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.
