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[Instructor] So we're going to look at

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a simple linear regression

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with a couple independent variables.

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So we're using the dataset
hprice or home price.

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So to do a regular linear regression,

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we go to the Analyze menu
to Regression and Linear.

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And you can see I already
have the dependent

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of the variable is the selling
price of the the homes.

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And the two independents are
the square feet of the homes

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and the number of bedrooms.

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So one thing that I want to show you

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is how to save the residuals
and the predicted value.

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So if you go to the Save menu,

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and you click on the
Unstandardized predicted,

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that's y-hat, and the
Unstandardized residuals,

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which we call u-hat,

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and hit Continue.

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And then it will give
you those values as well.

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So we hit OK

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and we get our results.

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So first of all, we see
R Squared is a fairly 63%

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of the variation is
explained by our regressors.

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And another way of seeing
that it is the ratio

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between this number and this number.

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So 63% is explained

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and about 37 is unexplained.

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You could also do the math that
this plus this equals this.

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So this is the explained sum of squares.

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This is the unexplained sum of squares.

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And this is the total sum of squares.

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You see that our overall
model is very significant

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with a p-value of less than 0.001

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and a nice big F stat.

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Just let's scroll down
and look at the results.

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So what we're seeing here

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is it's saying only the
square feet is significant.

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So for every additional square foot,

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looks like you gain about 12 cents

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or 13 cents,

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or yeah, and then, so
that's the results of that.

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The other thing that
I want to show you is,

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I'm going to make this small,

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and we now have two new variables.

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So Pre 1 is y-hat and Res 1 is u-hat.

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And you can see that price
equals y-hat plus u-hat.

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So this is the actual y,

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well, the actual value of it.

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This is the predicted value,

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and this is the residual.

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If you were to take the mean
of price and the mean of y-hat,

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they would be the same.

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And if you took either the
sum or the mean of u-hat,

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that would be, it would
both sum and mean to 0.

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So let's bring our data back up,

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and let's have another look and
let's do another regression.

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So I want to show you
that if add regressors,

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it's going to change the
value of all the betas.

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So we're going to do another one.

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We're going to go Regression, Linear.

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This time we're going to turn
off the y-hats and the u-hats.

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We really don't need them.

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And let's add a few more.

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So let's add lot size
and the assessed value.

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Yeah, lot size,

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and then whether or not it is a colonial.

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And I'm just picking out a few here

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just to show you what happens.

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So again, we hit OK.

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Note that when we add regressors,

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R Squared always gets bigger,
which is what happened.

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It's still highly significant.

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Our F stat is bigger.

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And note now that only the assess,

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so controlling for all
these other factors,

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only the assessed value.

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Note too, that if we take our beta

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and divide by our standard error,

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we always get our t.

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And that big t is small significance.

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So what we see here is explaining

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that the only one that matters here

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is the assessed value
based on the significance.

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So hopefully this all
makes sense and thank you.