Can you relate in multiple ways? Multiple linear regression and stepwise regression - Improving the User Experience through Practical Data Analytics - page 242

Table 10.1 Multiple Regression Data for Illustrative Example; Excel
per the sidebar. The dependent variable column [column D in Figure 10.1 ] need not be
next to the X columns, but it is natural to input the data so that it is. Notice also that we are
asking for the output to be in a sheet arbitrarily called “seth” [see arrow in Figure 10.1 ].)
After clicking on OK, we see the output in Figure 10.2 . There is a lot to discuss
about the output.
First, note that the value of r 2 is 0.877 (see horizontal arrow in Figure 10.2 ).
This says that the three X's as a group explain about 87.7% of the variability in Y. In
essence, the three X's explain about 87.7% of the reason that the value of Y comes
out what it does. In a context such as this one, that is a relatively high value for r 2 !
We mentioned in Chapter 9 that the t-test and the F -test for the single X variable
yielded exactly the same results, and that this was evidenced by the same p -value.
However, when performing a multiple regression, the results of the F -test and the
t-test are not the same and have different meanings.
Here, the F -test has a p -value of 1.03197E-09 (see vertical solid arrow in
Figure 10.2 ); this means in “Excel speak” 1.03197*10 −9 , which, in turn, equals
0.00000000103197. Remember that Excel refers to the p -value of the F -test as
“signiicance F.” This is very close to zero—it's about one in a billion! In multiple
regression, what this is saying is that beyond any reasonable doubt , the three X's as
a group do provide predictive value about Y.