Regression

Regression models an outcome variable as a function of one or more predictors, estimating how much the outcome changes for a one-unit change in each predictor while the others are held constant. Simple regression uses a single predictor; multiple regression uses several.

Interpretation centres on the coefficients. Unstandardised B expresses change in the outcome's own units, while standardised beta places predictors on a common scale so their relative importance can be compared. R squared reports the proportion of variance explained, and adjusted R squared penalises predictors that do not earn their place in the model.

The assumptions deserve real attention: linearity, independence of errors (Durbin-Watson), homoscedasticity, approximately normal residuals and no severe multicollinearity, with VIF below roughly 5 to 10. Inspect residual plots rather than trusting the summary output alone. When the outcome is categorical, logistic regression replaces the linear model.