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

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

Why N minus two? Well cause there other things that we're estimating in the regression equation.

So again, here's the simple regression equation.

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.

Now it's about eighteen.

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

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

And that's true of any sample statistic.

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

Either way it's up to you.

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

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

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.

Right?

That's not a very compelling story.

We just had one predictor.

What are these numbers, what does this mean?

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

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

But for now, it's the square root of the sum to squares residual over N 2.

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

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

I just drew in magenta. The curve that I just drew purple and magenta.

In this case 2, 3, and 5 are the prime factors of 30.

I'll walk you through all of this and show you where this comes from in R.

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

So let's start the first segment.

Armed with these definitions, we are now ready to build the support vector machine.

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

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

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

The software will automatically give you.

I'm just showing you what's new.

That's the term that a single training example contributes to the overall objective function for logistic regression.

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.

In Laplace Smoothing, we use a different estimate.

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.

How strong is the relationship?

Tropic of Cancer

Tropic of Capricorn

KHTML Regression Testing Utility

And co variance will be an important concept as we move forward, especially into multiple regression and the analysis of variance.