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So that's our discussion on high leverage
points and influential observations,

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but I wanna think about whether
if you go back to our data.

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I think it's easier to discuss this,
looking at our observations.

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Here what we see on the top part,

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there's a collection of five
different observations.

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So these are five different
towns that have very high value

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compared to what you see for
all of the other towns.

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So question is even though these
points aren't high leverage points,

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because they are in this typical x range,
Are they influential observations?

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Meaning if we remove these observations
will the fit change very much.

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So, not let's just see what
happens in this data set.

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Okay, so we're gonna remove these, what
we're saying here we're gonna remove these

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high value outlier neighborhoods and
redo our analysis.

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So what we're doing here is
we're creating a data set,

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which I'm gonna call sales underscore
no high end for no high end towns.

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Which takes our data set,
still with center city removed, and

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just filters out all the towns that have
average values greater than $350,000.

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Okay, so let's fit this new data set.

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And again, let's compare coefficients.

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So I'm gonna compare the coefficients
to our fit with Center City removed

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to the fit that further
removes these high end houses,

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or sorry, these high end towns.

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And what you see is, yeah, there is some
influence on The estimated coefficient.

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But not nearly as significant as what
we saw by simply removing center city.

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So in this case,
we've removed five observations

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out of a total of 97 observations.

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And we see that impact of crime
rate on predicted decrease and

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house value changes by a couple hundred
dollars, but not by the amount that we saw

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by just removing that one center
city observation earlier on.

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So this shows that high leverage
points can be much more

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likely to be influential observations for
just small deviations from the data set.

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Then outline observations that
are within our x, our typical x range.

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Okay, so
the summary of all of this analysis and

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discussion is the fact that when you have
your data, and you're making some fit and

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making predictions or
interpreting the coefficients.

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It's really, really important
to do some data analysis to do

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visualizations of your data or
different checks for

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whether you have these high leverage
points or these outline observations and

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checking whether they might potentially
be these influential observations.

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Because that can dramatically
change how you're interpreting or

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what you're predicting based
on your estimated fit.

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