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,
