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[Instructor] And so I wanna
show you how to do an F-test

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that tests the significance
of a number of variables,

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even when, individually,

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they don't pass a T-test for significance.

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So we'll go to the MLB dataset,

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and we're gonna run this
regression right here.

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So log salary and the regressors
are years, games per year,

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batting average, home runs
per year and RBIs per year.

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So we'll go to the data and
we run a linear regression,

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where L salary

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is the dependent and then
the independent is years,

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games per year, home runs per year,

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RBIs per year, and batting average.

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We don't need to save or
plot or anything like that.

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We're just gonna

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run it.

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And we find that

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our three,

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oh, oh, it didn't include
the batting average.

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Hold on.

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Let's run that again.

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Regression, linear, and then
we just need batting average

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in there too.

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I must not have added it.

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So games per year, home runs per year,

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years, RBIs per year, batting average.

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Let's make sure that those are there.

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Years, games per year, batting
average home runs per year,

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and RBIs per year on log salary.

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Yep, good.

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So now we go, boom.

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And we find that,

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again, our three batting stats
here are not significant.

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And take note of the sum
of squared residuals here.

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308.

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And we're gonna use that soon.

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So now we're gonna restrict our model,

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and take out those three,

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gonna take out home runs per year,

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RBIs per year and batting average.

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And we're just gonna run it
with these two regressors.

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And now what we see are
some of squared residuals

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has gone down as we expect because

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taking regressors out
makes it less significant,

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or makes it, decreases
the explanatory power.

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So we're gonna look at
this number now too,

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and we're gonna go to the F-stat.

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And note that it's gone from 183 to 198,

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and our queue is three.

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I'm gonna move it so you
can see this a bit better.

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And our F-stat is big, it is about eight,

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and eight is big.

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And as with any other F-stat,

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when you have

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a big F-stat,

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that is grounds to reject our null,

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and assume our null is not true,

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that these three batting
statistics jointly

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are all equal to zero.

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So again, our null is
that these three things

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that we took out.

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That's wrong.

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It's here.

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These three batting stats here,

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home runs, RBI and batting average.

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We make the assumption a
null, that they're all zero.

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We drop 'em out of the
model, we do an F-test,

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we get a huge F-stat and
well out in the tails,

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very unlikely that we would
get that if our null was true,

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we conclude our null is then not true.

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We reject our null and in this case,

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we would use this full
model and say that, jointly,

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home runs per year, RBIs per
year and the batting average,

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jointly, they matter even
though the P-value is not such

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that we would reject the
null for the full model.