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Okay, so, let's talk about this problem
of predicting the value of a house.

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So, this is a very important problem,
at least in the United States.

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It's estimated that household wealth
is nearly 50% invested in real estate.

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So, this is clearly important.

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Both to consumers, individuals,
as well as policy makers.

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Okay, so I'm here and
I wanna sell my house.

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I have this nice, big, lime green house,
but I don't know how much to list it for.

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So I'm not sure what value my house has,
and so

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how do I think about estimating
the value of the house?

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Well, it might make sense
that what I do is I look

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at other recent sales that have
occurred in my neighborhood.

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So I look locally,
at the region around me, and

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I say how much are the other houses sold
for and what do those houses look like?

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So what I'm gonna do is
I'm gonna record for

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each one of these recent sales
what was the sales price?

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And also, what was the size
of the house that was sold?

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I'm gonna say that that's what signifies
whether that house is similar to mine

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or not.

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Okay, so being a statistician, I'm gonna
take all these observations I had and

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I'm gonna make a plot of them.

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So in the US at least, the size of
the house is measured by square feet.

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So that's gonna be my x axis.

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And then my y axis is gonna be
the sales price of the house.

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Okay, so that's my y variable and

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each one of these points represents
some individual house sale.

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So here this is one previous
house sale in my neighborhood.

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And just to introduce a little bit
of terminology here when we're

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talking about regression,
people often refer to x, this variable x,

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as being the feature,
that's the terminology we've been using.

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People also talk about it being
the covariate or the predictor,

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and in some cases,
it's called the independent variable.

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And then our observation
y is as I've just said,

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I tend to refer to it as an observation.

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People also call it a response or
the dependent variable.

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Okay, so

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the question is how am I gonna use these
observations to estimate my house value?

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Well I might look at
how big my house is and

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look for
other sales of houses of that size.

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Well, most likely there
are gonna be exactly zero house

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sales of other houses that had exactly
the same square footage as my house.

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Okay, so
I say well I can't use this approach.

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I'm gonna be a little
bit more flexible and

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I'm gonna look at some neighborhood, not
geographic neighborhood some little range

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of square footage around my
actual square footage here.

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So I'm going to say okay let's look
at all house sales that were for

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houses within this range
of square footage.

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But even with that approach,
in this case for example,

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I only have two house sales that
I'm gonna base my estimate off of.

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So I don't really feel very
comfortable with that.

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And what I'm actually doing here is I'm
throwing out all these other observations

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as if they had nothing to do
with the value of my house.

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And the question is, is that reasonable?

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Do we actually believe that
there's actually no information

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in these other observations?

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Well, when I look at this data and when I
think about data I like to leverage all

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the information that I can to
come up with good predictions.