and the ANOVA table is a test of whether this R-squared is significantly greater
than 0. And if you look at the table here, what we want to do is we want to look at
the column labeled Sig., and if this p value here which is what this is, is less
than .05, then that means that the test is significant, the regression's
significant, in other words, R-squared is significantly greater than 0.
So since this is less than .05, we know that this value of R-squared is
significantly greater than 0, and that means that our predictors are able to
account for a significant amount of variance in college GPA. So, in other
words, the regression model is significant.
And we could interpret the results of the ANOVA table as follows, and you'll
often see this written up in research reports or journal articles as the
following, the overall regression model was significant and then here we have F 3
and 26, which you can see right here under df for Regression and Residual,
respectively.
Then we have an F value of 8.51, which you see here reported under F, and I rounded it
to two decimal places. And then p is less than .001, since we see SPSS is
rounded down here to .000, since it was less than .005.
And then I also put the R-squared here at the end. This is very typical to do
this,
R-squared equals .50. And that of course came from the Model Summary table.
OK so once again this tells us, overall, our regression analysis was
statistically significant. When I take those three predictors together as a
group, they predict college GPA significantly. Next we'll look at the Coefficients
table. And this is the table now where, those first two tables, Model Summary and
ANOVA, looked at the regression analysis overall, or the predictors taken as a set,
the Coefficients table looks at each of the predictors individually. So whether a
given predictor was significant on its own right, and so forth. And what we do
here is we're going to look at each of our predictors and we want to zero in on
the Sig. column, once again, which are the p-values for each of the tests. Now
in this analysis the Constant is not important to us whatsoever. What we want
to focus on are the three p values for SAT score, social support, and gender. So
we're going to evaluate each of these tests at an alpha of .05. So looking at SAT
score, we can see that that p-value which was rounded down to .000 and you can see
in the yellow box there the exact value. This was definitely less than
point .05,
so that is significant. SAT score is a significant predictor of college GPA. And
in just a few moments I'll explain exactly what that means. But let's go and
look at the next two predictors first. Social support, with a p-value of .024, is
also a significant predictor of college GPA, since this p-value is less than
.05.
And then finally, gender, with a p-value of .658, is not a significant predictor
of college GPA. And that's not really that surprising if we think about it, because
males and females typically don't differ significantly in their overall GPA in
college. But I wanted to include this variable both to give you an example of
a dichotomous variable and so that you could also see what a non-significant
result looks like. We could summarize the results of the Coefficients table as
follows,