The intuition behind a test of joint significance is that if a subset of variables is jointly significant,then
A)the unexplained sum of squares should be much larger in the restricted regression than in the unrestricted regression.
B)the unexplained sum of squares should be much smaller in the restricted regression than in the unrestricted regression.
C)the explained sum of squares should be much smaller in the restricted regression than in the unrestricted regression.
D)the total sum of squares should be much larger in the restricted regression than in the unrestricted regression.

Question

Quizplus · Accepted Answer

The intuition behind a test of joint significance is that if a subset of variables is jointly significant, then the model with the subset of variables should be a better fit than the model without them. This translates to the unexplained sum of squares being much smaller in the restricted regression (with the subset of variables) than in the unrestricted regression (without the subset of variables). Therefore, choice B is the correct answer as it states that the unexplained sum of squares should be much smaller in the restricted regression than in the unrestricted regression.

The Intuition Behind a Test of Joint Significance Is That