Introduction to Multiple Regression

Statistics · Axiom Academy

LESSON Introduction to Multiple Regression Predicting outcomes using multiple predictor variables simultaneously 1. The Multiple Regression Equation In simple linear regression, we predict using one variable. Multiple regression extends this to include multiple predictors: Each predictor has its own coefficient that describes its relationship with the outcome. The intercept represents the predicted value when all predictors equal zero. 2. Why Use Multiple Predictors? Better Predictions: Combining multiple pieces of information typically gives more accurate forecasts than using just one variable. Control for Confounders: Multiple regression helps isolate the effect of one variable while accounting for others, reducing spurious correlations. The key to multiple regression is understanding that each coefficient represents the change in the outcome for a one-unit increase in that predictor, holding all other variables constant . This "holding constant" interpretation is crucial. It means we're isolating each predictor's individual effect. 4. Measuring Model Quality: Adjusted R² While regular R² measures the proportion of variance explained, it always increases when we add more predictors—even irrelevant ones. Adjusted R² accounts for the number of predictors and only increases if a new variable improves the model more than expected by chance.

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