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ALLISON O'HAIR:
--previous video, we

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used data in linear
regression to show

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that if a team
scores at least 135

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more runs than their opponent
throughout the regular season,

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then we predict that that team
will win at least 95 games

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and make the playoffs.

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This means that we need to
know how many runs a team will

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score, which we will show
can be predicted using

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batting statistics, and how
many runs a team will allow,

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which we will show can be
predicted using fielding

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and pitching statistics.

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Let's start by creating
a linear regression

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model to predict runs scored.

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The Oakland A's are interested
in answering the question,

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how does a team score more runs?

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They discovered that
two baseball statistics

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were significantly more
important than anything else.

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These were on-base
percentage, or OBP,

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which is the percentage
of time a player gets

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on base, including walks,
and slugging percentage,

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or SLG, which measures how
far a player gets around

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the bases on his turn and
measures the power of a hitter.

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Most teams and
people in baseball

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focused instead on
batting average, or BA,

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which measures how
often a hitter gets

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on base by hitting the ball.

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This focuses on hits
instead of walks.

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The Oakland A's claimed
that on-base percentage

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was the most important.

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Slugging percentage
was important.

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And batting average
was overvalued.

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Let's see if we can use
linear regression in R

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to verify which
baseball statistics are

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more important to predict runs.

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In the previous video, we
created her dataset in R

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and called it Moneyball.

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Let's take a look at the
structure of our data again.

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Our dataset includes
many variables including

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runs scored, or RS,
on-base percentage, OBP,

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slugging percentage, SLG,
and batting average, BA.

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We want to see if we can use
linear regression to predict

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runs scored using the
three hitting statistics,

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on-base percentage, slugging
percentage, and batting

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average.

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So let's build a linear
regression equation using

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the LM function to
predict runs scored

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using the independent
variables OBP, SLG, and BA.

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Our dataset is Moneyball.

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If we look at the summary
of our regression equation,

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we can see that all of
our independent variables

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are highly significant.

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And our R squared is 0.93.

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If we look at our
coefficients, we

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see that the coefficient for
batting average is negative.

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This says that all other
things being equal,

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a team with a higher batting
average will score fewer runs.

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But this is a bit
counterintuitive.

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What's going on here is a
case of multi-collinearity.

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These three hitting statistics
are highly correlated.

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So it's hard to
interpret our model.

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Let's see if we can remove
batting average, the variable

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with the negative coefficient
and the least significance,

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to see if we can improve the
interpretability of our model.

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So let's rerun our
regression equation

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without the variable BA.

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If we look at the summary of
our new regression equation,

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we can see that our variables
are again highly significant.

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The coefficients
are all positive,

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as we would expect them to be.

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And our R squared is now 0.9296,
or about the same as before.

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So this model is simpler
with one fewer variable,

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but has about the same
predictive ability

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as a three variable model.

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You can experiment
and see that if we

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had taken out on-base percentage
or slugging percentage

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instead of batting
average, our R squared

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would have gone down more.

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If we look at the
coefficients, we

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can see that the coefficient
for on-base percentage

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is significantly higher
than the coefficient

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for slugging percentage.

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Since these variables are
on about the same scale,

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this tells us that on-base
percentage is worth more

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than slugging percentage.

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So using linear regression we're
able to verify the claims made

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in Moneyball that batting
average is overvalued,

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on-base percentage is the
most important, and slugging

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percentage is important.

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We can create a
very similar model

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to predict runs allowed
or opponent runs.

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This model uses pitching
statistics, opponents

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on-base percentage, or OOBP, and
opponents slugging percentage,

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or OSLG.

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The statistics are
computed in the same way

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as on-base percentage
and slugging percentage,

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but use the actions of
the opposing batters

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against our team's
pitcher and fielders.

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Using our dataset in R, we can
build a linear regression model

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to predict runs allowed using
opponents on-base percentage

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and opponents
slugging percentage.

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This is, again, a very strong
model with an R squared

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value of 0.91.

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And both variables
are significant.

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In the next video,
we'll show how

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we can apply these models
to predict whether or not

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a team will make the playoffs.