here's the results here, so SAT is significant, social support once again
was significant, and then gender was not significant, as its p-value is greater
than .05.
Now an important point in this table here is, that if a test is significant,
that means that the amount of unique variance a predictor accounts for is
statistically significant.
So in other words, SAT score, since it was significant,
it accounts for a significant amount of unique variance in college GPA. And what
we mean by unique there, is that the amount of variance that SAT score
accounts for, predicts, or explains in college GPA unique to itself, is
significant.
Now when I say unique to itself that means that SAT score explains something
in college GPA that social support and gender did not explain or didn't get at.
So, in other words, SAT score explains uniquely, all to its own, a significant
amount of variance in college GPA. OK since social support is significant, that
also means that social support explained a significant amount of unique variance
in college GPA. So that's what these tests are in the Coefficients table. And
as a way to try to understand this a little bit better,
suppose that SAT score and social support were perfectly correlated, just
hypothetically.So if SAT score and social support were correlated perfectly, they had
a correlation of 1.0.
If I ran this regression analysis, and I was able to get it to run successfully, there
are some problems when variables are perfectly correlated that can occur,
which I'll talk about in another video, but let's assume that it ran fine
everything came out. If these two variables were perfectly correlated, then
the p-values for both of these would not be significant, and in fact they should
be 1.0 if they are perfectly correlated. Because if SAT score and social support
were perfectly correlated, then that would mean that SAT score offers
nothing uniquely in terms of predicting college GPA. And social support offers
nothing uniquely in terms of predicting college GPA, because whatever social
support offers, SAT also offers completely. So they offer nothing
uniquely if they were in fact correlated perfectly. So if a test is significant
here, we know that it's offering a unique contribution to our dependent variable,
or college GPA in this example. So that's important to note and it's an area
that's often confused in regression.
So in summary once again the Model Summary and ANOVA tables, those tell us
overall did our model, with all the predictors included, what was the
R-squared first of all, how much variance did it account for, that's our R-squared,
and then was that variance that it accounted for
statistically significant, that's the ANOVA, the p-value here.
And then Coefficients once again told us, on an individual level, which if any of
the predictors are statistically significant. And if a predictor is
significant, recall that that means that it accounts for a unique amount of variance
in the dependent or criterion variable.
Now there is a situation that can come up that thankfully doesn't happen that
often, but it is an unfortunate situation when it does occur, and that is that we
have a meaningful R-squared that is statistically significant but then when
you look down here at the predictors, the individual tests,
none of them are significant, their p values are all greater than
.05. And what do you think happened if that were to come up?
R-squared is is fairly large, it's significant, but none of these values are
significant.
Well if that's the case, then that means that our predictors are correlated with
each other to such a degree, it doesn't have to be 1.0, but to such a degree that
none of them offers any significant amount of unique variance in explaining
the dependent variable.
So that can come up, I don't see it very often, usually at least one of the
predictors is significant, but that is possible to occur in practice.
OK one last thing I want to talk about before closing, and that is in multiple
regression, if you have a categorical variable that is dichotomous, that is, it
has two categories, such as gender, it's completely fine to enter into the
analysis as we did, where we just go ahead and move it over into our analysis
into our Independent(s) box. If there's two categories to the variable, that's
completely fine. But if you have a categorical variable that has more than
two categories, such as let's say ethnicity, and it had four categories,
then you can't just enter that variable into the regression analysis directly,
but instead you need to re-express that variable first prior to entering it. And
how that works basically is that if a variable has four categories, then you
need to take the number of categories minus one, and that's how many new
predictors there will be for given variable. So if we had ethnicity where
there were four different categories of ethnicity, then I would have to create an
ethnicity1 variable, an ethnicity2 variable, and an ethnicity3 variable,
or 4-1 is three, so three different variables that collectively measure
ethnicity. And how to do that is beyond the scope of this video, but it's
important to be aware of that.
So if I have a categorical variable that has more than two categories,
I can't enter it directly into the analysis. But for all quantitative
variables, or what one can think of as a continuous variable, they can always be
moved in directly without a problem,
it only occurs with categorical variables that have more than two levels.
OK that's it for an overview of multiple regression. Thanks for watching.