Can you relate in multiple ways? Multiple linear regression and stepwise regression - Improving the User Experience through Practical Data Analytics - page 243

FIGURE 10.1
Regression dialog box in Excel; illustrative example.
SIDEBAR: F -TEST: THE TEST OF THE OVERALL MODEL
In multiple regression, the F -test is testing:
H0: The X's as a group do not help you predict Y.
H1: The X's as a group do, indeed, help you predict Y.
In other words, the F -test is testing whether all of the independent variables together help us
predict the dependent variable (Y).
But here's an important heads-up: the F -test tells us we are getting predictive value about Y, but
says nothing about which of the X's are providing this predictive value . At this point, it could be all
of three X's, any two of the three X's, or only one of the three X's. In fact, this is why the F -test is
referred to as the “Test of the Overall Model.”
To address the issue of which X's are giving us the predictive value (which surely is, logically,
the next step in the analysis), we need to examine the t-test for each of the X variables, as explained
below.
By the way, if the F -test had not been signiicant (i.e., its p -value > 0.05), you would basically
stop your analysis (and lament the fact that none of the X's are of any value to you in predicting Y).