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