[MUSIC] Now we're gonna discuss an important issue
of the influence of what are called high leverage points. And these are points that can be
considered influential observations. But to have this discussion, I think it's
really useful to just look at some data. So to start with, let's fire up
graphlab and then let's load some data. And for this,
we're gonna load our data into our SFrame. And I'm gonna assume that you guys are
familiar with a lot of what I'm doing here from the foundations course where
we went through pretty slowly, a lot of the graphlab related
code that we're seeing here. And I wanna emphasize that throughout
this course you'll actually learn how to implement these methods, but for
the sake of this demo and other demos in this course, we're gonna just use
graphlab Create to keep the discussion at a much higher level about the concepts
that we're trying to convey. Okay, so the data set that we're
looking at here In this example is a Philadelphia housing data set,
where in particular, our data set consists of
the average house price in a whole collection of towns in
the greater Philadelphia region. And we also have information about
crime rates in each one of these towns. As well as how far that town
is from Center City and Center City is the downtown
region of Philadelphia. So, let's start analyzing this data. And to do this, what we're going to
start with is just making a scatter plot of what's the relationship between average
house sales prices, and crime rates. Okay, so here we are, we're gonna do just a .show command to show a scatter plot of, on the x axis we have crime rate. And each one of these little
blue circles or cyan, light blue circles is
a different town in our dataset. And we have a total of 98 different towns. And on the y axis what we have is
the average house value in that town. Okay. And so, from this you can see that
there's some relationship between our crime rate and our house sales price. In particular, we see that for
towns that have lower crime rates, they tend to have higher house values and
vice versa. So that makes a lot of sense. So let's try and actually fit
a relationship between crime rate and house price. So we're gonna go through and fit this
regression model doing our standard dot linear regression command,
taking out target, or our output,
to be that house price in that region, and taking our features to just be a single
feature, which is crime rate in that town. Okay, so now what we've done is we've
output this to something called crime underscore model and
now let's look at what this fit resulted. So I just Import our map plot library to start making some plots here,
and what we're gonna show is
we're gonna show a plot of the observations that we showed
before as well as our fitted line. So this is our fitted simple linear
regression model is this green line. So these are our predictions
of house values for each crime rate going from 0 up to somewhere around,
I don't know, 360 or something like this. So we do see a trend where house value decreases as crime increases,
the slope of this line is negative. But one thing that we pretty immediately
see is there's an observation out here, there's this blue dot which has
extremely high crime rates but the house value is I mean it's low-ish,
but it's not as low as the house values in other regions
that have significantly lower crime rates. And we see that our line, our fitted line, is getting pulled towards this
observation that's all the way out here. So it's being,
at least it looks like from the picture, being heavily influenced
by this one observation. And that's really,
really far on the x axis.