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[Instructor] Now, I'm gonna show you how

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to estimate an equation,

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both for all the respondents

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and also how to split the sample

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into two groups so that
we could do a Chow test.

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So the first thing that I'm gonna do is

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to run this model right here where,

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this model estimates how much sleep

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that an individual gets
based on how much they work,

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their education, their age,

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the square of their age, and
whether they have young kids.

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So we go to the dataset, and
we do a linear regression,

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where sleep is the Dependent

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and then the Independents
are the total work, educ,

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age, age squared, and the
last one is young kids.

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So this looks at just these variables.

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And note that we're not
controlling here for gender,

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that we do have a dummy variable, male,

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but we're not going to use that yet.

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So we're gonna say OK.

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We look at the results, and we see that,

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again not a huge R-squared,
this is as before,

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that R-squared is the
regression divided by the total.

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It looks like it's .115.

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And then, here, we see that
the only significant value is,

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well, total work is and
education is, it's significant,

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just barely.

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So the more that you work
and the higher education

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that you have, the more that you sleep.

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So now, we're gonna say,
"Does gender matter?"

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Well, one of the ways
that we could do that is

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to just include the dummy variable male.

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So let's do that.

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Let's go back to our data
and run the same regression,

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except now we're just gonna
add male to it, and say OK.

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And when we scroll down,

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we see that male is pretty significant

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and with a strong positive beta.

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So being male means that you sleep more.

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So two ways that we could do this is to,

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if we think that the effect of
male on work, and education,

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and age, and all of these
other things is different

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for males and non-males, we
could create interaction terms.

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And I actually did that.

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So I'll show you what that looks like.

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The way that you would do that
is to transform and compute.

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I won't actually do it, but you could do,

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name it something, and then
call it the equals male times,

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and then say age, and name it that.

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I already did that.

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So you'll see that in the dataset,

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but that's how you would do
it or that's how I did it.

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But we're gonna get rid of this.

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So now, let's run it with
all of those interactions.

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So again, we're just gonna
run a linear regression.

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We're gonna leave all those things in.

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And now, we're also gonna add
all these interaction terms.

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And note that,

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we're gonna lose a bunch
of degrees of freedom

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by doing this.

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But let's see what we get and
let's look at the results.

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So again, we added a regressor
so R-squared goes up.

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And now, we see that, really,

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these are not very significant.

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We see male is no longer significant,

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but age and age squared are just barely.

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So work is, and male, young kid is barely.

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So the last thing I wanted
to do is to run a Chow test

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and we're gonna get rid
of all of these regressors

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that have male in them, but
we're gonna split the sample.

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So the way that you do that is,

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you go to Data, and we split our file,

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and we are gonna Compare Groups by male.

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So we put male there.

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We say OK.

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Make sure that,

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so this is the kind of
thing that you have to sort

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of turn on and off.

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So if you don't want,

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you need to go back there

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and just re-click Analyze All
Cases, which is the default.

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So now, what we're saying,

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do males and non-males sort of
experience sleep differently?

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Is our better model having
a separate set of betas

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for males and non-males?

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So here, we're gonna do the
same thing, a regression.

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Now, we need to get rid of all of these

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because these would be perfectly colinear

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because they would be all the males.

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It would just be a column of one.

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All the females for all of these,

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it would be a column of zeros.

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So we need to get rid of
those or the model won't work.

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And let's make sure that
we're back to where we wanted,

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total work, educ, age,
age squared, young kid.

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And note that we split the sample,

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so we're gonna see it as two groups now.

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And then, we say OK.

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And it did that.

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So you see that we could
get our own R-squared

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for both males, which are coded as 1,

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and non-males, which are coded as 0.

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Nice big F-stat.

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Each group gets its own R-squared.

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And then, also, each group
gets its own coefficients.

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So this is the non-male group here.

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Work is significant, and that's
it actually for both groups.

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Now, what we would do
is to run a Chow test.

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And I'm gonna go to my
Excel spreadsheet here.

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And I've gotta make sure
that you can see this.

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So we ran it as a pool.

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So we're looking at the
sum-of-squared residuals

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for all of these.

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And this number comes from,

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let's go up to the very
first one that we ran here,

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it's this, the number right here.

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So before we split the sample,

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so you could copy and paste that.

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And then, the other two numbers come

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from our last regression,
the residuals for each group.

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These are for non-males
and this is for male.

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So we take this number, and this number,

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and put it into our spreadsheet.

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And I did the math here,

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and the numerator and
the denominator here,

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the various degrees of freedom,

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and our F-stat is 2.12 and
the critical value is 1.77.

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And I think I can show
you that on the table,

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where it's six degrees of freedom

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and an infinite number
at the 0.10 is 1.6677.

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At 0.05, it's 2.21, it looks like.

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So it's very close.

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So since it's bigger, then,

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we would reject our null that males

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and non-males have the same coefficients.

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And we would say that running the model

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as two different groups
is the better model

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as a result of our Chow test.