[MUSIC] So that's our discussion on high leverage
points and influential observations, but I wanna think about whether
if you go back to our data. I think it's easier to discuss this,
looking at our observations. Here what we see on the top part, there's a collection of five
different observations. So these are five different
towns that have very high value compared to what you see for
all of the other towns. So question is even though these
points aren't high leverage points, because they are in this typical x range,
Are they influential observations? Meaning if we remove these observations
will the fit change very much. So, not let's just see what
happens in this data set. Okay, so we're gonna remove these, what
we're saying here we're gonna remove these high value outlier neighborhoods and
redo our analysis. So what we're doing here is
we're creating a data set, which I'm gonna call sales underscore
no high end for no high end towns. Which takes our data set,
still with center city removed, and just filters out all the towns that have
average values greater than $350,000. Okay, so let's fit this new data set. And again, let's compare coefficients. So I'm gonna compare the coefficients
to our fit with Center City removed to the fit that further
removes these high end houses, or sorry, these high end towns. And what you see is, yeah, there is some
influence on The estimated coefficient. But not nearly as significant as what
we saw by simply removing center city. So in this case,
we've removed five observations out of a total of 97 observations. And we see that impact of crime
rate on predicted decrease and house value changes by a couple hundred
dollars, but not by the amount that we saw by just removing that one center
city observation earlier on. So this shows that high leverage
points can be much more likely to be influential observations for
just small deviations from the data set. Then outline observations that
are within our x, our typical x range. Okay, so
the summary of all of this analysis and discussion is the fact that when you have
your data, and you're making some fit and making predictions or
interpreting the coefficients. It's really, really important
to do some data analysis to do visualizations of your data or
different checks for whether you have these high leverage
points or these outline observations and checking whether they might potentially
be these influential observations. Because that can dramatically
change how you're interpreting or what you're predicting based
on your estimated fit. [MUSIC]