Casualty Actuarial Society MAS-1 Practice Exam

When you want to know if a predictor truly helps explain the outcome beyond what the other predictors already explain, you compare the full model (including that predictor) to a reduced model (excluding it) using a partial F-test. The F-statistic used for this purpose is the ratio of the mean square attributed to that predictor to the mean square error from the full model. The numerator, the mean square due to the predictor, reflects the incremental increase in explained variation when you add that predictor to the model, adjusted for the other predictors. Since a single predictor contributes one degree of freedom, this MSR is SSR for that predictor divided by 1. The denominator is the residual mean square from the full model (the MSE), which estimates the typical squared size of the errors after fitting all the predictors. If the predictor has no real effect, the extra explained variance is small and the F statistic is near 1. If the predictor does have a real effect, the predictor’s MSR is large relative to the MSE, and the F statistic is large, signaling significance. So the statement is true: the F-statistic for testing a predictor in regression is the ratio of its mean square (the incremental, adjusted contribution) to the mean square error from the full model.