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Multiple Regression in Excel - P-Value; R-Square; Beta Weight; ANOVA table (Part 2 of 3) - YouTube
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and then I also want to go ahead and
dial down these decimals.
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Let's do it to two decimal places. And
then we'll go back and increase our
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p-values just a bit. So dial that down
to two, that looks good. And then for my p
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value, which is significance F under
ANOVA, and then the p-values here, let's go
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to increase these a bit more. So if we're
comparing them to any other results, from
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any other analyses, SPSS or what-have-you,
we can go ahead and make sure that they
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match up.
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OK that looks good. So I'll go ahead
and shrink these just a bit more.
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Alright, so in multiple regression,
there's two things that we're dealing
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with.
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We're dealing with the overall fit of
what's called our model, and our model is
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where we use our three predictors to try
and predict first-year college GPA. So
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that's our model, our whole, all of our
values, that constitutes our model. And
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we're trying to assess how well the
model fits overall, how well of a job did
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the three predictors help us predict
college GPA overall, and then we also
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want to know how did the individual
predictors do. So we're looking at two
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things, we're looking at the overall
usefulness of the model, and then the
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usefulness of the individual predictors
SAT score, social support, and gender. So
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we'll get started first with the overall
fit. And that really concerns this first
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table of output, as well as the second
table output. So let's start here. And in
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this video, we're just going to highlight
some of the key features of multiple
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regression. In other videos we'll be
diving in in more detail into some of these
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other aspects, such as the ANOVA tables,
where these values come from, and so
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forth.
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So what we want to do in this video,
focusing on the key values, we're going to
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be looking at R-square, we're going to
be looking at the significance F, or the
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p-value under the ANOVA results, and
we're also going to be looking at the
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p-values under, I'll call this
coefficients here, for these three values,
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for our 3 predictors. OK so I put in
boldface type the key values that we're
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interested in in this video. And the
first is R-squared. R-squared indicates
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how well our three predictors, SAT score,
social support, and gender, did as a set
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in predicting college GPA.
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Did they do a good job, did they do a bad
job and so on. That's what R-squared is a
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measure of. And R-square ranges from 0 to 1.
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And the way we would interpret it, first of
all, in this example, R-square is equal to
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.50, and we could interpret it as
follows:
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taken as a set, the predictors SAT score,
social support, and gender, account for
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50% of the variance in college
GPA.
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So in other words when we have an
R-square what we do is we convert this
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to a percentage, in terms of
interpretation, and that indicates the
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amount of variance in the dependent
variable that was accounted for by the
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set of the independent variables. So
since our decimal is .50, we convert that
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to a percent. That tells us that our
predictors, SAT score, social support, and
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gender, collectively as a group, accounted
for 50% of the variance in
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college GPA. Now it's important to note
here that this doesn't mean that each of
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these three predictors accounted for
one-third, exactly, of the 50%
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as there are three of them. So
approximately SAT score accounted for
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17%, social support accounted
for 17%, and gender accounted
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for 17%. It does not mean
that whatsoever.
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All it means is that when all three of
those predictors are entered into this
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analysis or into this model, we can call
it, as a group, they account for fifty
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percent of the variance in college GPA.
Now it may be that SAT score accounts for
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45% of the 50, we don't
know yet at this point. All we know is a
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group, they account for 50%.
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How much variance we account for really
depends on the discipline that one is
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working in. It can vary quite a bit. In
the social sciences accounting for 50,
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60, or 70% of the variance, in most
applications, is pretty good. But in
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other areas, biology, chemistry, you may
expect R-Square of .99 if you
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expect some process to be replicated
almost identically. So it really depends
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on what you're working in, what area. But
in the work I do, 50% would be
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considered pretty good we're working
with predicting behavior in people.
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OK, next we have the ANOVA table. So the
ANOVA table tells us whether or not this
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R-squared is significantly greater than
0. So the ANOVA table is testing, overall,
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the three predictors, SAT score, social
support, and gender, do they predict
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college GPA significantly.
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