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[MUSIC]

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Okay, so now,

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let's talk about how we're gonna interpret
the coefficients of our fitted line.

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And let's start by talking about W-hat 0,
our estimated intercept.

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So, that's this point right here, this
green star, and what does that represent?

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Well, it's the predicted value
of a house with 0 square feet.

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So, we can think of that just as land,

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because we have that Y-hat
is = W-hat 0 when X=0.

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So, when there's no square feet,
we have that our predicted

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house value is exactly equal to W-hat 0.

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But I'll say that in general,
this is not normally that meaningful.

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In many scenarios, you don't really
think of having no input and

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having the output have
some meaningful value.

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And actually in our case,
if you go back and look at the number,

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we had that our intercept was -44,850.

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So, it's saying that land you should
actually as the seller be giving

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the buyer money,
to take that land off your hands.

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But remember that our
dataset's really noisy,

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it's not a perfect model
of what's going on.

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So, of course, we have to think
about interpreting our parameters

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in the context of what we've
included in our model.

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Okay, we'll talk more about
that in the next module.

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But, I also want to talk about W-hat
1 which is our estimated slope.

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And that tends to have a bit
more meaning associated with it.

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So, the estimated slope, I'm highlighting
with this green triangle here,

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saying that per unit change,
in our inputs, so for

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1 unit, so 1 square foot,

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what's our predicted change
in the value of the house.

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So, for example,
let's say I'm looking at estimating

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the value of a house
with 1001 square feet.

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And I want to look at the difference
relative to the estimated value of a house

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with just 1000 square feet.

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Well, what is this, this is equal to,
if I look at the first term

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estimating a house with 1,001 square feet,
how would I estimate that?

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I would take W-hat 0,

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+ W-hat 1 * 1,001 square feet.

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And then, I'm gonna subtract for

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the second term I have it's
estimated value is again

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W-hat 0 + W-hat 1 * 1,000 square feet.

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And these W-hat 0's are gonna cancel.

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And the difference between
these numbers is just 1.

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So, this will just be W-hat 1.

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So again,

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W-hat 1 represents

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the predicted change

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in the output per unit

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change in the input.

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Okay, so that's how we're
going to interpret W-hat 1.

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But one thing I want to make very,

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very clear is that
the magnitude of this slope,

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depends both on the units of our input,
and on the units of our output.

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So, in this case, the slope,
the units of slope,

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are dollars per square feet.

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And so, if I gave you a house that
was measured in some other unit,

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then this coefficient would no
longer be appropriate for that.

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So, let's make this
a little bit more explicit.

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So now that we know that there
are units attached to these numbers,

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I'm gonna put these in, so
our intercept has units just dollars.

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So, let me be clear what I'm
actually highlighting here.

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The intercept has units dollars, and the
slope has units dollars per square feet.

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And when I went through and

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did my calculation of predicting the value
of a house with a given square feet,

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if I actually put in these units,
I see that everything works out.

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Here I have dollars,
here I have dollars per square feet, and

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then I'm multiplying by square feet.

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So when I multiply these two
things the resulting units of

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this is just gonna be dollars, so the end
result is something in terms of dollars.

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That's great.

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And likewise, when I use the equation
in reverse, I have dollars,

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dollars divided by
dollars per square feet,

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and I end up with something
that's in square feet.

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So, I'll just say units work out,

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which is great.

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But what if the house was measured in
square meters instead of square feet,

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well, clearly I can't just
plug into that equation, and

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likewise what if the price was measured
in Chinese Yuan instead of in US Dollars.

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Again, can't just plug into that equation,
so when I think about magnitude,

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it only has meaning in terms of the units
that I use for my input and output.

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