Judge how much of the variation in the explained variable a multiple regression captures, using ANOVA output and goodness-of-fit statistics
The idea
The ANOVA table splits the total sum of squares into the part the regression explains (RSS) and the residual part (SSE). R² is RSS ÷ SST, but it never falls when a variable is added, so it flatters bigger models. Adjusted R² = 1 − [(n − 1) ÷ (n − k − 1)] × (1 − R²) penalises extra variables and can fall. The overall F-statistic is (RSS ÷ k) ÷ [SSE ÷ (n − k − 1)] and tests whether all slopes are zero together. To compare models, use the Akaike criterion for forecasting or the Schwarz Bayesian criterion for fit; lower is better. The usual slip is using n − k instead of n − k − 1.
In the app: 3 practice questions on this outcome, a narrated walkthrough with diagrams, spaced review that brings it back before you forget it.
Take the free diagnostic →More in Evaluating Regression Model Fit and Interpreting Model Results
- Set up tests of whether a multiple regression's coefficients, taken two or more at a time, are jointly significant and explain what the outcome of such joint tests tells you
- Work out a forecast of the dependent variable from a fitted regression and given values of the explanatory variable, and explain what it means