Okay, so, let's talk about this problem
of predicting the value of a house. So, this is a very important problem,
at least in the United States. It's estimated that household wealth
is nearly 50% invested in real estate. So, this is clearly important. Both to consumers, individuals,
as well as policy makers. Okay, so I'm here and
I wanna sell my house. I have this nice, big, lime green house,
but I don't know how much to list it for. So I'm not sure what value my house has,
and so how do I think about estimating
the value of the house? Well, it might make sense
that what I do is I look at other recent sales that have
occurred in my neighborhood. So I look locally,
at the region around me, and I say how much are the other houses sold
for and what do those houses look like? So what I'm gonna do is
I'm gonna record for each one of these recent sales
what was the sales price? And also, what was the size
of the house that was sold? I'm gonna say that that's what signifies
whether that house is similar to mine or not. Okay, so being a statistician, I'm gonna
take all these observations I had and I'm gonna make a plot of them. So in the US at least, the size of
the house is measured by square feet. So that's gonna be my x axis. And then my y axis is gonna be
the sales price of the house. Okay, so that's my y variable and each one of these points represents
some individual house sale. So here this is one previous
house sale in my neighborhood. And just to introduce a little bit
of terminology here when we're talking about regression,
people often refer to x, this variable x, as being the feature,
that's the terminology we've been using. People also talk about it being
the covariate or the predictor, and in some cases,
it's called the independent variable. And then our observation
y is as I've just said, I tend to refer to it as an observation. People also call it a response or
the dependent variable. Okay, so the question is how am I gonna use these
observations to estimate my house value? Well I might look at
how big my house is and look for
other sales of houses of that size. Well, most likely there
are gonna be exactly zero house sales of other houses that had exactly
the same square footage as my house. Okay, so
I say well I can't use this approach. I'm gonna be a little
bit more flexible and I'm gonna look at some neighborhood, not
geographic neighborhood some little range of square footage around my
actual square footage here. So I'm going to say okay let's look
at all house sales that were for houses within this range
of square footage. But even with that approach,
in this case for example, I only have two house sales that
I'm gonna base my estimate off of. So I don't really feel very
comfortable with that. And what I'm actually doing here is I'm
throwing out all these other observations as if they had nothing to do
with the value of my house. And the question is, is that reasonable? Do we actually believe that
there's actually no information in these other observations? Well, when I look at this data and when I
think about data I like to leverage all the information that I can to
come up with good predictions.