These are old faculty salaries.

We can just conclude that. This more complex model.

That's a bit unusual.

And in this example, I wanna use working memory capacity to predict, SAT.

I'll use'X' and'Y' as I've been for the predictor and outcome respectively.

So, in the last lecture we talked about simple regression.

Before, when we just did simple regression, that was our equation.

I am just going to show you two. So we have, our first one is uh, we can predict why from the mediator variable.

So, observe variables, and some people will call these manifest variables are represented by rectangles.

And we're looking at physical endurance in this, in this group of people.

That would be the x is here, it would the input features.

So, again the rows correspond to individual subjects, or cases.

So first, let's talk about just what regression is.

I can then do, model comparisons.

I'm going to go back to this example we used in mediation.

And then, we'll do multiple regression. And we're not gonna get crazy, we're just gonna put two predictors in.

We're still going to have an intercept, that's still the predicted score on Y when the X's are zero.

That has to be for us to just do mediation analysis in the first place.

The regression coefficient again it's always just for a one unit increase in x it's the predicted change in Y.

Just two simple regressions and model three is the multiple regression with both predictors in there.

We then post multiply that by the cross products.

So keep it simple. There's just four variables.

We're not saying anything about the causes of x.

However many people we have on our study, or however many cases, that's how many predicted scores we have.

We just came up with a better predictor. But we could do other things.

So I'll compare model one to model three and I'll compare model two to model three.

So in correlation, we simply had two variables, X and Y. Now, we're going to have still just one Y variable, and that's the outcome variable.

Those are the coefficients that go into the regression equation.

But for a lot of students this is helpful.

But we'll look at the correlation analysis and you'll see that that's the correlation coefficient.

And again, the take home message from this.

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

And in associated P value, that's the Null Hypothesis Significance testing part.

In this segment, and in this part of the course, I'll typically refer to Y as the outcome variable, and X as a predictor variable.

What is your model getting wrong?

Let's represent that in terms of a Venn diagram.

So this summarizing all the results of the regression analysis.

We can also refer to that as sums of squares for the model.

Again, I'm using Y as the outcome variable.

The betas they're just a K by one vector.

What we're doing now is we're going to add in as many predictors as we like.

So, I'll show you in that in the Venn Diagram in a moment.

But now imagine, what if we had not only the size of the house as a feature or as a variable of which to try to predict the price, but that we also knew the number of bedrooms, the number of house and the age of the home and years.

And this, this, this, this particular linear combination of predictors.

This is an example inaudible I've used inaudible .