Adjusted R-squared measures the proportion of response variance explained by a regression model while accounting for how many predictors it uses. Unlike R-squared, it can decrease when added predictors fail to improve predictive power. section 5.7.3
Use adjusted R-squared to interpret model fit more cautiously:
- R-squared naturally increases as predictors are added, even when some contribute little. section 5.7.3
- Adjusted R-squared penalizes unnecessary complexity, so noise-producing predictors can lower the statistic. section 5.7.3
- Compare it across competing regressions rather than treating it as a complete measure of model quality. section 5.7.6
NBA wins regression
A model with five predictors has R-squared = 0.20 and adjusted R-squared = 0.14, meaning the predictors collectively explain about 20% of win variance, but roughly 14% after accounting for model complexity. Removing two nonsignificant predictors produces fit2, whose adjusted R-squared rises slightly to 0.16. section 5.7.3 section 5.7.6
tidy(fit1) ## # A tibble: 6 × 5 ## term estimate std.error statistic p.value ## <chr> <dbl> <dbl> <dbl> <dbl> ## 1 (Intercept) -62.9 38.6 -1.63 0.108 ## 2 screen_assists_pts 1.04 0.441 2.35 0.0219 ## 3 deflections 2.23 0.882 2.53 0.0138 ## 4 loose_balls 5.38 2.19 2.45 0.0170 ## 5 contested_2pt 0.525 0.763 0.688 0.494 ## 6 contested_shots -0.241 0.790 -0.305 0.761
Inspect coefficient estimates and p-values alongside adjusted R-squared to identify predictors that may add noise. section 5.7.3
