Track 9 · Correlation and Regression · Lesson 9 of 15
Multiple regression
Fit a regression with several predictors, interpret each slope as an association holding the other predictors fixed, and judge the model with adjusted R² and F tests.
Bigger houses cost more — but bigger houses are also often newer or further from the centre. To ask how price relates to floor area among houses of the same age and distance, an analyst needs a model with all three predictors at once. That is multiple regression, the workhorse of applied statistics.
A multiple regression predicts a numeric response from several explanatory variables at once. Least squares still chooses the coefficients that make the sum of squared residuals as small as possible; the only change is that the fitted “line” is now a plane (or a higher-dimensional surface).
Included with a Formula Quest membership
It has 7 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Fit a multiple regression and write the fitted equation
- Interpret each slope in units, holding the other predictors fixed, without causal language
- Explain why a slope changes when another correlated predictor is added
- Compare models with adjusted R², the overall F test and a nested F test