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The goal of a basketball team
is similar to that of a baseball

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team, making the playoffs.

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So how many games
does a team need

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to win in order to
make the playoffs?

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Recall that in the lecture
we found this number

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by looking at a graph.

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Here in R, let's use
the table command

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to figure this out for the NBA.

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So that's just
table(NBA$W, NBA$Playoffs).

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So our table pops up.

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Let's scroll to the top
so we see what's going on.

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OK so as we typed in, we've
got the number of wins

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here as the rows.

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And 0 if a team didn't make
the playoffs, 1 if a team did

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make the playoffs
in the columns.

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So for all of our
data, for example,

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consider all the times
that a team won 17 games.

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So this happened
11 times in total.

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And all 11 times the teams
didn't make it to the playoffs

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when they won 17 games.

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Let's scroll down and look
at a much higher number

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for contrast.

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For example, 61 wins.

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If a team 61 games then 10
of those times they made it

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to the playoffs, and
0 times they didn't.

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So it seems like
if you win 61 games

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you are definitely going
to make it to the playoffs.

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But I'm sure we can find
a much better threshold.

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Let's take a look at the table,
say around the middle section.

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OK, so here we can
see that a team who

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wins say about 35 games
or fewer almost never

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makes it to the playoffs.

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We see a lot of 0s and 1s
in this column up until 35.

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After 35 we start seeing
some numbers over here.

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So teams are starting to
make it to the playoffs.

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And if we scroll down, we
see that after about 45 wins,

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teams almost always
make it to the playoffs.

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We see very few 1s and 0s in
the category of not making it.

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So it seems like
a good goal would

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be to try to win about 42 games.

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If a team can win
about 42 games then

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they have a very good chance
of making it to the playoffs.

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So in basketball, games are
won by scoring more points

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than the other team.

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Can we use the difference
between points scored

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and points allowed throughout
the regular season in order

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to predict the number of
games that a team will win?

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Let's give it a try.

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First we add a variable that is
the difference between points

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scored and points allowed.

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Let's call this NBA$PTSdiff.

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And that's just the difference
between points scored,

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which is points, and
points allowed, which

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is opponent's points.

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All right, so we've
created a variable.

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Let's first make a
scatter plot to see

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if it looks like there's
a linear relationship

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between the number of
wins that a team wins

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and the point difference.

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So this is easy to do just
with the Plot command.

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NBA$PTSdiff and NBA$W.

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So our graph pops
up and it looks

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like there's an incredibly
strong linear relationship

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between these two variables.

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So it seems like
linear regression

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is going to be a good way
to predict how many wins

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a team will have given
the point difference.

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Let's try to verify this.

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So we're going to
have points diff

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as our independent
variable in our regression,

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and W for wins as the
dependent variable.

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So let's call this WinsReg.

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And we just use the lm command
as before progressing w

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on the points diff and
using the NBA data.

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All right, so we've
created our regression.

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Let's take a look
at the summary.

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OK, so the first
thing that we notice

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is that we've got very
significant variables

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over here.

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And an R squared of
0.9423, which is very high.

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And this is verifying
the scatter plot

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we saw before that there's a
very strong linear relationship

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between the wins and
the points difference.

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So let's write
down the regression

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equation that we found.

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We see that the number of
wins, W, is equal to 41.

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That's coming from the
coefficient estimate

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for the intercept.

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Plus 0.0326*PTSdiff.

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And that 0.0326 is coming
from the coefficient estimate

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for points difference.

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So we saw earlier with
the table that a team

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would want to win
about at least 42 games

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in order to have a good chance
of making it to the playoffs.

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So what does this mean in terms
of their points difference?

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Well, we can calculate it.

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If we want this to be
greater than or equal to 42,

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that means that the
points difference

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would need to be greater
than or equal to 42 minus 41

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divided by 0.0326.

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So if we actually
do that calculation,

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we see that this
is equal to 30.67.

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So we need to score at
least 31 more points

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than we allow in order
to win at least 42 games.