Statistics for CSAI 2

by Albert Major

Simple regression recap

• Simple regression predicts one outcome from one predictor.

• The model has an intercept, a slope, and error.

• The slope shows how much the outcome changes when the predictor increases by one unit.

Multiple regression

• Multiple regression predicts one outcome from two or more predictors.

• The equation expands by adding more predictors with their own coefficients.

• Each coefficient represents the effect of one predictor while holding all other predictors constant.

• R syntax mirrors the equation. You add predictors with plus signs.

Interpreting multiple regression coefficients

• Unstandardized coefficients use the original units of the variables.

• They tell you how much the outcome changes when a predictor changes by one unit, while other predictors stay constant.

• They are not directly comparable across predictors if predictors use different scales.

• Standardized coefficients (beta weights) express effects in units of standard deviation.

• Beta weights allow direct comparison of strengths across predictors.

Intercept interpretation

• The intercept is the predicted value of the outcome when all predictors equal zero.