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.

And that's true of any sample statistic.

Now it's about eighteen.

We have x of 1, 2, and 3 and y of 4, 7, and 13.

But again, now that we're in multiple regression, this is not the same as the correlation coefficient.

That's ordinary least squares, is the approach we'll take at first.

And the reason we did that is so that we could see exactly how the regression coefficients are estimated in a multiple regression.

This is when I put active years in the regression equation by itself and I use the scale function and R to get the standardized regression coefficient.

And then, we can have multiple predictors and multiple regression coefficients.

What are these numbers, what does this mean?

Than looking at either one alone. And, the other thing that this segment.

How strong is the relationship?

We can calculate it, for. A slope, of a regression line.

Again, the regression constant now is zero because we've standardized.

It gets even easier if we want to look at the standardized regression coefficient.

The software will automatically give you.

I'm just showing you what's new.

But for the sake of time, I didn't wanna go through that here.

Either way it's up to you.

To demonstrate matrix algebra. But remember, at the end we arrived at the correlation matrix.

So, we can just plug values in and get a predicted score.

If you go back and look at the scatter plot, you sort of see how we would get that value.

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

In the first two simple regression models, here are the results.

Then, we can apply that to the multiple regression example.

Aspect of R that's a little bit unique. In most software packages if you run a regression analysis it will just.

What I've done at the top of the slide to regression equation its'Y' equals the regression constant'B sub Zero' plus the regression co efficient for the predictor'P sub 1' times'X1'.'X1' in this case was age.

Uh, the regression coefficient B2 should no longer, uh, be significant if there is full mediation. It's possible though, that.

So let's start the first segment.

Okay?

Sounds a little scary, and this is a little more of a math lecture, than, most of the, the lectures I've given so far.

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.

So the main topic of this segment is just again estimation of regression coefficients in multiple regression.

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

So you'll see that the regression model is really just the equation.

Based on.

The.

And the columns correspond to individual predictors.

We, just ran a multiple regression analysis.

Another thing I did here is I standardized everything, just to make this a little easier on us.

That's not so interesting. It's just the predicted score on Y, when both X's are zero.

So that predictor X should no longer be a significant predictor of Y.

So now the regression constant is zero.

It says rise over run, and if we want to do this just by hand, we could do it with this, simple formula.

And what we see is that both extroversion and diversity of life experiences both of those regression coefficients are significant.