| Date | Topics | References |
|---|---|---|
| Jan 7 | Introduction to linear regression |
slidesfatherson.csv
|
| Jan 12 | Simple regression |
slidesmall_sales.csv
|
| Jan 14 |
Multiple regression, The (weak) linear model, |
slides |
| Jan 21 |
video lecture: Estimation for linear models, Interpreting linear models, Statistical Properties of \(\hat{\beta}\) |
slides |
| Jan 26 | Statistical Properties of \(\hat{\beta}\) |
slides, iPad derivations |
| Jan 28 |
Quantifying Model Fit: SSE, SST, and \(R^2\), Testing statistical hypotheses |
slides |
| Feb 2 |
Testing hypotheses for the slope, Confidence intervals for \(\beta_j\) |
slides |
| Feb 4 |
video lecture: The (overall) \(\mathcal{F}\)-test, Analysis of Variance (ANOVA), The partial \(\mathcal{F}\)-test |
slides |
| Feb 9 |
Inference for linear combinations of slope coefficients, Inference for conditional expectations |
slides, iPad derivations |
| Feb 11 |
Inference for the regression function, Prediction intervals |
slides |
| Feb 16 |
Regression diagnostics: assessing linearity, homoskedasticity, normality |
slides |
| Feb 18 |
Influential observations (and outliers): leverage scores, testing for outliers, Cook's distance |
slides |
| Feb 23 |
Multicollinearity: partial regression, variance inflation factor, condition number |
slides |
| Feb 25 | Midterm I | |
| Mar 9 |
Multicollinearity, Multiple hypothesis testing, Corrections for multiple comparisons, Simultaneous confidence bands |
slides |
| Mar 11 |
Heteroskedasticity, estimation, and inference, Weighted least squares, Heteroskedasticity-consistent standard errors |
slides |
| Mar 16 |
Non-Gaussian/normal error terms, Asymptotically valid inference under non-normality, The bootstrap |
slides |
| Mar 18 |
Bootstrapping regression, Log transformations, Log-Log-transformations |
slides |
| Mar 23 |
Polynomial regression, Overfitting, Bias-variance decomposition |
slides |
| Mar 25 |
Bias-variance tradeoff, Training and test evaluations |
slides, Bias-variance decomposition derivation |
| Mar 30 |
Regression splines, Natural splines, Generalized additive models |
slides |
| Apr 1 |
Test-based methods, Criterion-based methods |
slides, Mallow's \(C_p\) derivation |
| Apr 6 |
Criterion-based methods, Sample-splitting |
slides |
| Apr 8 |
Cross-validation, Inference after model selection, Regularization |
slides |
| Apr 13 |
video lecture shrinkage methods |
slides |
| Apr 15 |
Logistic regression, Maximum likelihood, Generalized linear models |
slides |
| Apr 20 | Midterm II |