Linear Regression

Summary

Builds linear regression starting from the equation Y equals beta zero plus beta one X plus epsilon, anchored by a birth-weight-and-gestational-age example with five thousand births. Develops ordinary least squares estimation, the meaning of residuals and the sum of squared residuals, standard errors, confidence intervals, t-tests, and the limits of R-squared as a model-quality verdict. Extends to multiple regression where each coefficient gives the partial effect holding other predictors constant, distinguishes multiple from multivariable from multivariate, and closes with residual plots, leverage, Cook's distance, and other diagnostics that tell you whether the model is trustworthy.