

• Theory (recap): A marginal distribution is obtained by summing/integrating a joint distribution over the other variable(s).

• Practice: Compute marginal distributions from a joint PMF table.

Day 183: Conditional distributions - Introduction

• Objective: Grasp the core intuition behind conditional distributions before the mechanics.

• Theory: A conditional distribution describes one variable's behavior given a fixed value of another.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 184: Conditional distributions - Deep Dive

• Objective: Understand the full mechanics/derivation behind conditional distributions.

• Theory: A conditional distribution describes one variable's behavior given a fixed value of another.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 185: Conditional distributions - Applied Practice

• Objective: Apply conditional distributions to a concrete problem or dataset.

• Theory (recap): A conditional distribution describes one variable's behavior given a fixed value of another.

• Practice: Compute a conditional distribution from a joint PMF table and compare to the marginal.

Day 186: Transformation of random variables - Foundations

• Objective: Build a solid conceptual understanding of transformation of random variables.

• Theory: Applying a function to a random variable changes its distribution; the change-of-variables formula tracks this precisely.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 187: Transformation of random variables - Applied Practice

• Objective: Apply transformation of random variables to solve concrete problems and solidify intuition.

• Theory (recap): Applying a function to a random variable changes its distribution; the change-of-variables formula tracks this precisely.

• Practice: Derive the distribution of Y=X^2 when X is Uniform(-1,1).

Day 188: Moment generating functions (intro) - Foundations

• Objective: Build a solid conceptual understanding of moment generating functions (intro).

• Theory: The MGF encodes all moments of a distribution and helps prove properties like sums of independent variables.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 189: Moment generating functions (intro) - Applied Practice

• Objective: Apply moment generating functions (intro) to solve concrete problems and solidify intuition.

• Theory (recap): The MGF encodes all moments of a distribution and helps prove properties like sums of independent variables.

• Practice: Derive the MGF of a Bernoulli random variable and use it to find the mean and variance.

Day 190: Practice: probability distributions problem set

• Objective: Understand and internalize practice: probability distributions problem set.

• Theory: Consolidate all distributions learned by applying them to varied word problems.

• Practice: Solve 15 mixed word problems, each requiring identification of the correct distribution.

Day 191: Practice: joint/marginal/conditional distributions

• Objective: Understand and internalize practice: joint/marginal/conditional distributions.

• Theory: Apply joint, marginal, and conditional distribution concepts together on a realistic dataset.

• Practice: Analyze a 2-variable dataset (e.g. weather and umbrella sales) using joint/marginal/conditional probabilities.

PHASE 3 - SAMPLING THEORY

Day 192: Population vs sample - Foundations

• Objective: Build a solid conceptual understanding of population vs sample.

• Theory: The population is the entire group of interest; a sample is a subset used to make inferences about it.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 193: Population vs sample - Applied Practice

• Objective: Apply population vs sample to solve concrete problems and solidify intuition.

• Theory (recap): The population is the entire group of interest; a sample is a subset used to make inferences about it.

• Practice: Identify the population and sample in 5 real research scenarios.

Day 194: Sampling bias - Introduction

• Objective: Grasp the core intuition behind sampling bias before the mechanics.

• Theory: Sampling bias occurs when the sample systematically differs from the population, distorting conclusions.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 195: Sampling bias - Deep Dive

• Objective: Understand the full mechanics/derivation behind sampling bias.

• Theory: Sampling bias occurs when the sample systematically differs from the population, distorting conclusions.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 196: Sampling bias - Applied Practice

• Objective: Apply sampling bias to a concrete problem or dataset.

• Theory (recap): Sampling bias occurs when the sample systematically differs from the population, distorting conclusions.

• Practice: Identify the sampling bias in 3 famous flawed surveys (e.g. Literary Digest 1936).

Day 197: Simple random sampling - Foundations

• Objective: Build a solid conceptual understanding of simple random sampling.

• Theory: Every member of the population has an equal chance of being selected, minimizing systematic bias.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 198: Simple random sampling - Applied Practice

• Objective: Apply simple random sampling to solve concrete problems and solidify intuition.

• Theory (recap): Every member of the population has an equal chance of being selected, minimizing systematic bias.

• Practice: Simulate simple random sampling from a population and compare sample statistics to the true parameter.

Day 199: Stratified sampling - Foundations

• Objective: Build a solid conceptual understanding of stratified sampling.

• Theory: The population is divided into subgroups (strata), and samples are drawn proportionally from each, improving representativeness.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 200: Stratified sampling - Applied Practice

• Objective: Apply stratified sampling to solve concrete problems and solidify intuition.

• Theory (recap): The population is divided into subgroups (strata), and samples are drawn proportionally from each, improving representativeness.

• Practice: Design a stratified sampling plan for a survey across age groups.

Day 201: Cluster sampling - Foundations

• Objective: Build a solid conceptual understanding of cluster sampling.

• Theory: Natural clusters (e.g. schools, cities) are randomly selected, and all/some members within are sampled, useful for cost efficiency.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 202: Cluster sampling - Applied Practice

• Objective: Apply cluster sampling to solve concrete problems and solidify intuition.

• Theory (recap): Natural clusters (e.g. schools, cities) are randomly selected, and all/some members within are sampled, useful for cost efficiency.

• Practice: Compare cluster sampling vs stratified sampling for a nationwide survey design.

Day 203: Sampling with vs without replacement - Foundations

• Objective: Build a solid conceptual understanding of sampling with vs without replacement.

• Theory: Sampling without replacement changes the population for subsequent draws; sampling with replacement keeps probabilities constant.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 204: Sampling with vs without replacement - Applied Practice

• Objective: Apply sampling with vs without replacement to solve concrete problems and solidify intuition.

• Theory (recap): Sampling without replacement changes the population for subsequent draws; sampling with replacement keeps probabilities constant.

• Practice: Compute probabilities for a card-drawing scenario both with and without replacement.

Day 205: Law of Large Numbers - Introduction

• Objective: Grasp the core intuition behind law of large numbers before the mechanics.

• Theory: As sample size grows, the sample mean converges to the true population mean.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 206: Law of Large Numbers - Deep Dive

• Objective: Understand the full mechanics/derivation behind law of large numbers.

• Theory: As sample size grows, the sample mean converges to the true population mean.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 207: Law of Large Numbers - Applied Practice

• Objective: Apply law of large numbers to a concrete problem or dataset.

• Theory (recap): As sample size grows, the sample mean converges to the true population mean.

• Practice: Simulate increasing sample sizes and plot how the sample mean converges to the true mean.

Day 208: Central Limit Theorem: statement - Introduction

• Objective: Grasp the core intuition behind central limit theorem: statement before the mechanics.

• Theory: Regardless of the population's original distribution, the sampling distribution of the mean approaches Normal as sample size grows.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 209: Central Limit Theorem: statement - Deep Dive

• Objective: Understand the full mechanics/derivation behind central limit theorem: statement.

• Theory: Regardless of the population's original distribution, the sampling distribution of the mean approaches Normal as sample size grows.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 210: Central Limit Theorem: statement - Applied Practice

• Objective: Apply central limit theorem: statement to a concrete problem or dataset.

• Theory (recap): Regardless of the population's original distribution, the sampling distribution of the mean approaches Normal as sample size grows.

• Practice: State the CLT precisely, including its conditions (independence, finite variance).

Day 211: Central Limit Theorem: why Normal appears everywhere - Introduction

• Objective: Grasp the core intuition behind central limit theorem: why normal appears everywhere before the mechanics.

• Theory: Many real-world quantities are sums/averages of many small independent effects, which is exactly what the CLT describes.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 212: Central Limit Theorem: why Normal appears everywhere - Deep Dive

• Objective: Understand the full mechanics/derivation behind central limit theorem: why normal appears everywhere.

• Theory: Many real-world quantities are sums/averages of many small independent effects, which is exactly what the CLT describes.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 213: Central Limit Theorem: why Normal appears everywhere - Applied Practice

• Objective: Apply central limit theorem: why normal appears everywhere to a concrete problem or dataset.

• Theory (recap): Many real-world quantities are sums/averages of many small independent effects, which is exactly what the CLT describes.

• Practice: Explain, using the CLT, why measurement errors in physical experiments tend to be Normally distributed.

Day 214: Central Limit Theorem: simulation practice - Foundations

• Objective: Build a solid conceptual understanding of central limit theorem: simulation practice.

• Theory: Empirically verify the CLT by simulating sample means from a non-Normal population.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 215: Central Limit Theorem: simulation practice - Applied Practice

• Objective: Apply central limit theorem: simulation practice to solve concrete problems and solidify intuition.

• Theory (recap): Empirically verify the CLT by simulating sample means from a non-Normal population.

• Practice: Simulate sample means from a skewed population at increasing sample sizes and plot the resulting distributions.

Day 216: Standard deviation vs standard error - Introduction

• Objective: Grasp the core intuition behind standard deviation vs standard error before the mechanics.

• Theory: Standard deviation describes spread of individual data points; standard error describes spread of a sample statistic (like the mean) across repeated samples.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 217: Standard deviation vs standard error - Deep Dive

• Objective: Understand the full mechanics/derivation behind standard deviation vs standard error.

• Theory: Standard deviation describes spread of individual data points; standard error describes spread of a sample statistic (like the mean) across repeated samples.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 218: Standard deviation vs standard error - Applied Practice

• Objective: Apply standard deviation vs standard error to a concrete problem or dataset.

• Theory (recap): Standard deviation describes spread of individual data points; standard error describes spread of a sample statistic (like the mean) across repeated samples.

• Practice: Compute both SD and SE for a dataset and explain in one sentence what each answers.

Day 219: Sampling distribution of an estimator - Foundations

• Objective: Build a solid conceptual understanding of sampling distribution of an estimator.

• Theory: Any statistic computed from a sample (mean, variance, proportion) has its own distribution across repeated sampling.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 220: Sampling distribution of an estimator - Applied Practice

• Objective: Apply sampling distribution of an estimator to solve concrete problems and solidify intuition.

• Theory (recap): Any statistic computed from a sample (mean, variance, proportion) has its own distribution across repeated sampling.

• Practice: Simulate the sampling distribution of the sample variance and observe its shape.

Day 221: Sampling distribution of the sample mean - Foundations

• Objective: Build a solid conceptual understanding of sampling distribution of the sample mean.

• Theory: The sample mean's distribution has mean equal to the population mean and standard deviation equal to SE = sigma/sqrt(n).

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 222: Sampling distribution of the sample mean - Applied Practice

• Objective: Apply sampling distribution of the sample mean to solve concrete problems and solidify intuition.

• Theory (recap): The sample mean's distribution has mean equal to the population mean and standard deviation equal to SE = sigma/sqrt(n).

• Practice: Verify empirically that SE shrinks proportionally to 1/sqrt(n) as sample size increases.

Day 223: Practice: sampling distribution simulation

• Objective: Understand and internalize practice: sampling distribution simulation.

• Theory: Apply everything learned about sampling distributions in one integrated simulation exercise.

• Practice: Build a simulation comparing sampling distributions of mean, median, and variance for the same population.

PHASE 4 - STATISTICAL INFERENCE

Day 224: Point estimation: concept - Foundations

• Objective: Build a solid conceptual understanding of point estimation: concept.

• Theory: Point estimation uses sample data to produce a single 'best guess' value for an unknown population parameter.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 225: Point estimation: concept - Applied Practice

• Objective: Apply point estimation: concept to solve concrete problems and solidify intuition.

• Theory (recap): Point estimation uses sample data to produce a single 'best guess' value for an unknown population parameter.

• Practice: List 3 point estimators you already know and what parameter each estimates.

Day 226: Estimator for the mean - Foundations

• Objective: Build a solid conceptual understanding of estimator for the mean.

• Theory: The sample mean is the standard unbiased estimator of the population mean.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 227: Estimator for the mean - Applied Practice

• Objective: Apply estimator for the mean to solve concrete problems and solidify intuition.

• Theory (recap): The sample mean is the standard unbiased estimator of the population mean.

• Practice: Prove that the sample mean is an unbiased estimator of the population mean.

Day 228: Estimator for the variance - Introduction

• Objective: Grasp the core intuition behind estimator for the variance before the mechanics.

• Theory: The sample variance (dividing by n-1) is an unbiased estimator of the population variance.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 229: Estimator for the variance - Deep Dive

• Objective: Understand the full mechanics/derivation behind estimator for the variance.

• Theory: The sample variance (dividing by n-1) is an unbiased estimator of the population variance.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 230: Estimator for the variance - Applied Practice

• Objective: Apply estimator for the variance to a concrete problem or dataset.

• Theory (recap): The sample variance (dividing by n-1) is an unbiased estimator of the population variance.

• Practice: Show via simulation that dividing by n underestimates variance on average, while n-1 corrects it.

Day 231: Bias and consistency of estimators - Foundations

• Objective: Build a solid conceptual understanding of bias and consistency of estimators.

• Theory: An estimator is unbiased if its expected value equals the true parameter; it is consistent if it converges to the true value as n grows.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 232: Bias and consistency of estimators - Applied Practice

• Objective: Apply bias and consistency of estimators to solve concrete problems and solidify intuition.

• Theory (recap): An estimator is unbiased if its expected value equals the true parameter; it is consistent if it converges to the true value as n grows.

• Practice: Compare a biased and unbiased estimator for the same parameter via simulation.

Day 233: Confidence intervals: concept - Foundations

• Objective: Build a solid conceptual understanding of confidence intervals: concept.

• Theory: A confidence interval gives a range of plausible values for a parameter, with a stated long-run coverage probability (e.g. 95%).

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 234: Confidence intervals: concept - Applied Practice

• Objective: Apply confidence intervals: concept to solve concrete problems and solidify intuition.

• Theory (recap): A confidence interval gives a range of plausible values for a parameter, with a stated long-run coverage probability (e.g. 95%).

• Practice: Explain in plain language what '95% confidence' does and does not mean.

Day 235: Z-interval for the mean - Introduction

• Objective: Grasp the core intuition behind z-interval for the mean before the mechanics.

• Theory: The Z-interval is used when the population standard deviation is known (or n is large): mean +/- z * SE.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 236: Z-interval for the mean - Deep Dive

• Objective: Understand the full mechanics/derivation behind z-interval for the mean.

• Theory: The Z-interval is used when the population standard deviation is known (or n is large): mean +/- z * SE.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 237: Z-interval for the mean - Applied Practice

• Objective: Apply z-interval for the mean to a concrete problem or dataset.

• Theory (recap): The Z-interval is used when the population standard deviation is known (or n is large): mean +/- z * SE.

• Practice: Construct a 95% Z-confidence interval for a sample mean by hand.

Day 238: T-interval for the mean - Foundations

• Objective: Build a solid conceptual understanding of t-interval for the mean.

• Theory: The T-interval is used when the population standard deviation is unknown and must be estimated from the sample.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 239: T-interval for the mean - Applied Practice

• Objective: Apply t-interval for the mean to solve concrete problems and solidify intuition.

• Theory (recap): The T-interval is used when the population standard deviation is unknown and must be estimated from the sample.

• Practice: Construct a 95% T-confidence interval for a small sample and compare width to the Z-interval.

Day 240: Interpreting confidence intervals correctly - Introduction

• Objective: Grasp the core intuition behind interpreting confidence intervals correctly before the mechanics.

• Theory: A CI is a statement about the procedure's long-run reliability, not the probability that this specific interval contains the parameter.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 241: Interpreting confidence intervals correctly - Deep Dive

• Objective: Understand the full mechanics/derivation behind interpreting confidence intervals correctly.

• Theory: A CI is a statement about the procedure's long-run reliability, not the probability that this specific interval contains the parameter.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 242: Interpreting confidence intervals correctly - Applied Practice

• Objective: Apply interpreting confidence intervals correctly to a concrete problem or dataset.

• Theory (recap): A CI is a statement about the procedure's long-run reliability, not the probability that this specific interval contains the parameter.

• Practice: Simulate 100 confidence intervals from repeated sampling and count how many actually contain the true parameter.

Day 243: Hypothesis testing: null and alternative hypotheses - Foundations

• Objective: Build a solid conceptual understanding of hypothesis testing: null and alternative hypotheses.

• Theory: The null hypothesis represents 'no effect'; the alternative represents the effect being tested for.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 244: Hypothesis testing: null and alternative hypotheses - Applied Practice

• Objective: Apply hypothesis testing: null and alternative hypotheses to solve concrete problems and solidify intuition.

• Theory (recap): The null hypothesis represents 'no effect'; the alternative represents the effect being tested for.

• Practice: Formulate null and alternative hypotheses for 5 different research questions.

Day 245: Hypothesis testing: test statistic and decision rule - Introduction

• Objective: Grasp the core intuition behind hypothesis testing: test statistic and decision rule before the mechanics.

• Theory: A test statistic summarizes the evidence against the null; it is compared to a critical value or converted to a p-value to decide.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 246: Hypothesis testing: test statistic and decision rule - Deep Dive

• Objective: Understand the full mechanics/derivation behind hypothesis testing: test statistic and decision rule.

• Theory: A test statistic summarizes the evidence against the null; it is compared to a critical value or converted to a p-value to decide.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 247: Hypothesis testing: test statistic and decision rule - Applied Practice

• Objective: Apply hypothesis testing: test statistic and decision rule to a concrete problem or dataset.

• Theory (recap): A test statistic summarizes the evidence against the null; it is compared to a critical value or converted to a p-value to decide.

• Practice: Compute a test statistic by hand for a one-sample mean test and make a decision at alpha=0.05.

Day 248: Z-score: definition and standardization - Foundations

• Objective: Build a solid conceptual understanding of z-score: definition and standardization.

• Theory: A Z-score expresses how many standard deviations a value is from the mean, standardizing values for comparison.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 249: Z-score: definition and standardization - Applied Practice

• Objective: Apply z-score: definition and standardization to solve concrete problems and solidify intuition.

• Theory (recap): A Z-score expresses how many standard deviations a value is from the mean, standardizing values for comparison.

• Practice: Convert 5 raw scores from different scales into Z-scores and compare them directly.

Day 250: Z-score: practice - Foundations

• Objective: Build a solid conceptual understanding of z-score: practice.

• Theory: Apply Z-score standardization to compare across distributions.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 251: Z-score: practice - Applied Practice

• Objective: Apply z-score: practice to solve concrete problems and solidify intuition.

• Theory (recap): Apply Z-score standardization to compare across distributions.

• Practice: Use Z-scores to determine which of two students performed relatively better on different exams.

Day 252: P-value: what it really means - Introduction

• Objective: Grasp the core intuition behind p-value: what it really means before the mechanics.

• Theory: The p-value is the probability of observing data as extreme as (or more extreme than) what was seen, assuming the null hypothesis is true.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 253: P-value: what it really means - Deep Dive

• Objective: Understand the full mechanics/derivation behind p-value: what it really means.

• Theory: The p-value is the probability of observing data as extreme as (or more extreme than) what was seen, assuming the null hypothesis is true.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 254: P-value: what it really means - Applied Practice

• Objective: Apply p-value: what it really means to a concrete problem or dataset.

• Theory (recap): The p-value is the probability of observing data as extreme as (or more extreme than) what was seen, assuming the null hypothesis is true.

• Practice: Write, in your own words, a correct one-sentence definition of the p-value and test it against 3 common misstatements.

Day 255: P-value: common misconceptions - Introduction

• Objective: Grasp the core intuition behind p-value: common misconceptions before the mechanics.

• Theory: A p-value is NOT the probability the null hypothesis is true, nor the probability of a Type I error for this specific test.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 256: P-value: common misconceptions - Deep Dive

• Objective: Understand the full mechanics/derivation behind p-value: common misconceptions.

• Theory: A p-value is NOT the probability the null hypothesis is true, nor the probability of a Type I error for this specific test.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 257: P-value: common misconceptions - Applied Practice

• Objective: Apply p-value: common misconceptions to a concrete problem or dataset.

• Theory (recap): A p-value is NOT the probability the null hypothesis is true, nor the probability of a Type I error for this specific test.

• Practice: Identify the error in 5 real (or paraphrased) media misinterpretations of p-values.

Day 258: One-tailed vs two-tailed tests - Foundations

• Objective: Build a solid conceptual understanding of one-tailed vs two-tailed tests.

• Theory: A one-tailed test checks for an effect in one specific direction; a two-tailed test checks for an effect in either direction.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 259: One-tailed vs two-tailed tests - Applied Practice

• Objective: Apply one-tailed vs two-tailed tests to solve concrete problems and solidify intuition.

• Theory (recap): A one-tailed test checks for an effect in one specific direction; a two-tailed test checks for an effect in either direction.

• Practice: Decide whether 5 example hypotheses call for a one-tailed or two-tailed test.

Day 260: Type I error - Foundations

• Objective: Build a solid conceptual understanding of type i error.

• Theory: A Type I error is rejecting a true null hypothesis (a false positive); its probability is denoted alpha.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 261: Type I error - Applied Practice

• Objective: Apply type i error to solve concrete problems and solidify intuition.

• Theory (recap): A Type I error is rejecting a true null hypothesis (a false positive); its probability is denoted alpha.

• Practice: Explain the real-world cost of a Type I error in a medical screening context.

Day 262: Type II error - Foundations

• Objective: Build a solid conceptual understanding of type ii error.

• Theory: A Type II error is failing to reject a false null hypothesis (a false negative); its probability is denoted beta.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 263: Type II error - Applied Practice

• Objective: Apply type ii error to solve concrete problems and solidify intuition.

• Theory (recap): A Type II error is failing to reject a false null hypothesis (a false negative); its probability is denoted beta.

• Practice: Explain the real-world cost of a Type II error in the same medical screening context.

Day 264: Statistical power - Foundations

• Objective: Build a solid conceptual understanding of statistical power.

• Theory: Power = 1 - beta is the probability of correctly detecting a true effect; it increases with sample size and effect size.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 265: Statistical power - Applied Practice

• Objective: Apply statistical power to solve concrete problems and solidify intuition.

• Theory (recap): Power = 1 - beta is the probability of correctly detecting a true effect; it increases with sample size and effect size.

• Practice: Plot how statistical power changes as sample size increases, holding effect size fixed.

Day 266: Power analysis: sample size determination - Foundations

• Objective: Build a solid conceptual understanding of power analysis: sample size determination.

• Theory: Power analysis works backward from a desired power level to determine the minimum sample size needed.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 267: Power analysis: sample size determination - Applied Practice

• Objective: Apply power analysis: sample size determination to solve concrete problems and solidify intuition.

• Theory (recap): Power analysis works backward from a desired power level to determine the minimum sample size needed.

• Practice: Compute the required sample size for an A/B test given a target power of 0.8.

Day 268: Multiple testing problem - Introduction

• Objective: Grasp the core intuition behind multiple testing problem before the mechanics.

• Theory: Running many hypothesis tests inflates the overall chance of at least one false positive, even if each individual test uses alpha=0.05.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 269: Multiple testing problem - Deep Dive

• Objective: Understand the full mechanics/derivation behind multiple testing problem.

• Theory: Running many hypothesis tests inflates the overall chance of at least one false positive, even if each individual test uses alpha=0.05.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 270: Multiple testing problem - Applied Practice

• Objective: Apply multiple testing problem to a concrete problem or dataset.

• Theory (recap): Running many hypothesis tests inflates the overall chance of at least one false positive, even if each individual test uses alpha=0.05.

• Practice: Simulate 100 independent null tests at alpha=0.05 and count how many falsely reject by chance.

Day 271: Bonferroni correction - Foundations

• Objective: Build a solid conceptual understanding of bonferroni correction.

• Theory: The Bonferroni correction divides alpha by the number of tests, controlling the family-wise error rate conservatively.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 272: Bonferroni correction - Applied Practice

• Objective: Apply bonferroni correction to solve concrete problems and solidify intuition.

• Theory (recap): The Bonferroni correction divides alpha by the number of tests, controlling the family-wise error rate conservatively.

• Practice: Apply Bonferroni correction to a set of 20 simultaneous hypothesis tests.

Day 273: False Discovery Rate (FDR) - Foundations

• Objective: Build a solid conceptual understanding of false discovery rate (fdr).

• Theory: FDR control allows a controlled proportion of false positives among rejected hypotheses, less conservative than Bonferroni.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 274: False Discovery Rate (FDR) - Applied Practice

• Objective: Apply false discovery rate (fdr) to solve concrete problems and solidify intuition.

• Theory (recap): FDR control allows a controlled proportion of false positives among rejected hypotheses, less conservative than Bonferroni.

• Practice: Compare Bonferroni vs FDR-adjusted results on the same set of 20 tests.

Day 275: Benjamini-Hochberg procedure - Introduction

• Objective: Grasp the core intuition behind benjamini-hochberg procedure before the mechanics.

• Theory: The Benjamini-Hochberg procedure ranks p-values and applies a step-up threshold to control FDR.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 276: Benjamini-Hochberg procedure - Deep Dive

• Objective: Understand the full mechanics/derivation behind benjamini-hochberg procedure.

• Theory: The Benjamini-Hochberg procedure ranks p-values and applies a step-up threshold to control FDR.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 277: Benjamini-Hochberg procedure - Applied Practice

• Objective: Apply benjamini-hochberg procedure to a concrete problem or dataset.

• Theory (recap): The Benjamini-Hochberg procedure ranks p-values and applies a step-up threshold to control FDR.

• Practice: Implement the Benjamini-Hochberg procedure by hand on a small set of p-values.

Day 278: Effect size: Cohen's d - Foundations

• Objective: Build a solid conceptual understanding of effect size: cohen's d.

• Theory: Cohen's d expresses the standardized difference between two means, independent of sample size.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 279: Effect size: Cohen's d - Applied Practice

• Objective: Apply effect size: cohen's d to solve concrete problems and solidify intuition.

• Theory (recap): Cohen's d expresses the standardized difference between two means, independent of sample size.

• Practice: Compute Cohen's d for a two-group comparison and interpret its magnitude (small/medium/large).

Day 280: Effect size vs statistical significance - Foundations

• Objective: Build a solid conceptual understanding of effect size vs statistical significance.

• Theory: A statistically significant result can have a tiny, practically meaningless effect size, especially with large samples.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 281: Effect size vs statistical significance - Applied Practice

• Objective: Apply effect size vs statistical significance to solve concrete problems and solidify intuition.

• Theory (recap): A statistically significant result can have a tiny, practically meaningless effect size, especially with large samples.

• Practice: Find/construct an example where p<0.05 but the effect size is negligible, and explain the implication.

Day 282: Non-parametric tests: Mann-Whitney U test - Introduction

• Objective: Grasp the core intuition behind non-parametric tests: mann-whitney u test before the mechanics.

• Theory: The Mann-Whitney U test compares two independent groups without assuming Normality, using rank information.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 283: Non-parametric tests: Mann-Whitney U test - Deep Dive

• Objective: Understand the full mechanics/derivation behind non-parametric tests: mann-whitney u test.

• Theory: The Mann-Whitney U test compares two independent groups without assuming Normality, using rank information.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 284: Non-parametric tests: Mann-Whitney U test - Applied Practice

• Objective: Apply non-parametric tests: mann-whitney u test to a concrete problem or dataset.

• Theory (recap): The Mann-Whitney U test compares two independent groups without assuming Normality, using rank information.

• Practice: Apply the Mann-Whitney U test to a skewed two-group dataset and compare with a t-test result.

Day 285: Non-parametric tests: Wilcoxon signed-rank test - Foundations

• Objective: Build a solid conceptual understanding of non-parametric tests: wilcoxon signed-rank test.

• Theory: The Wilcoxon signed-rank test compares paired samples without assuming Normality of differences.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 286: Non-parametric tests: Wilcoxon signed-rank test - Applied Practice

• Objective: Apply non-parametric tests: wilcoxon signed-rank test to solve concrete problems and solidify intuition.

• Theory (recap): The Wilcoxon signed-rank test compares paired samples without assuming Normality of differences.

• Practice: Apply the Wilcoxon signed-rank test to a before/after paired dataset.

Day 287: Non-parametric tests: Kruskal-Wallis test - Foundations

• Objective: Build a solid conceptual understanding of non-parametric tests: kruskal-wallis test.

• Theory: The Kruskal-Wallis test extends Mann-Whitney to compare more than two independent groups without Normality assumptions.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 288: Non-parametric tests: Kruskal-Wallis test - Applied Practice

• Objective: Apply non-parametric tests: kruskal-wallis test to solve concrete problems and solidify intuition.

• Theory (recap): The Kruskal-Wallis test extends Mann-Whitney to compare more than two independent groups without Normality assumptions.

• Practice: Apply the Kruskal-Wallis test to a 3-group dataset and compare with one-way ANOVA.

Day 289: Spearman rank correlation - Introduction

• Objective: Grasp the core intuition behind spearman rank correlation before the mechanics.

• Theory: Spearman correlation measures monotonic (not necessarily linear) association based on ranks.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 290: Spearman rank correlation - Deep Dive

• Objective: Understand the full mechanics/derivation behind spearman rank correlation.

• Theory: Spearman correlation measures monotonic (not necessarily linear) association based on ranks.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 291: Spearman rank correlation - Applied Practice

• Objective: Apply spearman rank correlation to a concrete problem or dataset.

• Theory (recap): Spearman correlation measures monotonic (not necessarily linear) association based on ranks.

• Practice: Compute Spearman correlation for a non-linear monotonic relationship and compare to Pearson correlation.

Day 292: Practice: hypothesis testing on real data

• Objective: Understand and internalize practice: hypothesis testing on real data.

• Theory: Integrate the full hypothesis-testing workflow: hypotheses, test selection, statistic, p-value, decision, effect size.

• Practice: Run a complete hypothesis test (parametric or non-parametric as appropriate) on a real public dataset and write up conclusions.

PHASE 5 - REGRESSION

Day 293: Correlation: Pearson correlation coefficient - Foundations

• Objective: Build a solid conceptual understanding of correlation: pearson correlation coefficient.

• Theory: Pearson's r measures the strength and direction of a linear relationship between two continuous variables.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 294: Correlation: Pearson correlation coefficient - Applied Practice

• Objective: Apply correlation: pearson correlation coefficient to solve concrete problems and solidify intuition.

• Theory (recap): Pearson's r measures the strength and direction of a linear relationship between two continuous variables.

• Practice: Compute Pearson's r for a dataset and visualize with a scatterplot.

Day 295: Correlation vs causation - Foundations

• Objective: Build a solid conceptual understanding of correlation vs causation.

• Theory: A strong correlation does not imply that one variable causes the other; confounders can create spurious associations.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 296: Correlation vs causation - Applied Practice

• Objective: Apply correlation vs causation to solve concrete problems and solidify intuition.

• Theory (recap): A strong correlation does not imply that one variable causes the other; confounders can create spurious associations.

• Practice: Find a real 'spurious correlation' example and explain the likely confounder.

Day 297: Simple linear regression: model setup - Foundations

• Objective: Build a solid conceptual understanding of simple linear regression: model setup.

• Theory: Simple linear regression models Y as a linear function of a single predictor X plus random error: Y = b0 + b1*X + e.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 298: Simple linear regression: model setup - Applied Practice

• Objective: Apply simple linear regression: model setup to solve concrete problems and solidify intuition.

• Theory (recap): Simple linear regression models Y as a linear function of a single predictor X plus random error: Y = b0 + b1*X + e.

• Practice: Write out the simple linear regression model and identify its assumptions.

Day 299: Least squares estimation - Introduction

• Objective: Grasp the core intuition behind least squares estimation before the mechanics.

• Theory: Least squares finds coefficients that minimize the sum of squared residuals between predicted and actual values.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 300: Least squares estimation - Deep Dive

• Objective: Understand the full mechanics/derivation behind least squares estimation.

• Theory: Least squares finds coefficients that minimize the sum of squared residuals between predicted and actual values.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 301: Least squares estimation - Applied Practice

• Objective: Apply least squares estimation to a concrete problem or dataset.

• Theory (recap): Least squares finds coefficients that minimize the sum of squared residuals between predicted and actual values.

• Practice: Derive the least-squares formulas for slope and intercept by hand using calculus.

Day 302: Interpreting regression coefficients - Foundations

• Objective: Build a solid conceptual understanding of interpreting regression coefficients.

• Theory: The slope represents the expected change in Y per one-unit change in X; the intercept is the predicted Y when X=0.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 303: Interpreting regression coefficients - Applied Practice

• Objective: Apply interpreting regression coefficients to solve concrete problems and solidify intuition.

• Theory (recap): The slope represents the expected change in Y per one-unit change in X; the intercept is the predicted Y when X=0.

• Practice: Fit a regression on real data and write a plain-language interpretation of each coefficient.

Day 304: R-squared and goodness of fit - Introduction

• Objective: Grasp the core intuition behind r-squared and goodness of fit before the mechanics.

• Theory: R-squared measures the proportion of variance in Y explained by the model, ranging from 0 to 1.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 305: R-squared and goodness of fit - Deep Dive

• Objective: Understand the full mechanics/derivation behind r-squared and goodness of fit.

• Theory: R-squared measures the proportion of variance in Y explained by the model, ranging from 0 to 1.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 306: R-squared and goodness of fit - Applied Practice

• Objective: Apply r-squared and goodness of fit to a concrete problem or dataset.

• Theory (recap): R-squared measures the proportion of variance in Y explained by the model, ranging from 0 to 1.

• Practice: Compute R-squared by hand from residual and total sums of squares for a fitted model.

Day 307: Multiple regression: multiple predictors - Foundations

• Objective: Build a solid conceptual understanding of multiple regression: multiple predictors.

• Theory: Multiple regression extends simple regression to several predictors simultaneously, holding others constant when interpreting each coefficient.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 308: Multiple regression: multiple predictors - Applied Practice

• Objective: Apply multiple regression: multiple predictors to solve concrete problems and solidify intuition.

• Theory (recap): Multiple regression extends simple regression to several predictors simultaneously, holding others constant when interpreting each coefficient.

• Practice: Fit a multiple regression with 3 predictors and interpret each coefficient 'holding others constant'.

Day 309: Interaction terms - Foundations

• Objective: Build a solid conceptual understanding of interaction terms.

• Theory: Interaction terms allow the effect of one predictor to depend on the value of another.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 310: Interaction terms - Applied Practice

• Objective: Apply interaction terms to solve concrete problems and solidify intuition.

• Theory (recap): Interaction terms allow the effect of one predictor to depend on the value of another.

• Practice: Fit a regression with an interaction term and interpret how the effect of X1 changes across levels of X2.

Day 311: Polynomial regression - Introduction

• Objective: Grasp the core intuition behind polynomial regression before the mechanics.

• Theory: Polynomial regression fits curved relationships by including powers of a predictor (X, X^2, X^3, ...) in a linear model.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 312: Polynomial regression - Deep Dive

• Objective: Understand the full mechanics/derivation behind polynomial regression.

• Theory: Polynomial regression fits curved relationships by including powers of a predictor (X, X^2, X^3, ...) in a linear model.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 313: Polynomial regression - Applied Practice

• Objective: Apply polynomial regression to a concrete problem or dataset.

• Theory (recap): Polynomial regression fits curved relationships by including powers of a predictor (X, X^2, X^3, ...) in a linear model.

• Practice: Fit linear vs quadratic models to a curved dataset and compare fit quality.

Day 314: Residual analysis - Foundations

• Objective: Build a solid conceptual understanding of residual analysis.

• Theory: Residual plots reveal violations of regression assumptions such as non-linearity or non-constant variance.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 315: Residual analysis - Applied Practice

• Objective: Apply residual analysis to solve concrete problems and solidify intuition.

• Theory (recap): Residual plots reveal violations of regression assumptions such as non-linearity or non-constant variance.

• Practice: Plot residuals vs fitted values for a regression model and diagnose any visible patterns.

Day 316: Heteroscedasticity - Foundations

• Objective: Build a solid conceptual understanding of heteroscedasticity.

• Theory: Heteroscedasticity occurs when the variance of residuals is not constant across predictor values, violating a key OLS assumption.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 317: Heteroscedasticity - Applied Practice

• Objective: Apply heteroscedasticity to solve concrete problems and solidify intuition.

• Theory (recap): Heteroscedasticity occurs when the variance of residuals is not constant across predictor values, violating a key OLS assumption.

• Practice: Identify heteroscedasticity in a residual plot and apply a variance-stabilizing transformation.

Day 318: Multicollinearity - Introduction

• Objective: Grasp the core intuition behind multicollinearity before the mechanics.

• Theory: Multicollinearity occurs when predictors are highly correlated with each other, destabilizing coefficient estimates.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 319: Multicollinearity - Deep Dive

• Objective: Understand the full mechanics/derivation behind multicollinearity.

• Theory: Multicollinearity occurs when predictors are highly correlated with each other, destabilizing coefficient estimates.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 320: Multicollinearity - Applied Practice

• Objective: Apply multicollinearity to a concrete problem or dataset.

• Theory (recap): Multicollinearity occurs when predictors are highly correlated with each other, destabilizing coefficient estimates.

• Practice: Detect multicollinearity in a dataset by examining a correlation matrix among predictors.

Day 321: Variance Inflation Factor (VIF) - Foundations

• Objective: Build a solid conceptual understanding of variance inflation factor (vif).

• Theory: VIF quantifies how much a coefficient's variance is inflated due to multicollinearity; VIF > 5-10 signals a problem.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 322: Variance Inflation Factor (VIF) - Applied Practice

• Objective: Apply variance inflation factor (vif) to solve concrete problems and solidify intuition.

• Theory (recap): VIF quantifies how much a coefficient's variance is inflated due to multicollinearity; VIF > 5-10 signals a problem.

• Practice: Compute VIF for each predictor in a multiple regression and decide which to drop or combine.

Day 323: Robust regression: Huber loss - Foundations

• Objective: Build a solid conceptual understanding of robust regression: huber loss.

• Theory: Huber loss blends squared error and absolute error, reducing the influence of outliers compared to standard least squares.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 324: Robust regression: Huber loss - Applied Practice

• Objective: Apply robust regression: huber loss to solve concrete problems and solidify intuition.

• Theory (recap): Huber loss blends squared error and absolute error, reducing the influence of outliers compared to standard least squares.

• Practice: Fit an OLS and a Huber-loss regression on data with outliers and compare coefficient stability.

Day 325: Robust regression: RANSAC - Introduction

• Objective: Grasp the core intuition behind robust regression: ransac before the mechanics.

• Theory: RANSAC iteratively fits models to random subsets to find a fit robust to a large fraction of outliers.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 326: Robust regression: RANSAC - Deep Dive

• Objective: Understand the full mechanics/derivation behind robust regression: ransac.

• Theory: RANSAC iteratively fits models to random subsets to find a fit robust to a large fraction of outliers.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 327: Robust regression: RANSAC - Applied Practice

• Objective: Apply robust regression: ransac to a concrete problem or dataset.

• Theory (recap): RANSAC iteratively fits models to random subsets to find a fit robust to a large fraction of outliers.

• Practice: Apply RANSAC regression to a dataset with heavy contamination and compare to OLS.

Day 328: Quantile regression - Foundations

• Objective: Build a solid conceptual understanding of quantile regression.

• Theory: Quantile regression models conditional quantiles (e.g. the median) of Y given X, rather than just the conditional mean.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 329: Quantile regression - Applied Practice

• Objective: Apply quantile regression to solve concrete problems and solidify intuition.

• Theory (recap): Quantile regression models conditional quantiles (e.g. the median) of Y given X, rather than just the conditional mean.

• Practice: Fit a median (quantile=0.5) regression alongside OLS and compare on skewed data.

Day 330: Generalized Linear Models: concept - Foundations

• Objective: Build a solid conceptual understanding of generalized linear models: concept.

• Theory: GLMs extend linear regression to non-Normal outcomes via a link function and an appropriate error distribution.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 331: Generalized Linear Models: concept - Applied Practice

• Objective: Apply generalized linear models: concept to solve concrete problems and solidify intuition.

• Theory (recap): GLMs extend linear regression to non-Normal outcomes via a link function and an appropriate error distribution.

• Practice: Explain, in your own words, how a GLM generalizes OLS using a link function.

Day 332: Logistic regression - Introduction

• Objective: Grasp the core intuition behind logistic regression before the mechanics.

• Theory: Logistic regression models the log-odds of a binary outcome as a linear function of predictors.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 333: Logistic regression - Deep Dive

• Objective: Understand the full mechanics/derivation behind logistic regression.

• Theory: Logistic regression models the log-odds of a binary outcome as a linear function of predictors.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 334: Logistic regression - Applied Practice

• Objective: Apply logistic regression to a concrete problem or dataset.

• Theory (recap): Logistic regression models the log-odds of a binary outcome as a linear function of predictors.

• Practice: Fit a logistic regression on a binary-outcome dataset and interpret coefficients as odds ratios.

Day 335: Poisson regression - Introduction

• Objective: Grasp the core intuition behind poisson regression before the mechanics.

• Theory: Poisson regression models count outcomes, assuming the log of the expected count is linear in the predictors.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 336: Poisson regression - Deep Dive

• Objective: Understand the full mechanics/derivation behind poisson regression.

• Theory: Poisson regression models count outcomes, assuming the log of the expected count is linear in the predictors.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 337: Poisson regression - Applied Practice

• Objective: Apply poisson regression to a concrete problem or dataset.

• Theory (recap): Poisson regression models count outcomes, assuming the log of the expected count is linear in the predictors.

• Practice: Fit a Poisson regression on count data (e.g. number of customer complaints) and interpret coefficients.

Day 338: Practice: full regression workflow

• Objective: Understand and internalize practice: full regression workflow.

• Theory: Combine model fitting, diagnostics, and interpretation into one complete regression analysis.

• Practice: Perform a full regression analysis on a real dataset: fit, diagnose, refine, and report results.

PHASE 6 - EXPERIMENTAL DESIGN

Day 339: A/B testing: fundamentals - Foundations

• Objective: Build a solid conceptual understanding of a/b testing: fundamentals.

• Theory: A/B testing randomly assigns users to control and treatment groups to estimate the causal effect of a change.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 340: A/B testing: fundamentals - Applied Practice

• Objective: Apply a/b testing: fundamentals to solve concrete problems and solidify intuition.

• Theory (recap): A/B testing randomly assigns users to control and treatment groups to estimate the causal effect of a change.

• Practice: Design an A/B test plan for a hypothetical website change, specifying metric and hypotheses.

Day 341: Randomization - Foundations

• Objective: Build a solid conceptual understanding of randomization.

• Theory: Randomization balances known and unknown confounders across groups, enabling causal interpretation of the comparison.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 342: Randomization - Applied Practice

• Objective: Apply randomization to solve concrete problems and solidify intuition.

• Theory (recap): Randomization balances known and unknown confounders across groups, enabling causal interpretation of the comparison.

• Practice: Explain why randomization, not just a large sample, is essential for causal claims in an experiment.

Day 343: Sample size calculation for A/B tests - Introduction

• Objective: Grasp the core intuition behind sample size calculation for a/b tests before the mechanics.

• Theory: Sample size for an A/B test depends on baseline rate, minimum detectable effect, significance level, and power.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 344: Sample size calculation for A/B tests - Deep Dive

• Objective: Understand the full mechanics/derivation behind sample size calculation for a/b tests.

• Theory: Sample size for an A/B test depends on baseline rate, minimum detectable effect, significance level, and power.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 345: Sample size calculation for A/B tests - Applied Practice

• Objective: Apply sample size calculation for a/b tests to a concrete problem or dataset.

• Theory (recap): Sample size for an A/B test depends on baseline rate, minimum detectable effect, significance level, and power.

• Practice: Calculate the required sample size for an A/B test given a baseline conversion rate and target MDE.

Day 346: Design of experiments: factorial design - Introduction

• Objective: Grasp the core intuition behind design of experiments: factorial design before the mechanics.

• Theory: Factorial designs test multiple factors simultaneously, allowing estimation of main effects and interactions efficiently.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 347: Design of experiments: factorial design - Deep Dive

• Objective: Understand the full mechanics/derivation behind design of experiments: factorial design.

• Theory: Factorial designs test multiple factors simultaneously, allowing estimation of main effects and interactions efficiently.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 348: Design of experiments: factorial design - Applied Practice

• Objective: Apply design of experiments: factorial design to a concrete problem or dataset.

• Theory (recap): Factorial designs test multiple factors simultaneously, allowing estimation of main effects and interactions efficiently.

• Practice: Design a 2x2 factorial experiment testing two factors and list all treatment combinations.

Day 349: Blocking - Foundations

• Objective: Build a solid conceptual understanding of blocking.

• Theory: Blocking groups similar experimental units together to reduce the influence of a known nuisance variable.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 350: Blocking - Applied Practice

• Objective: Apply blocking to solve concrete problems and solidify intuition.

• Theory (recap): Blocking groups similar experimental units together to reduce the influence of a known nuisance variable.

• Practice: Design a blocked experiment controlling for a nuisance factor (e.g. time of day).

Day 351: Latin square design - Foundations

• Objective: Build a solid conceptual understanding of latin square design.

• Theory: A Latin square design controls for two nuisance factors simultaneously using a structured grid layout.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 352: Latin square design - Applied Practice

• Objective: Apply latin square design to solve concrete problems and solidify intuition.

• Theory (recap): A Latin square design controls for two nuisance factors simultaneously using a structured grid layout.

• Practice: Construct a Latin square design for an experiment with two blocking factors.

Day 353: ANOVA: decomposition of variance - Introduction

• Objective: Grasp the core intuition behind anova: decomposition of variance before the mechanics.

• Theory: ANOVA decomposes total variance into between-group and within-group components to test for differences among group means.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 354: ANOVA: decomposition of variance - Deep Dive

• Objective: Understand the full mechanics/derivation behind anova: decomposition of variance.

• Theory: ANOVA decomposes total variance into between-group and within-group components to test for differences among group means.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 355: ANOVA: decomposition of variance - Applied Practice

• Objective: Apply anova: decomposition of variance to a concrete problem or dataset.

• Theory (recap): ANOVA decomposes total variance into between-group and within-group components to test for differences among group means.

• Practice: Manually decompose total sum of squares into between- and within-group components for a small dataset.

Day 356: One-way ANOVA - Introduction

• Objective: Grasp the core intuition behind one-way anova before the mechanics.

• Theory: One-way ANOVA tests whether means differ across 3+ groups defined by a single factor.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 357: One-way ANOVA - Deep Dive

• Objective: Understand the full mechanics/derivation behind one-way anova.

• Theory: One-way ANOVA tests whether means differ across 3+ groups defined by a single factor.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 358: One-way ANOVA - Applied Practice

• Objective: Apply one-way anova to a concrete problem or dataset.

• Theory (recap): One-way ANOVA tests whether means differ across 3+ groups defined by a single factor.

• Practice: Run a one-way ANOVA on a 3-group dataset and interpret the F-statistic and p-value.

Day 359: Two-way ANOVA - Foundations

• Objective: Build a solid conceptual understanding of two-way anova.

• Theory: Two-way ANOVA tests the effects of two factors and their interaction simultaneously.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 360: Two-way ANOVA - Applied Practice

• Objective: Apply two-way anova to solve concrete problems and solidify intuition.

• Theory (recap): Two-way ANOVA tests the effects of two factors and their interaction simultaneously.

• Practice: Run a two-way ANOVA and interpret both main effects and the interaction effect.

Day 361: Post-hoc tests (Tukey HSD) - Foundations

• Objective: Build a solid conceptual understanding of post-hoc tests (tukey hsd).

• Theory: Post-hoc tests like Tukey HSD identify which specific group pairs differ after a significant ANOVA result.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 362: Post-hoc tests (Tukey HSD) - Applied Practice

• Objective: Apply post-hoc tests (tukey hsd) to solve concrete problems and solidify intuition.

• Theory (recap): Post-hoc tests like Tukey HSD identify which specific group pairs differ after a significant ANOVA result.

• Practice: Apply Tukey HSD after a significant one-way ANOVA and identify which group pairs differ.

Day 363: Chi-square goodness-of-fit test - Introduction

• Objective: Grasp the core intuition behind chi-square goodness-of-fit test before the mechanics.

• Theory: The goodness-of-fit test checks whether observed categorical frequencies match an expected distribution.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 364: Chi-square goodness-of-fit test - Deep Dive

• Objective: Understand the full mechanics/derivation behind chi-square goodness-of-fit test.

• Theory: The goodness-of-fit test checks whether observed categorical frequencies match an expected distribution.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 365: Chi-square goodness-of-fit test - Applied Practice

• Objective: Apply chi-square goodness-of-fit test to a concrete problem or dataset.

• Theory (recap): The goodness-of-fit test checks whether observed categorical frequencies match an expected distribution.

• Practice: Run a chi-square goodness-of-fit test on dice-roll data against a uniform expectation.

Day 366: Chi-square test of independence - Foundations

• Objective: Build a solid conceptual understanding of chi-square test of independence.

• Theory: The test of independence checks whether two categorical variables are associated using a contingency table.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 367: Chi-square test of independence - Applied Practice

• Objective: Apply chi-square test of independence to solve concrete problems and solidify intuition.

• Theory (recap): The test of independence checks whether two categorical variables are associated using a contingency table.

• Practice: Run a chi-square test of independence on a 2x2 contingency table (e.g. treatment vs outcome).

Day 368: Practice: designing and analyzing an experiment

• Objective: Understand and internalize practice: designing and analyzing an experiment.

• Theory: Integrate design principles and the appropriate statistical test into one complete experiment.

• Practice: Design, simulate, and analyze a full experiment from hypothesis to conclusion.

PHASE 7 - MULTIVARIATE STATISTICS

Day 369: PCA: covariance matrix - Foundations

• Objective: Build a solid conceptual understanding of pca: covariance matrix.

• Theory: PCA begins by computing the covariance matrix of standardized variables, capturing how features co-vary.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 370: PCA: covariance matrix - Applied Practice

• Objective: Apply pca: covariance matrix to solve concrete problems and solidify intuition.

• Theory (recap): PCA begins by computing the covariance matrix of standardized variables, capturing how features co-vary.

• Practice: Compute the covariance matrix for a multi-feature dataset and inspect it for strong relationships.

Day 371: PCA: eigenvectors and variance explained - Introduction

• Objective: Grasp the core intuition behind pca: eigenvectors and variance explained before the mechanics.

• Theory: Principal components are the eigenvectors of the covariance matrix, ordered by the variance (eigenvalue) they explain.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 372: PCA: eigenvectors and variance explained - Deep Dive

• Objective: Understand the full mechanics/derivation behind pca: eigenvectors and variance explained.

• Theory: Principal components are the eigenvectors of the covariance matrix, ordered by the variance (eigenvalue) they explain.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 373: PCA: eigenvectors and variance explained - Applied Practice

• Objective: Apply pca: eigenvectors and variance explained to a concrete problem or dataset.

• Theory (recap): Principal components are the eigenvectors of the covariance matrix, ordered by the variance (eigenvalue) they explain.

• Practice: Perform PCA on a dataset and plot the proportion of variance explained by each component.

Day 374: PCA: practice - Foundations

• Objective: Build a solid conceptual understanding of pca: practice.

• Theory: Apply PCA for dimensionality reduction on a real, moderately high-dimensional dataset.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 375: PCA: practice - Applied Practice

• Objective: Apply pca: practice to solve concrete problems and solidify intuition.

• Theory (recap): Apply PCA for dimensionality reduction on a real, moderately high-dimensional dataset.

• Practice: Reduce a dataset to 2 principal components and visualize the result, labeling by a known category.

Day 376: Factor Analysis: latent variables - Introduction

• Objective: Grasp the core intuition behind factor analysis: latent variables before the mechanics.

• Theory: Factor Analysis assumes observed correlations arise from a smaller number of unobserved latent factors.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 377: Factor Analysis: latent variables - Deep Dive

• Objective: Understand the full mechanics/derivation behind factor analysis: latent variables.

• Theory: Factor Analysis assumes observed correlations arise from a smaller number of unobserved latent factors.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 378: Factor Analysis: latent variables - Applied Practice

• Objective: Apply factor analysis: latent variables to a concrete problem or dataset.

• Theory (recap): Factor Analysis assumes observed correlations arise from a smaller number of unobserved latent factors.

• Practice: Run exploratory factor analysis on a survey dataset and interpret the resulting factors.

Day 379: Factor Analysis: practice - Foundations

• Objective: Build a solid conceptual understanding of factor analysis: practice.

• Theory: Compare and contrast the practical output of Factor Analysis against PCA on the same data.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 380: Factor Analysis: practice - Applied Practice

• Objective: Apply factor analysis: practice to solve concrete problems and solidify intuition.

• Theory (recap): Compare and contrast the practical output of Factor Analysis against PCA on the same data.

• Practice: Run PCA and Factor Analysis on the same dataset and compare the resulting components/factors.

Day 381: K-means clustering - Introduction

• Objective: Grasp the core intuition behind k-means clustering before the mechanics.

• Theory: K-means partitions data into k clusters by iteratively minimizing within-cluster variance around centroids.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 382: K-means clustering - Deep Dive

• Objective: Understand the full mechanics/derivation behind k-means clustering.

• Theory: K-means partitions data into k clusters by iteratively minimizing within-cluster variance around centroids.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 383: K-means clustering - Applied Practice

• Objective: Apply k-means clustering to a concrete problem or dataset.

• Theory (recap): K-means partitions data into k clusters by iteratively minimizing within-cluster variance around centroids.

• Practice: Run K-means on a dataset, choose k using the elbow method, and visualize the clusters.

Day 384: Hierarchical clustering - Foundations

• Objective: Build a solid conceptual understanding of hierarchical clustering.

• Theory: Hierarchical clustering builds a tree (dendrogram) of nested clusters via agglomerative or divisive merging.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 385: Hierarchical clustering - Applied Practice

• Objective: Apply hierarchical clustering to solve concrete problems and solidify intuition.

• Theory (recap): Hierarchical clustering builds a tree (dendrogram) of nested clusters via agglomerative or divisive merging.

• Practice: Build a dendrogram for a small dataset and choose a cut point to define clusters.

Day 386: Clustering evaluation metrics - Foundations

• Objective: Build a solid conceptual understanding of clustering evaluation metrics.

• Theory: Metrics like silhouette score and within-cluster sum of squares assess clustering quality without ground-truth labels.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 387: Clustering evaluation metrics - Applied Practice

• Objective: Apply clustering evaluation metrics to solve concrete problems and solidify intuition.

• Theory (recap): Metrics like silhouette score and within-cluster sum of squares assess clustering quality without ground-truth labels.

• Practice: Compute the silhouette score for K-means results across different values of k.

Day 388: Multivariate regression - Introduction

• Objective: Grasp the core intuition behind multivariate regression before the mechanics.

• Theory: Multivariate regression models multiple dependent variables simultaneously as functions of the same predictors.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 389: Multivariate regression - Deep Dive

• Objective: Understand the full mechanics/derivation behind multivariate regression.

• Theory: Multivariate regression models multiple dependent variables simultaneously as functions of the same predictors.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 390: Multivariate regression - Applied Practice

• Objective: Apply multivariate regression to a concrete problem or dataset.

• Theory (recap): Multivariate regression models multiple dependent variables simultaneously as functions of the same predictors.

• Practice: Fit a multivariate regression with two dependent variables and interpret the coefficient matrix.

Day 391: MANOVA - Foundations

• Objective: Build a solid conceptual understanding of manova.

• Theory: MANOVA extends ANOVA to test differences in group means across multiple dependent variables jointly.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 392: MANOVA - Applied Practice

• Objective: Apply manova to solve concrete problems and solidify intuition.

• Theory (recap): MANOVA extends ANOVA to test differences in group means across multiple dependent variables jointly.

• Practice: Run a MANOVA comparing groups on two correlated outcome variables simultaneously.

Day 393: Canonical correlation analysis - Foundations

• Objective: Build a solid conceptual understanding of canonical correlation analysis.

• Theory: Canonical correlation finds linear combinations of two variable sets that are maximally correlated with each other.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 394: Canonical correlation analysis - Applied Practice

• Objective: Apply canonical correlation analysis to solve concrete problems and solidify intuition.

• Theory (recap): Canonical correlation finds linear combinations of two variable sets that are maximally correlated with each other.

• Practice: Run canonical correlation analysis between two feature sets and interpret the leading canonical pair.

Day 395: Practice: multivariate analysis on real dataset

• Objective: Understand and internalize practice: multivariate analysis on real dataset.

• Theory: Combine PCA/Factor Analysis and clustering into one integrated multivariate exploration.

• Practice: Explore a real multivariate dataset end-to-end: reduce dimensions, cluster, and interpret results.

PHASE 8 - BAYESIAN STATISTICS

Day 396: Bayesian thinking: prior and posterior - Introduction

• Objective: Grasp the core intuition behind bayesian thinking: prior and posterior before the mechanics.

• Theory: Bayesian inference updates a prior belief into a posterior belief using observed data via Bayes' theorem.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 397: Bayesian thinking: prior and posterior - Deep Dive

• Objective: Understand the full mechanics/derivation behind bayesian thinking: prior and posterior.

• Theory: Bayesian inference updates a prior belief into a posterior belief using observed data via Bayes' theorem.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 398: Bayesian thinking: prior and posterior - Applied Practice

• Objective: Apply bayesian thinking: prior and posterior to a concrete problem or dataset.

• Theory (recap): Bayesian inference updates a prior belief into a posterior belief using observed data via Bayes' theorem.

• Practice: Update a simple prior belief about a coin's fairness after observing 10 flips.

Day 399: Choosing priors - Foundations

• Objective: Build a solid conceptual understanding of choosing priors.

• Theory: Priors can be informative (encoding real prior knowledge) or weakly informative/non-informative (letting the data dominate).

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 400: Choosing priors - Applied Practice

• Objective: Apply choosing priors to solve concrete problems and solidify intuition.

• Theory (recap): Priors can be informative (encoding real prior knowledge) or weakly informative/non-informative (letting the data dominate).

• Practice: Compare posteriors resulting from an informative vs a flat prior on the same data.

Day 401: Conjugate priors: Beta-Binomial - Introduction

• Objective: Grasp the core intuition behind conjugate priors: beta-binomial before the mechanics.

• Theory: The Beta distribution is the conjugate prior for a Binomial likelihood, giving a closed-form Beta posterior.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 402: Conjugate priors: Beta-Binomial - Deep Dive

• Objective: Understand the full mechanics/derivation behind conjugate priors: beta-binomial.

• Theory: The Beta distribution is the conjugate prior for a Binomial likelihood, giving a closed-form Beta posterior.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 403: Conjugate priors: Beta-Binomial - Applied Practice

• Objective: Apply conjugate priors: beta-binomial to a concrete problem or dataset.

• Theory (recap): The Beta distribution is the conjugate prior for a Binomial likelihood, giving a closed-form Beta posterior.

• Practice: Derive the Beta posterior update formula from a Beta prior and Binomial data by hand.

Day 404: Conjugate priors: Gamma-Poisson - Introduction

• Objective: Grasp the core intuition behind conjugate priors: gamma-poisson before the mechanics.

• Theory: The Gamma distribution is the conjugate prior for a Poisson likelihood, giving a closed-form Gamma posterior.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 405: Conjugate priors: Gamma-Poisson - Deep Dive

• Objective: Understand the full mechanics/derivation behind conjugate priors: gamma-poisson.

• Theory: The Gamma distribution is the conjugate prior for a Poisson likelihood, giving a closed-form Gamma posterior.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 406: Conjugate priors: Gamma-Poisson - Applied Practice

• Objective: Apply conjugate priors: gamma-poisson to a concrete problem or dataset.

• Theory (recap): The Gamma distribution is the conjugate prior for a Poisson likelihood, giving a closed-form Gamma posterior.

• Practice: Derive the Gamma posterior update formula for Poisson-distributed count data.

Day 407: Markov Chain Monte Carlo: concept - Introduction

• Objective: Grasp the core intuition behind markov chain monte carlo: concept before the mechanics.

• Theory: MCMC generates samples from a posterior distribution that is too complex to compute analytically, by constructing a Markov chain whose stationary distribution is the posterior.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 408: Markov Chain Monte Carlo: concept - Deep Dive

• Objective: Understand the full mechanics/derivation behind markov chain monte carlo: concept.

• Theory: MCMC generates samples from a posterior distribution that is too complex to compute analytically, by constructing a Markov chain whose stationary distribution is the posterior.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 409: Markov Chain Monte Carlo: concept - Applied Practice

• Objective: Apply markov chain monte carlo: concept to a concrete problem or dataset.

• Theory (recap): MCMC generates samples from a posterior distribution that is too complex to compute analytically, by constructing a Markov chain whose stationary distribution is the posterior.

• Practice: Explain in your own words why MCMC is needed when conjugate priors are unavailable.

Day 410: Metropolis-Hastings algorithm - Introduction

• Objective: Grasp the core intuition behind metropolis-hastings algorithm before the mechanics.

• Theory: Metropolis-Hastings proposes new parameter values and accepts/rejects them based on a probability ratio to explore the posterior.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 411: Metropolis-Hastings algorithm - Deep Dive

• Objective: Understand the full mechanics/derivation behind metropolis-hastings algorithm.

• Theory: Metropolis-Hastings proposes new parameter values and accepts/rejects them based on a probability ratio to explore the posterior.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 412: Metropolis-Hastings algorithm - Applied Practice

• Objective: Apply metropolis-hastings algorithm to a concrete problem or dataset.

• Theory (recap): Metropolis-Hastings proposes new parameter values and accepts/rejects them based on a probability ratio to explore the posterior.

• Practice: Implement a basic Metropolis-Hastings sampler from scratch for a simple 1-parameter model.

Day 413: Gibbs sampling - Introduction

• Objective: Grasp the core intuition behind gibbs sampling before the mechanics.

• Theory: Gibbs sampling draws each parameter in turn from its full conditional distribution given the others, useful when those conditionals are known.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 414: Gibbs sampling - Deep Dive

• Objective: Understand the full mechanics/derivation behind gibbs sampling.

• Theory: Gibbs sampling draws each parameter in turn from its full conditional distribution given the others, useful when those conditionals are known.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 415: Gibbs sampling - Applied Practice

• Objective: Apply gibbs sampling to a concrete problem or dataset.

• Theory (recap): Gibbs sampling draws each parameter in turn from its full conditional distribution given the others, useful when those conditionals are known.

• Practice: Implement Gibbs sampling for a simple two-parameter conjugate model.

Day 416: Convergence diagnostics for MCMC - Foundations

• Objective: Build a solid conceptual understanding of convergence diagnostics for mcmc.

• Theory: Trace plots, R-hat, and effective sample size diagnose whether an MCMC chain has converged to the target distribution.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 417: Convergence diagnostics for MCMC - Applied Practice

• Objective: Apply convergence diagnostics for mcmc to solve concrete problems and solidify intuition.

• Theory (recap): Trace plots, R-hat, and effective sample size diagnose whether an MCMC chain has converged to the target distribution.

• Practice: Run an MCMC chain and evaluate convergence using trace plots and R-hat.

Day 418: Probabilistic programming: PyMC - Introduction

• Objective: Grasp the core intuition behind probabilistic programming: pymc before the mechanics.

• Theory: PyMC lets you specify Bayesian models declaratively and automatically handles sampling via MCMC/HMC.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 419: Probabilistic programming: PyMC - Deep Dive

• Objective: Understand the full mechanics/derivation behind probabilistic programming: pymc.

• Theory: PyMC lets you specify Bayesian models declaratively and automatically handles sampling via MCMC/HMC.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 420: Probabilistic programming: PyMC - Applied Practice

• Objective: Apply probabilistic programming: pymc to a concrete problem or dataset.

• Theory (recap): PyMC lets you specify Bayesian models declaratively and automatically handles sampling via MCMC/HMC.

• Practice: Build and fit a simple Bayesian linear regression model in PyMC.

Day 421: Probabilistic programming: Stan - Foundations

• Objective: Build a solid conceptual understanding of probabilistic programming: stan.

• Theory: Stan is a high-performance probabilistic programming language using Hamiltonian Monte Carlo for efficient sampling.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 422: Probabilistic programming: Stan - Applied Practice

• Objective: Apply probabilistic programming: stan to solve concrete problems and solidify intuition.

• Theory (recap): Stan is a high-performance probabilistic programming language using Hamiltonian Monte Carlo for efficient sampling.

• Practice: Build and fit the same Bayesian model in Stan and compare results/runtime with PyMC.

Day 423: Model comparison: AIC and BIC - Introduction

• Objective: Grasp the core intuition behind model comparison: aic and bic before the mechanics.

• Theory: AIC and BIC balance model fit against complexity, penalizing extra parameters to avoid overfitting when comparing models.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 424: Model comparison: AIC and BIC - Deep Dive

• Objective: Understand the full mechanics/derivation behind model comparison: aic and bic.

• Theory: AIC and BIC balance model fit against complexity, penalizing extra parameters to avoid overfitting when comparing models.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 425: Model comparison: AIC and BIC - Applied Practice

• Objective: Apply model comparison: aic and bic to a concrete problem or dataset.

• Theory (recap): AIC and BIC balance model fit against complexity, penalizing extra parameters to avoid overfitting when comparing models.

• Practice: Compare 3 nested regression models using AIC and BIC and select the best one.

Day 426: Model comparison: WAIC - Foundations

• Objective: Build a solid conceptual understanding of model comparison: waic.

• Theory: WAIC is a Bayesian, fully-generative alternative to AIC that uses the full posterior distribution rather than a point estimate.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 427: Model comparison: WAIC - Applied Practice

• Objective: Apply model comparison: waic to solve concrete problems and solidify intuition.

• Theory (recap): WAIC is a Bayesian, fully-generative alternative to AIC that uses the full posterior distribution rather than a point estimate.

• Practice: Compute WAIC for two Bayesian models fit in PyMC and compare to AIC/BIC results.

Day 428: Posterior predictive checks - Introduction

• Objective: Grasp the core intuition behind posterior predictive checks before the mechanics.

• Theory: Posterior predictive checks simulate new data from the fitted model and compare it to observed data to assess model fit.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 429: Posterior predictive checks - Deep Dive

• Objective: Understand the full mechanics/derivation behind posterior predictive checks.

• Theory: Posterior predictive checks simulate new data from the fitted model and compare it to observed data to assess model fit.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 430: Posterior predictive checks - Applied Practice

• Objective: Apply posterior predictive checks to a concrete problem or dataset.

• Theory (recap): Posterior predictive checks simulate new data from the fitted model and compare it to observed data to assess model fit.

• Practice: Run posterior predictive checks on a fitted Bayesian model and visually assess fit quality.

Day 431: Practice: full Bayesian analysis workflow

• Objective: Understand and internalize practice: full bayesian analysis workflow.

• Theory: Integrate prior specification, sampling, diagnostics, and model checking into one full Bayesian analysis.

• Practice: Perform a complete Bayesian analysis on a real dataset from prior choice through posterior predictive checks.

PHASE 9 - STATISTICAL COMPUTING

Day 432: R: tidyverse fundamentals - Foundations

• Objective: Build a solid conceptual understanding of r: tidyverse fundamentals.

• Theory: The tidyverse is a coherent set of R packages built around tidy data principles (one row per observation, one column per variable).

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 433: R: tidyverse fundamentals - Applied Practice

• Objective: Apply r: tidyverse fundamentals to solve concrete problems and solidify intuition.

• Theory (recap): The tidyverse is a coherent set of R packages built around tidy data principles (one row per observation, one column per variable).

• Practice: Load a dataset in R and reshape it into tidy format using tidyr.

Day 434: R: data manipulation with dplyr - Foundations

• Objective: Build a solid conceptual understanding of r: data manipulation with dplyr.

• Theory: dplyr provides verbs (filter, select, mutate, summarize, group_by) for expressive, chainable data manipulation.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 435: R: data manipulation with dplyr - Applied Practice

• Objective: Apply r: data manipulation with dplyr to solve concrete problems and solidify intuition.

• Theory (recap): dplyr provides verbs (filter, select, mutate, summarize, group_by) for expressive, chainable data manipulation.

• Practice: Perform a group-by-summarize analysis in R using dplyr on a real dataset.

Day 436: R: ggplot2 basics - Introduction

• Objective: Grasp the core intuition behind r: ggplot2 basics before the mechanics.

• Theory: ggplot2 builds visualizations by layering data, aesthetic mappings, and geometric objects according to the Grammar of Graphics.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 437: R: ggplot2 basics - Deep Dive

• Objective: Understand the full mechanics/derivation behind r: ggplot2 basics.

• Theory: ggplot2 builds visualizations by layering data, aesthetic mappings, and geometric objects according to the Grammar of Graphics.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 438: R: ggplot2 basics - Applied Practice

• Objective: Apply r: ggplot2 basics to a concrete problem or dataset.

• Theory (recap): ggplot2 builds visualizations by layering data, aesthetic mappings, and geometric objects according to the Grammar of Graphics.

• Practice: Recreate 3 different chart types (bar, scatter, boxplot) in ggplot2 from the same dataset.

Day 439: Python: NumPy fundamentals - Foundations

• Objective: Build a solid conceptual understanding of python: numpy fundamentals.

• Theory: NumPy provides fast array operations that underlie almost all numerical/statistical computing in Python.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 440: Python: NumPy fundamentals - Applied Practice

• Objective: Apply python: numpy fundamentals to solve concrete problems and solidify intuition.

• Theory (recap): NumPy provides fast array operations that underlie almost all numerical/statistical computing in Python.

• Practice: Perform vectorized statistical computations (mean, variance, matrix ops) using NumPy without explicit loops.

Day 441: Python: SciPy for statistics - Foundations

• Objective: Build a solid conceptual understanding of python: scipy for statistics.

• Theory: SciPy.stats provides distributions, hypothesis tests, and statistical functions built on NumPy.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 442: Python: SciPy for statistics - Applied Practice

• Objective: Apply python: scipy for statistics to solve concrete problems and solidify intuition.

• Theory (recap): SciPy.stats provides distributions, hypothesis tests, and statistical functions built on NumPy.

• Practice: Run 3 different hypothesis tests using scipy.stats on a real dataset.

Day 443: Python: Statsmodels - Introduction

• Objective: Grasp the core intuition behind python: statsmodels before the mechanics.

• Theory: Statsmodels provides classical statistical models (regression, ANOVA, time series) with detailed statistical output tables.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 444: Python: Statsmodels - Deep Dive

• Objective: Understand the full mechanics/derivation behind python: statsmodels.

• Theory: Statsmodels provides classical statistical models (regression, ANOVA, time series) with detailed statistical output tables.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 445: Python: Statsmodels - Applied Practice

• Objective: Apply python: statsmodels to a concrete problem or dataset.

• Theory (recap): Statsmodels provides classical statistical models (regression, ANOVA, time series) with detailed statistical output tables.

• Practice: Fit an OLS regression in Statsmodels and interpret the full summary output table.

Day 446: Visualization: histogram - Foundations

• Objective: Build a solid conceptual understanding of visualization: histogram.

• Theory: Histograms display the frequency distribution of a continuous variable by binning values.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 447: Visualization: histogram - Applied Practice

• Objective: Apply visualization: histogram to solve concrete problems and solidify intuition.

• Theory (recap): Histograms display the frequency distribution of a continuous variable by binning values.

• Practice: Plot histograms with 3 different bin-width choices on the same dataset and compare interpretations.

Day 448: Visualization: kernel density estimate (KDE) - Foundations

• Objective: Build a solid conceptual understanding of visualization: kernel density estimate (kde).

• Theory: KDE smooths a histogram into a continuous estimated density curve, avoiding arbitrary binning.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 449: Visualization: kernel density estimate (KDE) - Applied Practice

• Objective: Apply visualization: kernel density estimate (kde) to solve concrete problems and solidify intuition.

• Theory (recap): KDE smooths a histogram into a continuous estimated density curve, avoiding arbitrary binning.

• Practice: Overlay a KDE curve on a histogram for the same dataset and compare.

Day 450: Visualization: QQ plot - Foundations

• Objective: Build a solid conceptual understanding of visualization: qq plot.

• Theory: A QQ plot compares sample quantiles to theoretical distribution quantiles to visually assess distributional fit (e.g. Normality).

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 451: Visualization: QQ plot - Applied Practice

• Objective: Apply visualization: qq plot to solve concrete problems and solidify intuition.

• Theory (recap): A QQ plot compares sample quantiles to theoretical distribution quantiles to visually assess distributional fit (e.g. Normality).

• Practice: Create QQ plots for a Normal sample and a skewed sample, and interpret the deviation pattern.

Day 452: Visualization: box plot - Foundations

• Objective: Build a solid conceptual understanding of visualization: box plot.

• Theory: Box plots summarize the median, quartiles, and outliers of a distribution in a compact visual form.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 453: Visualization: box plot - Applied Practice

• Objective: Apply visualization: box plot to solve concrete problems and solidify intuition.

• Theory (recap): Box plots summarize the median, quartiles, and outliers of a distribution in a compact visual form.

• Practice: Create side-by-side box plots comparing a variable across several categories.

Day 454: Visualization principles for storytelling with data - Foundations

• Objective: Build a solid conceptual understanding of visualization principles for storytelling with data.

• Theory: Effective visualizations minimize clutter, choose the right chart for the data type, and highlight the intended insight clearly.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 455: Visualization principles for storytelling with data - Applied Practice

• Objective: Apply visualization principles for storytelling with data to solve concrete problems and solidify intuition.

• Theory (recap): Effective visualizations minimize clutter, choose the right chart for the data type, and highlight the intended insight clearly.

• Practice: Redesign a cluttered or misleading chart into a clear, well-labeled version.

Day 456: Practice: reproducible statistical analysis report

• Objective: Understand and internalize practice: reproducible statistical analysis report.

• Theory: A reproducible report combines code, results, and narrative so the analysis can be re-run and verified by others.

• Practice: Produce a reproducible analysis report (e.g. R Markdown/Jupyter) with code, plots, and written interpretation.

PHASE 10 - STATISTICS FOR MACHINE LEARNING

Day 457: Bias-variance tradeoff - Introduction

• Objective: Grasp the core intuition behind bias-variance tradeoff before the mechanics.

• Theory: Model error decomposes into bias (systematic error from overly simple models) and variance (sensitivity to training data); minimizing total error requires balancing both.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 458: Bias-variance tradeoff - Deep Dive

• Objective: Understand the full mechanics/derivation behind bias-variance tradeoff.

• Theory: Model error decomposes into bias (systematic error from overly simple models) and variance (sensitivity to training data); minimizing total error requires balancing both.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 459: Bias-variance tradeoff - Applied Practice

• Objective: Apply bias-variance tradeoff to a concrete problem or dataset.

• Theory (recap): Model error decomposes into bias (systematic error from overly simple models) and variance (sensitivity to training data); minimizing total error requires balancing both.

• Practice: Fit models of increasing complexity to the same data and plot training vs test error to visualize the tradeoff.

Day 460: Cross-validation: k-fold - Introduction

• Objective: Grasp the core intuition behind cross-validation: k-fold before the mechanics.

• Theory: K-fold cross-validation splits data into k parts, training on k-1 and validating on the remaining part, rotating through all folds.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 461: Cross-validation: k-fold - Deep Dive

• Objective: Understand the full mechanics/derivation behind cross-validation: k-fold.

• Theory: K-fold cross-validation splits data into k parts, training on k-1 and validating on the remaining part, rotating through all folds.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 462: Cross-validation: k-fold - Applied Practice

• Objective: Apply cross-validation: k-fold to a concrete problem or dataset.

• Theory (recap): K-fold cross-validation splits data into k parts, training on k-1 and validating on the remaining part, rotating through all folds.

• Practice: Implement 5-fold cross-validation manually and compare to a built-in library function.

Day 463: Cross-validation: leave-one-out - Foundations

• Objective: Build a solid conceptual understanding of cross-validation: leave-one-out.

• Theory: Leave-one-out CV is the extreme case of k-fold where k equals the number of observations, giving low bias but high variance and cost.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 464: Cross-validation: leave-one-out - Applied Practice

• Objective: Apply cross-validation: leave-one-out to solve concrete problems and solidify intuition.

• Theory (recap): Leave-one-out CV is the extreme case of k-fold where k equals the number of observations, giving low bias but high variance and cost.

• Practice: Compare leave-one-out CV and 5-fold CV results on a small dataset in terms of estimate and runtime.

Day 465: Regularization: Ridge regression - Introduction

• Objective: Grasp the core intuition behind regularization: ridge regression before the mechanics.

• Theory: Ridge regression adds an L2 penalty on coefficients, shrinking them toward zero to reduce variance and handle multicollinearity.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 466: Regularization: Ridge regression - Deep Dive

• Objective: Understand the full mechanics/derivation behind regularization: ridge regression.

• Theory: Ridge regression adds an L2 penalty on coefficients, shrinking them toward zero to reduce variance and handle multicollinearity.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 467: Regularization: Ridge regression - Applied Practice

• Objective: Apply regularization: ridge regression to a concrete problem or dataset.

• Theory (recap): Ridge regression adds an L2 penalty on coefficients, shrinking them toward zero to reduce variance and handle multicollinearity.

• Practice: Fit Ridge regression across a range of penalty values and plot the coefficient shrinkage path.

Day 468: Regularization: Lasso regression - Foundations

• Objective: Build a solid conceptual understanding of regularization: lasso regression.

• Theory: Lasso regression adds an L1 penalty, which can shrink some coefficients exactly to zero, performing implicit feature selection.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 469: Regularization: Lasso regression - Applied Practice

• Objective: Apply regularization: lasso regression to solve concrete problems and solidify intuition.

• Theory (recap): Lasso regression adds an L1 penalty, which can shrink some coefficients exactly to zero, performing implicit feature selection.

• Practice: Fit Lasso regression and identify which features are eliminated as the penalty increases.

Day 470: Regularization: Elastic Net - Introduction

• Objective: Grasp the core intuition behind regularization: elastic net before the mechanics.

• Theory: Elastic Net combines L1 and L2 penalties, balancing Lasso's feature selection with Ridge's stability under correlated predictors.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 471: Regularization: Elastic Net - Deep Dive

• Objective: Understand the full mechanics/derivation behind regularization: elastic net.

• Theory: Elastic Net combines L1 and L2 penalties, balancing Lasso's feature selection with Ridge's stability under correlated predictors.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 472: Regularization: Elastic Net - Applied Practice

• Objective: Apply regularization: elastic net to a concrete problem or dataset.

• Theory (recap): Elastic Net combines L1 and L2 penalties, balancing Lasso's feature selection with Ridge's stability under correlated predictors.

• Practice: Fit Elastic Net and compare selected features/coefficients to pure Ridge and pure Lasso.

Day 473: Model evaluation: ROC curve - Foundations

• Objective: Build a solid conceptual understanding of model evaluation: roc curve.

• Theory: The ROC curve plots true positive rate against false positive rate across all classification thresholds.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 474: Model evaluation: ROC curve - Applied Practice

• Objective: Apply model evaluation: roc curve to solve concrete problems and solidify intuition.

• Theory (recap): The ROC curve plots true positive rate against false positive rate across all classification thresholds.

• Practice: Plot an ROC curve for a binary classifier and identify a threshold matching a target false-positive rate.

Day 475: Model evaluation: AUC - Foundations

• Objective: Build a solid conceptual understanding of model evaluation: auc.

• Theory: AUC (area under the ROC curve) summarizes classifier performance across all thresholds in a single number.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 476: Model evaluation: AUC - Applied Practice

• Objective: Apply model evaluation: auc to solve concrete problems and solidify intuition.

• Theory (recap): AUC (area under the ROC curve) summarizes classifier performance across all thresholds in a single number.

• Practice: Compute AUC for two competing classifiers and determine which performs better overall.

Day 477: Model evaluation: precision and recall - Introduction

• Objective: Grasp the core intuition behind model evaluation: precision and recall before the mechanics.

• Theory: Precision measures correctness among positive predictions; recall measures coverage of actual positives - they trade off against each other.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 478: Model evaluation: precision and recall - Deep Dive

• Objective: Understand the full mechanics/derivation behind model evaluation: precision and recall.

• Theory: Precision measures correctness among positive predictions; recall measures coverage of actual positives - they trade off against each other.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 479: Model evaluation: precision and recall - Applied Practice

• Objective: Apply model evaluation: precision and recall to a concrete problem or dataset.

• Theory (recap): Precision measures correctness among positive predictions; recall measures coverage of actual positives - they trade off against each other.

• Practice: Compute precision and recall for a classifier on an imbalanced dataset and discuss the tradeoff.

Day 480: Model evaluation: F1 score - Foundations

• Objective: Build a solid conceptual understanding of model evaluation: f1 score.

• Theory: The F1 score is the harmonic mean of precision and recall, useful as a single balanced metric especially for imbalanced classes.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 481: Model evaluation: F1 score - Applied Practice

• Objective: Apply model evaluation: f1 score to solve concrete problems and solidify intuition.

• Theory (recap): The F1 score is the harmonic mean of precision and recall, useful as a single balanced metric especially for imbalanced classes.

• Practice: Compute F1 scores across different classification thresholds and find the threshold that maximizes it.

Day 482: Bootstrap resampling - Foundations

• Objective: Build a solid conceptual understanding of bootstrap resampling.

• Theory: Bootstrap resampling repeatedly draws samples with replacement from the data to estimate the sampling distribution of a statistic.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 483: Bootstrap resampling - Applied Practice

• Objective: Apply bootstrap resampling to solve concrete problems and solidify intuition.

• Theory (recap): Bootstrap resampling repeatedly draws samples with replacement from the data to estimate the sampling distribution of a statistic.

• Practice: Bootstrap a 95% confidence interval for the median of a skewed dataset.

Day 484: Permutation tests - Foundations

• Objective: Build a solid conceptual understanding of permutation tests.

• Theory: Permutation tests assess significance by repeatedly shuffling labels to build a null distribution directly from the data.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 485: Permutation tests - Applied Practice

• Objective: Apply permutation tests to solve concrete problems and solidify intuition.

• Theory (recap): Permutation tests assess significance by repeatedly shuffling labels to build a null distribution directly from the data.

• Practice: Run a permutation test to compare two group means without assuming Normality.

Day 486: Ensemble methods: bagging - Introduction

• Objective: Grasp the core intuition behind ensemble methods: bagging before the mechanics.

• Theory: Bagging trains many models on bootstrapped samples and averages their predictions to reduce variance (e.g. Random Forest).

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 487: Ensemble methods: bagging - Deep Dive

• Objective: Understand the full mechanics/derivation behind ensemble methods: bagging.

• Theory: Bagging trains many models on bootstrapped samples and averages their predictions to reduce variance (e.g. Random Forest).

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 488: Ensemble methods: bagging - Applied Practice

• Objective: Apply ensemble methods: bagging to a concrete problem or dataset.

• Theory (recap): Bagging trains many models on bootstrapped samples and averages their predictions to reduce variance (e.g. Random Forest).

• Practice: Train a Random Forest and compare its variance/stability to a single decision tree.

Day 489: Ensemble methods: boosting - Foundations

• Objective: Build a solid conceptual understanding of ensemble methods: boosting.

• Theory: Boosting trains models sequentially, each correcting the errors of the previous ones, reducing bias (e.g. XGBoost).

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 490: Ensemble methods: boosting - Applied Practice

• Objective: Apply ensemble methods: boosting to solve concrete problems and solidify intuition.

• Theory (recap): Boosting trains models sequentially, each correcting the errors of the previous ones, reducing bias (e.g. XGBoost).

• Practice: Train a gradient boosting model and compare performance to bagging on the same dataset.

Day 491: Information theory: entropy - Introduction

• Objective: Grasp the core intuition behind information theory: entropy before the mechanics.

• Theory: Entropy measures the average uncertainty/information content of a random variable's distribution; it underlies decision tree splitting and much of ML.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 492: Information theory: entropy - Deep Dive

• Objective: Understand the full mechanics/derivation behind information theory: entropy.

• Theory: Entropy measures the average uncertainty/information content of a random variable's distribution; it underlies decision tree splitting and much of ML.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 493: Information theory: entropy - Applied Practice

• Objective: Apply information theory: entropy to a concrete problem or dataset.

• Theory (recap): Entropy measures the average uncertainty/information content of a random variable's distribution; it underlies decision tree splitting and much of ML.

• Practice: Compute the entropy of several categorical distributions by hand and confirm with code.

Day 494: Information theory: KL divergence - Introduction

• Objective: Grasp the core intuition behind information theory: kl divergence before the mechanics.

• Theory: KL divergence measures how one probability distribution diverges from a reference distribution, central to variational inference and model comparison.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 495: Information theory: KL divergence - Deep Dive

• Objective: Understand the full mechanics/derivation behind information theory: kl divergence.

• Theory: KL divergence measures how one probability distribution diverges from a reference distribution, central to variational inference and model comparison.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 496: Information theory: KL divergence - Applied Practice

• Objective: Apply information theory: kl divergence to a concrete problem or dataset.

• Theory (recap): KL divergence measures how one probability distribution diverges from a reference distribution, central to variational inference and model comparison.

• Practice: Compute KL divergence between two Normal distributions with different parameters and interpret the result.

Day 497: Information theory: mutual information - Foundations

• Objective: Build a solid conceptual understanding of information theory: mutual information.

• Theory: Mutual information measures how much knowing one variable reduces uncertainty about another, useful for feature selection.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 498: Information theory: mutual information - Applied Practice

• Objective: Apply information theory: mutual information to solve concrete problems and solidify intuition.

• Theory (recap): Mutual information measures how much knowing one variable reduces uncertainty about another, useful for feature selection.

• Practice: Compute mutual information between a feature and target variable and compare to Pearson correlation.

Day 499: Practice: model evaluation and selection workflow

• Objective: Understand and internalize practice: model evaluation and selection workflow.

• Theory: Integrate cross-validation, regularization, and evaluation metrics into one complete model selection pipeline.

• Practice: Build a full model selection pipeline: cross-validate several regularized models and choose the best via appropriate metrics.

PHASE 11 - CAUSAL INFERENCE

Day 500: Potential outcomes framework - Introduction

• Objective: Grasp the core intuition behind potential outcomes framework before the mechanics.

• Theory: The potential outcomes framework defines causal effects as the difference between an outcome under treatment and under control for the same unit, only one of which is ever observed.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 501: Potential outcomes framework - Deep Dive

• Objective: Understand the full mechanics/derivation behind potential outcomes framework.

• Theory: The potential outcomes framework defines causal effects as the difference between an outcome under treatment and under control for the same unit, only one of which is ever observed.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 502: Potential outcomes framework - Applied Practice

• Objective: Apply potential outcomes framework to a concrete problem or dataset.

• Theory (recap): The potential outcomes framework defines causal effects as the difference between an outcome under treatment and under control for the same unit, only one of which is ever observed.

• Practice: Explain the 'fundamental problem of causal inference' in your own words using a concrete example.

Day 503: Directed Acyclic Graphs (DAGs): basics - Introduction

• Objective: Grasp the core intuition behind directed acyclic graphs (dags): basics before the mechanics.

• Theory: DAGs visually encode assumed causal relationships among variables using directed edges and no cycles.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 504: Directed Acyclic Graphs (DAGs): basics - Deep Dive

• Objective: Understand the full mechanics/derivation behind directed acyclic graphs (dags): basics.

• Theory: DAGs visually encode assumed causal relationships among variables using directed edges and no cycles.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 505: Directed Acyclic Graphs (DAGs): basics - Applied Practice

• Objective: Apply directed acyclic graphs (dags): basics to a concrete problem or dataset.

• Theory (recap): DAGs visually encode assumed causal relationships among variables using directed edges and no cycles.

• Practice: Draw a DAG for a real causal question you're interested in, listing all assumed relationships.

Day 506: DAGs: confounders, mediators, colliders - Foundations

• Objective: Build a solid conceptual understanding of dags: confounders, mediators, colliders.

• Theory: Confounders bias associations if uncontrolled; mediators lie on the causal path; colliders create bias if conditioned on.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 507: DAGs: confounders, mediators, colliders - Applied Practice

• Objective: Apply dags: confounders, mediators, colliders to solve concrete problems and solidify intuition.

• Theory (recap): Confounders bias associations if uncontrolled; mediators lie on the causal path; colliders create bias if conditioned on.

• Practice: Classify 5 variables in a given DAG as confounder, mediator, or collider.

Day 508: Backdoor criterion - Introduction

• Objective: Grasp the core intuition behind backdoor criterion before the mechanics.

• Theory: The backdoor criterion identifies which variables must be controlled for to block confounding paths and isolate a causal effect.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 509: Backdoor criterion - Deep Dive

• Objective: Understand the full mechanics/derivation behind backdoor criterion.

• Theory: The backdoor criterion identifies which variables must be controlled for to block confounding paths and isolate a causal effect.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 510: Backdoor criterion - Applied Practice

• Objective: Apply backdoor criterion to a concrete problem or dataset.

• Theory (recap): The backdoor criterion identifies which variables must be controlled for to block confounding paths and isolate a causal effect.

• Practice: Apply the backdoor criterion to a DAG to determine the minimal adjustment set.

Day 511: Propensity score: concept - Foundations

• Objective: Build a solid conceptual understanding of propensity score: concept.

• Theory: The propensity score is the probability of receiving treatment given observed covariates, used to balance groups in observational data.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 512: Propensity score: concept - Applied Practice

• Objective: Apply propensity score: concept to solve concrete problems and solidify intuition.

• Theory (recap): The propensity score is the probability of receiving treatment given observed covariates, used to balance groups in observational data.

• Practice: Estimate propensity scores using logistic regression on an observational dataset.

Day 513: Propensity score matching - Introduction

• Objective: Grasp the core intuition behind propensity score matching before the mechanics.

• Theory: Propensity score matching pairs treated and control units with similar propensity scores to approximate a randomized comparison.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 514: Propensity score matching - Deep Dive

• Objective: Understand the full mechanics/derivation behind propensity score matching.

• Theory: Propensity score matching pairs treated and control units with similar propensity scores to approximate a randomized comparison.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 515: Propensity score matching - Applied Practice

• Objective: Apply propensity score matching to a concrete problem or dataset.

• Theory (recap): Propensity score matching pairs treated and control units with similar propensity scores to approximate a randomized comparison.

• Practice: Perform propensity score matching and compare treatment effect estimates before and after matching.

Day 516: Difference-in-differences - Foundations

• Objective: Build a solid conceptual understanding of difference-in-differences.

• Theory: Difference-in-differences compares the change over time between a treated and control group to estimate a causal effect, controlling for time-invariant confounders.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 517: Difference-in-differences - Applied Practice

• Objective: Apply difference-in-differences to solve concrete problems and solidify intuition.

• Theory (recap): Difference-in-differences compares the change over time between a treated and control group to estimate a causal effect, controlling for time-invariant confounders.

• Practice: Estimate a treatment effect using difference-in-differences on a before/after, treatment/control dataset.

Day 518: Instrumental variables: concept - Introduction

• Objective: Grasp the core intuition behind instrumental variables: concept before the mechanics.

• Theory: An instrumental variable affects the outcome only through its effect on the treatment, allowing causal estimation despite unobserved confounding.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 519: Instrumental variables: concept - Deep Dive

• Objective: Understand the full mechanics/derivation behind instrumental variables: concept.

• Theory: An instrumental variable affects the outcome only through its effect on the treatment, allowing causal estimation despite unobserved confounding.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 520: Instrumental variables: concept - Applied Practice

• Objective: Apply instrumental variables: concept to a concrete problem or dataset.

• Theory (recap): An instrumental variable affects the outcome only through its effect on the treatment, allowing causal estimation despite unobserved confounding.

• Practice: Evaluate whether a proposed instrument satisfies relevance and exclusion restriction conditions for a given problem.

Day 521: Instrumental variables: two-stage least squares - Foundations

• Objective: Build a solid conceptual understanding of instrumental variables: two-stage least squares.

• Theory: 2SLS first predicts treatment from the instrument, then uses predicted treatment to estimate the causal effect on the outcome.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 522: Instrumental variables: two-stage least squares - Applied Practice

• Objective: Apply instrumental variables: two-stage least squares to solve concrete problems and solidify intuition.

• Theory (recap): 2SLS first predicts treatment from the instrument, then uses predicted treatment to estimate the causal effect on the outcome.

• Practice: Implement two-stage least squares by hand (two regression steps) on a simple IV dataset.

Day 523: Regression discontinuity design - Introduction

• Objective: Grasp the core intuition behind regression discontinuity design before the mechanics.

• Theory: RDD exploits a sharp threshold rule to compare units just above and below the cutoff, approximating random assignment locally.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 524: Regression discontinuity design - Deep Dive

• Objective: Understand the full mechanics/derivation behind regression discontinuity design.

• Theory: RDD exploits a sharp threshold rule to compare units just above and below the cutoff, approximating random assignment locally.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 525: Regression discontinuity design - Applied Practice

• Objective: Apply regression discontinuity design to a concrete problem or dataset.

• Theory (recap): RDD exploits a sharp threshold rule to compare units just above and below the cutoff, approximating random assignment locally.

• Practice: Design and analyze a regression discontinuity study around a policy eligibility cutoff.

Day 526: Practice: causal inference case study

• Objective: Understand and internalize practice: causal inference case study.

• Theory: Apply the appropriate causal inference method to a realistic observational research question end-to-end.

• Practice: Choose a causal question, select the right method (matching, DiD, IV, or RDD), and estimate the effect on real/simulated data.

PHASE 12 - ADVANCED STATISTICS

Day 527: Time series: autoregressive (AR) models - Foundations

• Objective: Build a solid conceptual understanding of time series: autoregressive (ar) models.

• Theory: AR models predict a value as a linear function of its own past values, capturing temporal dependence.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 528: Time series: autoregressive (AR) models - Applied Practice

• Objective: Apply time series: autoregressive (ar) models to solve concrete problems and solidify intuition.

• Theory (recap): AR models predict a value as a linear function of its own past values, capturing temporal dependence.

• Practice: Fit an AR(1) model to a time series and interpret the autoregressive coefficient.

Day 529: Time series: moving average (MA) models - Foundations

• Objective: Build a solid conceptual understanding of time series: moving average (ma) models.

• Theory: MA models predict a value as a linear function of past forecast errors rather than past values.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 530: Time series: moving average (MA) models - Applied Practice

• Objective: Apply time series: moving average (ma) models to solve concrete problems and solidify intuition.

• Theory (recap): MA models predict a value as a linear function of past forecast errors rather than past values.

• Practice: Fit an MA(1) model to a time series and compare residual behavior to the AR model.

Day 531: Time series: ARIMA - Introduction

• Objective: Grasp the core intuition behind time series: arima before the mechanics.

• Theory: ARIMA combines autoregression, differencing (for non-stationarity), and moving average components into one flexible model.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 532: Time series: ARIMA - Deep Dive

• Objective: Understand the full mechanics/derivation behind time series: arima.

• Theory: ARIMA combines autoregression, differencing (for non-stationarity), and moving average components into one flexible model.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 533: Time series: ARIMA - Applied Practice

• Objective: Apply time series: arima to a concrete problem or dataset.

• Theory (recap): ARIMA combines autoregression, differencing (for non-stationarity), and moving average components into one flexible model.

• Practice: Fit an ARIMA model to a real time series after determining appropriate p, d, q orders.

Day 534: Time series: SARIMA - Introduction

• Objective: Grasp the core intuition behind time series: sarima before the mechanics.

• Theory: SARIMA extends ARIMA with seasonal components to model recurring periodic patterns.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 535: Time series: SARIMA - Deep Dive

• Objective: Understand the full mechanics/derivation behind time series: sarima.

• Theory: SARIMA extends ARIMA with seasonal components to model recurring periodic patterns.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 536: Time series: SARIMA - Applied Practice

• Objective: Apply time series: sarima to a concrete problem or dataset.

• Theory (recap): SARIMA extends ARIMA with seasonal components to model recurring periodic patterns.

• Practice: Fit a SARIMA model to seasonal data (e.g. monthly sales) and forecast the next 12 periods.

Day 537: Time series: stationarity and unit root tests - Foundations

• Objective: Build a solid conceptual understanding of time series: stationarity and unit root tests.

• Theory: Stationarity means statistical properties don't change over time; the Augmented Dickey-Fuller test checks for a unit root (non-stationarity).

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 538: Time series: stationarity and unit root tests - Applied Practice

• Objective: Apply time series: stationarity and unit root tests to solve concrete problems and solidify intuition.

• Theory (recap): Stationarity means statistical properties don't change over time; the Augmented Dickey-Fuller test checks for a unit root (non-stationarity).

• Practice: Run an ADF test on a time series and, if non-stationary, apply differencing to achieve stationarity.

Day 539: State space models - Foundations

• Objective: Build a solid conceptual understanding of state space models.

• Theory: State space models represent a time series via unobserved evolving states, estimated using tools like the Kalman filter.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 540: State space models - Applied Practice

• Objective: Apply state space models to solve concrete problems and solidify intuition.

• Theory (recap): State space models represent a time series via unobserved evolving states, estimated using tools like the Kalman filter.

• Practice: Implement a simple local-level state space model and apply Kalman filtering to a noisy time series.

Day 541: Survival analysis: Kaplan-Meier estimator - Introduction

• Objective: Grasp the core intuition behind survival analysis: kaplan-meier estimator before the mechanics.

• Theory: The Kaplan-Meier estimator non-parametrically estimates the survival function from time-to-event data, handling censoring.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 542: Survival analysis: Kaplan-Meier estimator - Deep Dive

• Objective: Understand the full mechanics/derivation behind survival analysis: kaplan-meier estimator.

• Theory: The Kaplan-Meier estimator non-parametrically estimates the survival function from time-to-event data, handling censoring.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 543: Survival analysis: Kaplan-Meier estimator - Applied Practice

• Objective: Apply survival analysis: kaplan-meier estimator to a concrete problem or dataset.

• Theory (recap): The Kaplan-Meier estimator non-parametrically estimates the survival function from time-to-event data, handling censoring.

• Practice: Compute and plot a Kaplan-Meier survival curve for a censored time-to-event dataset.

Day 544: Survival analysis: Cox proportional hazards - Introduction

• Objective: Grasp the core intuition behind survival analysis: cox proportional hazards before the mechanics.

• Theory: The Cox model estimates how covariates affect the hazard rate without specifying the baseline hazard's exact form.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 545: Survival analysis: Cox proportional hazards - Deep Dive

• Objective: Understand the full mechanics/derivation behind survival analysis: cox proportional hazards.

• Theory: The Cox model estimates how covariates affect the hazard rate without specifying the baseline hazard's exact form.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 546: Survival analysis: Cox proportional hazards - Applied Practice

• Objective: Apply survival analysis: cox proportional hazards to a concrete problem or dataset.

• Theory (recap): The Cox model estimates how covariates affect the hazard rate without specifying the baseline hazard's exact form.

• Practice: Fit a Cox proportional hazards model and interpret hazard ratios for each covariate.

Day 547: Spatial statistics: basics - Foundations

• Objective: Build a solid conceptual understanding of spatial statistics: basics.

• Theory: Spatial statistics accounts for geographic dependence, where nearby observations tend to be more similar (spatial autocorrelation).

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 548: Spatial statistics: basics - Applied Practice

• Objective: Apply spatial statistics: basics to solve concrete problems and solidify intuition.

• Theory (recap): Spatial statistics accounts for geographic dependence, where nearby observations tend to be more similar (spatial autocorrelation).

• Practice: Compute Moran's I to test for spatial autocorrelation in a geographic dataset.

Day 549: Extreme value theory - Foundations

• Objective: Build a solid conceptual understanding of extreme value theory.

• Theory: Extreme value theory models the tail behavior of distributions, crucial for estimating the risk of rare, extreme events.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 550: Extreme value theory - Applied Practice

• Objective: Apply extreme value theory to solve concrete problems and solidify intuition.

• Theory (recap): Extreme value theory models the tail behavior of distributions, crucial for estimating the risk of rare, extreme events.

• Practice: Fit a Generalized Extreme Value distribution to block-maxima data (e.g. annual peak river flow).

Day 551: Stochastic processes: Markov chains - Introduction

• Objective: Grasp the core intuition behind stochastic processes: markov chains before the mechanics.

• Theory: A Markov chain's future state depends only on its current state, not its full history, described via a transition matrix.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 552: Stochastic processes: Markov chains - Deep Dive

• Objective: Understand the full mechanics/derivation behind stochastic processes: markov chains.

• Theory: A Markov chain's future state depends only on its current state, not its full history, described via a transition matrix.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 553: Stochastic processes: Markov chains - Applied Practice

• Objective: Apply stochastic processes: markov chains to a concrete problem or dataset.

• Theory (recap): A Markov chain's future state depends only on its current state, not its full history, described via a transition matrix.

• Practice: Build a transition matrix for a simple Markov chain and compute its long-run stationary distribution.

Day 554: Hidden Markov models - Introduction

• Objective: Grasp the core intuition behind hidden markov models before the mechanics.

• Theory: HMMs model systems with unobserved (hidden) states that are inferred from observed emissions, common in sequence data.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 555: Hidden Markov models - Deep Dive

• Objective: Understand the full mechanics/derivation behind hidden markov models.

• Theory: HMMs model systems with unobserved (hidden) states that are inferred from observed emissions, common in sequence data.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 556: Hidden Markov models - Applied Practice

• Objective: Apply hidden markov models to a concrete problem or dataset.

• Theory (recap): HMMs model systems with unobserved (hidden) states that are inferred from observed emissions, common in sequence data.

• Practice: Implement a simple HMM and use the Viterbi algorithm to decode the most likely hidden state sequence.

Day 557: Meta-analysis: combining study results - Foundations

• Objective: Build a solid conceptual understanding of meta-analysis: combining study results.

• Theory: Meta-analysis statistically combines effect estimates from multiple independent studies to produce a more precise overall estimate.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 558: Meta-analysis: combining study results - Applied Practice

• Objective: Apply meta-analysis: combining study results to solve concrete problems and solidify intuition.

• Theory (recap): Meta-analysis statistically combines effect estimates from multiple independent studies to produce a more precise overall estimate.

• Practice: Perform a simple fixed-effects meta-analysis combining effect sizes from 3 hypothetical studies.

Day 559: Missing data: MCAR, MAR, MNAR - Foundations

• Objective: Build a solid conceptual understanding of missing data: mcar, mar, mnar.

• Theory: Missingness mechanisms (Missing Completely At Random, At Random, Not At Random) determine which handling methods are valid.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 560: Missing data: MCAR, MAR, MNAR - Applied Practice

• Objective: Apply missing data: mcar, mar, mnar to solve concrete problems and solidify intuition.

• Theory (recap): Missingness mechanisms (Missing Completely At Random, At Random, Not At Random) determine which handling methods are valid.

• Practice: Classify 3 missing-data scenarios by mechanism and justify an appropriate handling strategy for each.

Day 561: Missing data: multiple imputation - Introduction

• Objective: Grasp the core intuition behind missing data: multiple imputation before the mechanics.

• Theory: Multiple imputation creates several plausible completed datasets, analyzes each, and pools results to properly reflect imputation uncertainty.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 562: Missing data: multiple imputation - Deep Dive

• Objective: Understand the full mechanics/derivation behind missing data: multiple imputation.

• Theory: Multiple imputation creates several plausible completed datasets, analyzes each, and pools results to properly reflect imputation uncertainty.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 563: Missing data: multiple imputation - Applied Practice

• Objective: Apply missing data: multiple imputation to a concrete problem or dataset.

• Theory (recap): Multiple imputation creates several plausible completed datasets, analyzes each, and pools results to properly reflect imputation uncertainty.

• Practice: Apply multiple imputation to a dataset with missing values and compare results to simple mean imputation.

Day 564: Statistical ethics: p-hacking and publication bias - Foundations

• Objective: Build a solid conceptual understanding of statistical ethics: p-hacking and publication bias.

• Theory: P-hacking (trying many analyses until significance appears) and publication bias (only significant results get published) distort the scientific record.

• Practice: Summarize the concept in your own words and give one real-world example before moving to application.

Day 565: Statistical ethics: p-hacking and publication bias - Applied Practice

• Objective: Apply statistical ethics: p-hacking and publication bias to solve concrete problems and solidify intuition.

• Theory (recap): P-hacking (trying many analyses until significance appears) and publication bias (only significant results get published) distort the scientific record.

• Practice: Identify signs of possible p-hacking in a real or hypothetical published study.

Day 566: Practice: capstone project - Introduction

• Objective: Grasp the core intuition behind practice: capstone project before the mechanics.

• Theory: Integrate multiple advanced topics from this phase into one substantial independent project.

• Practice: Explain the concept out loud (or in writing) to a hypothetical beginner, in 3-4 sentences.

Day 567: Practice: capstone project - Deep Dive

• Objective: Understand the full mechanics/derivation behind practice: capstone project.

• Theory: Integrate multiple advanced topics from this phase into one substantial independent project.

• Practice: Derive or re-derive the key formula/result by hand, step by step.

Day 568: Practice: capstone project - Applied Practice

• Objective: Apply practice: capstone project to a concrete problem or dataset.

• Theory (recap): Integrate multiple advanced topics from this phase into one substantial independent project.

• Practice: Design and execute a capstone project (e.g. survival analysis or time series forecasting) on a real dataset, with a full written report.