Well, we have to add in a moderator variable and a, what I'm going to call a product term.

Same exact structure using the OM function and the summary function.

Either way it's up to you.

So again, minimize sums of squares residuals, just like in simple regression.

That's what we have, we have three regression equations.

Down here big prediction error. For the rest of them, not so big, okay.

And here it is with active years abou.34. Let me just go back.

And, as you can see, I could extend this out to K predictors.

But for now I'll just go through this quickly.

And today, I'd like to introduce you to multiple regression.

little more sense.

So we have X, Z and the product all predicting one.

So first what we're gonna do is just. Run a simple regression.

Those are the residuals for those individual points.

And secondly we can predict the mediate, mediator variable from X. So the first regression equation, what I'm doing is just picking off this piece.

So here's a quick quiz for you.

The official answer,

It can be predictive from some constant plus some predictor variable x times the regression coefficient for x plus error.

Tropic of Cancer

Tropic of Capricorn

KHTML Regression Testing Utility

So, let's move to the equation.

So, happiness is 2.19 plus 0.28 times whatever somebody scores on extraversion.

From a wedding.

Yes yes it's a recurring expression.

So let's start the first segment.

So, sometimes we use linear regression with tens or hundreds thousands of features, but if you use the vectorized implementation of linear regression, usually that will run much faster than if you had say your old for loop that was you know, updating theta 0 then theta 1 then theta 2 yourself.

Hi, welcome back.

At first we've covered multiple regression analysis sort of conceptually, and how to interpret regression coefficients when there are multiple predictors in our regression equation.

And here's the output of, that analysis.

That's the model. That's what I, that's what I mean when I say model.

Regression testing output

Regression Testing Status

GUI for the khtml regression tester

Now let's look at the simple regression with active years in the equation.

And, it's necessary to understand how matrix algebra works to understand how these regression coefficients are estimated sort of simultaneously, in one equation.

The P value is a direct, is directly a function of the T value.

letters and then, we can look at the path models again.

So at least the points that we tried out seem to validate this solution that we got.

lectures back that if X and Y are correlated then we can predict Y from X and here's the simple regression equation.

So, let's dive into the first segment. This is Introduction to Regression.

We'll come back to that again in multiple regression, and in lecture nine in R. And then, the importance of this distinction between unstandardi zed and standardized regression coefficients.

Against my doctors' and family's wishes,

No formal response yet from India.

So, it, it went from just, you know, a nice, positive slope to just slightly less than, uh where it started.