In this video I want to show you how to
calculate R squared.
Now here I have an example with three
variables. If I'm trying to find R squared
for just two variables, one way we can go
about doing that is just running a
correlation. Let me show you what I mean
here. So if I go to analyze and then
correlate and then bivariate let's say
we want R square between SAT and
college GPA, so I'll move those two over and
then I'll click OK. Now this gives me not
R squared but it gives me r so the
correlation between SAT and college GPA
is .65 and that is in fact
significant at the .01 level. Now
that's r; so if I want R squared what I
can do is just simply square that. So .65
and then squared here is point .4225 so R
squared here is .42. Now
another way to do this is that if I have
more than two variables that I'm working
with, or if I just don't feel like
calculating R squared manually by
squaring r, what I can do is I can go
to analyze and then regression and
select linear. Now I have to decide here
what my dependent variable is, or what it
is that I'm trying to predict. Now SAT was
measured in high school and college GPA,
as the variable sounds, is GPA in college
during the first year, after one year
college. So it makes sense that SAT
would predict college GPA. So we'll put
the thing we're trying to predict in the
dependent box and then we'll put SAT and
the independent. OK let's go ahead and click OK. Now
if you recall from our earlier analysis, when
we squared that correlation we got
.4225.
So R square was .4225. And here
to find R squared we want to go to the
Model Summary table and
here's r this is the correlation
.65, we saw that in our previous
analysis.
And then R squared is right next to r,
notice .422. And that's exactly
what we got before within rounding error.
So we can run regression to calculate R
squared. Now in case you're not familiar
with what R squared is, it indicates the
amount of variance in the dependent
variable that is accounted for or
explained by the independent variable. So
since we're using SAT here to predict
college GPA,
What that means is. if we know a person's
SAT score, we can account for I can
convert this to a percentage, about
42% of the variance in
college GPA, which is pretty good.
OK so that's what R squared means, it's a
measure of how much we explained in one
variable using one or more other
variables. And one last thing here, if you
want to calculate R squared and you have
more than two variables at once, then you
really need to use this regression
approach here to find that. So let's say
we want to use both SAT and social
support to predict college GPA and we're
doing this two try and get our R square. So we're doing this to try and
see how well, overall, these two
predictors combined how much of college
GPA they account for or explain, which you
may recall is what R square really means.
How much of the variance did we account
for in a given variable using one or
more other variables. So go ahead and
click OK. And then here notice our R squared
increased, and it will when we add
another predictor in almost all
cases. And here our R squared is .511.
So using social support and SAT we
can account for about 51%
of the variance in college. So the
GPA in college after their first year.
OK that's it. Thanks for watching.