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.