Courses/Behavioral Research: Statistical Methods

Behavioral Research: Statistical Methods

CG3.402

Vinoo Alluri•Monsoon 2025-26•4 credits

Revision Notes/Unit 12 — Regression (Linear, Multiple)

Unit 12 — Regression (Linear, Multiple)

Simple regression Y = β₀ + β₁X + ε; OLS minimises sum of squared residuals; R² vs adjusted R²; LINeM assumptions (linearity, independence, normality, equal variance, no multicollinearity); residual diagnostics; categorical predictors via dummy coding.

OLS, Diagnostics, Multiple Regression

14 min

If ANOVA is the workhorse, regression is the racehorse. The same one model — fit a line, or a hyperplane, that minimises squared residuals — subsumes correlation, t-tests, ANOVA, and ANCOVA as special cases. Each coefficient $\beta_j$ asks: *holding all other predictors constant, how much does Y change per unit of $X_j$?* R² is the headline ('% variance explained'). But the model only earns its conclusions if six assumptions hold — and that's why half of regression is **diagnostics**, not estimation.