and if you recall, if we use an alpha .05, which is what we typically use and
we'll also use in this example. If this p-value is less than .05, then
that indicates the test is significant.
So this value is significant because .0004 is definitely less than .05. So
this indicates that the R-squared of .50 is significantly greater than zero. So in
other words, the variables SAT score, social support, and gender, once again
taken as a group, predict a significant amount of variance in college GPA. And we
could write that up as follows. We could say the overall regression model was
significant, and then we have F 3, 26 and that comes from right here, 3 and 26,
= 8.51, which is the F value here reported in the table,
p is less than .001, and I said that because this value is smaller than
.001. And I also put the R-squared here. R-squared = .50, and that of course
came from right here. So you'll often see results written up like this, in a
research article or what have you.
So this is one way to express the results of the ANOVA table. So if you're
reading a research article on multiple regression and you see this information
here,
most likely, this first part here is corresponding to the results of the
ANOVA table.
OK so these first two tables, as I had said earlier, they assess how well our three
predictors, taken as a set,
did at predicting first-year college GPA. Moving to our last table, this is where
we look at the individual predictors. Whether SAT score, on its own, social
support, on its own, and gender, once again on its own,
are these three variables significant predictors of college GPA. Now it may be that
one of them is signficant,
two of them are, or all three of them are significant, but that's what this
table assesses. So as we did before,
we'll use alpha .05, once again.
So we're going to assess each of these values against .05. And notice that SAT
score, this p-value definitely is less than .05, so SAT is
significant.
Social support, this p-value, while fairly close, is also less than .05, so social
support is significant as well. But notice gender, .66, that's definitely not
less than .05, so gender is not significant.
And that's really not that surprising because males and females don't
typically differ significantly in their college GPA, in their first year, or in
all four years for that matter. But I wanted to include this variable gender in
this model as well, so you can see an example of a non-significant result. So
once again this table is looking at the predictors individually, so this
indicates here that SAT score is a significant predictor of college GPA,
social support is also a significant predictor of college GPA, but gender is
not a significant predictor.
Now in this table here what we're assessing is whether these predictors
account for a significant amount of unique variance in college GPA. So in
other words what that means is that SAT scores significantly predicts college
GPA, so it accounts for a separate, significant part of college GPA than
social support, which is also significant, but it accounts for a unique part of
college GPA that SAT does not account for. So if a test is significant here,
that means that the variable accounts for a significant amount of variance in
college GPA uniquely to itself. And that's an important point to note here,
and that's frequently confused with multiple regression. So, a scenario, if
these two predictors were completely and perfectly correlated at 1.0, in other
words they're really getting at the exact same thing in college GPA, then
neither of these would be significant if that was the case, because neither of
them would be accounting for any unique information in college GPA whatsoever.
They would be totally redundant and they would both not be significant.
So if a predictor is significant here, as these both are, then that tells us that
they account for a significant amount of unique variance in college GPA.
So to wrap it all up here, to summarize, our regression overall was significant
as we see that in the ANOVA table, and the amount of variance that was
accounted for, when the three predictors were taken as a group, was 50%
of the variance, or half of the variance, which was pretty good.
When we looked at the
predictors individually, SAT score was a significant predictor of college GPA, as
was social support,
but gender was not significant.
This concludes the video on multiple regression in Microsoft Excel. Thanks for
watching.