Introduction
Start from the research question and distinguish description, prediction, and causation before choosing a method.
- Signal and noise
- Research design
- Cognitive bias
The complete learning map
Ideas made
visible.
All fourteen chapters at a glance, plus concept notes and deeper lessons adapted from the authors’ teaching slides. Each topic keeps the mathematics close to interpretation and code.
All fourteen chapters
One connected path
through regression.
Use the sequence as a course roadmap, or enter at the chapter that matches your empirical question.
IQuestions and foundationsChapters 1–4
Covariation in data
Move from visual patterns to covariance, correlation, the regression line, and residuals.
- Scatter plots
- Pearson & Spearman
- OLS intuition
Probability & inference
Connect population models to random variables, sampling distributions, estimation, and hypothesis tests.
- Conditional probability
- Expectation & variance
- Monte Carlo
Population correlation
Learn why a sample correlation varies and how Fisher transforms and tests quantify its uncertainty.
- Sampling variation
- Fisher transform
- Confidence intervals
IIRegression modelsChapters 5–9
Simple linear regression
Separate population and sample models, interpret slopes, and understand when exogeneity supports causal meaning.
- OLS geometry
- Robust inference
- Misspecification
Multiple regression
Interpret ceteris paribus comparisons and diagnose omitted-variable bias using regression anatomy.
- Partial effects
- FWL theorem
- Joint tests
Nonlinear form
Extend the linear model with polynomials, indicators, interactions, and logarithmic transformations.
- Quadratics
- Dummy variables
- Log models
Dependent errors
Adapt regression inference to clusters, multilevel structures, and repeated observations in panel data.
- Clustered SEs
- Hierarchical models
- Fixed effects
Binary outcomes
Model probabilities with logistic regression and interpret odds ratios, risk ratios, and risk differences.
- Logit
- Maximum likelihood
- Marginal effects
IIIPrediction and flexible modelsChapters 10–12
Prediction
Evaluate models out of sample and control complexity with cross-validation, regularization, and trees.
- Test error
- Bias–variance
- Ridge & lasso
Nonparametric regression
Estimate flexible conditional means with local averages, kernels, and data-driven bandwidths.
- Regressograms
- Kernel weights
- Local linear fits
Time series
Account for temporal dependence using stationarity, autocorrelation, autoregression, and ARIMA models.
- Trends & differences
- ACF
- Forecasting
IVCausal design and synthesisChapters 13–14
Causal analysis
Define effects through potential outcomes and connect identification to experiments and quasi-experiments.
- DiD
- IV
- RDD
Key concepts
Revisit the book’s central distinctions, assumptions, estimators, and diagnostic language as one toolkit.
- Exogeneity
- Consistency
- Model choice
Six essential notes
More than a chapter list.
Short explanations distilled from the teaching slides provide a bridge into the full book.
From a sample to a population
Descriptive statistics summarise the observed data. Statistical inference asks how those summaries would vary across repeated samples from a population model.
\[\hat\theta-\theta=\text{sampling error}\]Standard errors describe the scale of that variation.
What OLS is minimising
OLS selects the line whose fitted values make the sum of squared residuals as small as possible. The slope then describes a conditional mean—not automatically a causal effect.
\[\min_{b_0,b_1}\sum_i(y_i-b_0-b_1x_i)^2\]Causal interpretation additionally requires exogeneity.
Keep predicted probabilities bounded
A logistic model passes a linear index through a smooth cumulative distribution function, ensuring fitted probabilities stay between zero and one.
\[P(Y=1\mid X)=\frac{1}{1+e^{-X\beta}}\]Effects can be expressed through odds, risks, or probability differences.
Judge predictions on unseen data
Training error rewards complexity. Test error reveals whether that complexity captures stable signal or merely follows noise in the observed sample.
\[MSE=\text{bias}^2+\text{variance}+\text{noise}\]Cross-validation estimates performance without a single fragile split.
Bandwidth controls flexibility
Kernel regression gives nearby observations more weight. A narrow bandwidth follows local detail; a wide bandwidth produces a smoother, more stable curve.
local detailsmooth trend
Time order changes the model
When observations depend on their own past, random sampling logic no longer applies directly. Stationarity makes temporal relationships stable enough to estimate and forecast.
\[Y_t=c+\phi Y_{t-1}+U_t\]For a stationary AR(1), the effect of a shock decays over time.
Chapter 02 · Foundations
Covariation
in data
How do two variables move together, and how can a cloud of observations become a useful numerical summary?
01 · Begin with the picture
Look before you calculate.
A scatter plot reveals direction, form, strength, and unusual observations. In the running example, apartment size and sales price tend to rise together, but the cloud is wide enough that size alone cannot explain every price.
XY
02 · Standardise joint movement
Covariance carries units.
Correlation does not.
Covariance averages the products of paired deviations. Dividing by both standard deviations turns it into a unit-free measure bounded between −1 and 1.
Sample covariance\[s_{XY}=\frac{1}{n-1}\sum_{i=1}^{n}(x_i-\bar{x})(y_i-\bar{y})\]
Pearson correlation\[r_{XY}=\frac{s_{XY}}{s_Xs_Y}\]
Pearson correlation\[r_{XY}=\frac{s_{XY}}{s_Xs_Y}\]
+1
Perfect positive linear relationship
0
No linear relationship—not necessarily no relationship
−1
Perfect negative linear relationship
03 · Run the idea twice
One statistic,
two languages.
Always pair the coefficient with the scatter plot: correlation compresses the picture, but cannot diagnose nonlinearity or outliers by itself.
Chapter 2 companion code ↗R
cor(df$living_area,
df$price,
method = "pearson")Python
df["living_area"].corr(
df["price"],
method="pearson")Chapter 06 · Regression models
Multiple
regression
Move beyond a single predictor to interpret associations while holding other observed variables constant.
01 · The ceteris paribus idea
Compare like with like.
A simple regression can mix the association of interest with other differences. Multiple regression asks how expected price changes with size among apartments that share the same monthly fee.
X₁X₂Y
02 · From a line to a surface
The model grows.
The logic remains.
Each coefficient describes a conditional comparison. The error term collects determinants of the outcome not represented by the included regressors.
Multiple regression model\[Y=\beta_0+\beta_1X_1+\cdots+\beta_KX_K+U\]
Conditional slope\[\beta_1=\frac{\partial\,E[Y\mid X_1,X_2]}{\partial X_1}\]
Conditional slope\[\beta_1=\frac{\partial\,E[Y\mid X_1,X_2]}{\partial X_1}\]
03 · Omitted-variable bias
What did the short model leave behind?
Omitted variable ZaffectsRegressor Xand affectsOutcome Y
Bias appears when the omitted variable both helps determine the outcome and is associated with an included regressor. Adding variables mechanically is not the solution; controls must follow the question and causal structure.
04 · Robust inference
Estimate, then
report uncertainty.
These parallel examples fit price on living area and monthly fee and request heteroskedasticity-robust standard errors.
Chapter 6 companion code ↗R
fit <- lm(price ~ living_area +
monthly_fee, data=df)
coeftest(fit, vcov.=vcovHC(fit))Python
fit = smf.ols(
"price ~ living_area + monthly_fee",
data=df).fit(cov_type="HC1")Chapter 13 · Causal analysis
Thinking in
counterfactuals
Causal questions compare what happened with what would have happened under a different treatment state.
ObservedYᵢ(1)treated outcome
CounterfactualYᵢ(0)untreated outcome
\[\tau_i=Y_i(1)-Y_i(0)\]
01 · The fundamental problem
We never observe both worlds.
For the same unit at the same moment, only one potential outcome can be observed. Causal inference therefore needs a research design that makes another group, time, threshold, or assignment rule a credible stand-in for the missing counterfactual.
01Define the treatment
02Name the estimand
03State identifying assumptions
04Probe their credibility
02 · Why naive comparisons fail
Difference in means = effect + selection.
\[E[Y\mid D=1]-E[Y\mid D=0]\] \[=\underbrace{E[Y(1)-Y(0)\mid D=1]}_{\text{ATT}}+\underbrace{E[Y(0)\mid D=1]-E[Y(0)\mid D=0]}_{\text{selection bias}}\]
Random assignment
Treatment is independent of potential outcomes by design.
Parallel trends
Compare changes when untreated trends would have evolved similarly.
Exogenous variation
Use an instrument that shifts treatment without directly changing the outcome.
Threshold comparison
Compare units just above and below an assignment cutoff.
03 · Difference in differences
Compare changes,
not just levels.
The interaction coefficient captures the treatment group’s additional post-treatment change under the parallel-trends assumption.
Chapter 13 companion code ↗DiD regression\[Y_{igt}=\beta_0+\beta_1D_g+\beta_2T_t+\beta_3(D_g\times T_t)+U_{igt}\]
Target coefficient
Target coefficient
\(\beta_3\) is the difference in changes.
Continue learning
Read less.
Run more.
These pages are selective teaching notes, not a substitute for the book. Use the public companion repository to reproduce the examples in R and Python.
Open companion code ↗