The first thing to understand is the regression equation and the different components of the regression equation.

So again, here's the simple regression equation.

That regression, or that regression equation, we could run it in R, and get the regression equation. We'll, we'll do that in, in lecture nine.

So we have our simple regression equation. Here.

And that's what regression equation is showing us.

With this last regression equation. M should be significant.

We'll just put one predictor in the regression equation.

So, I'll just summarize the multiple regression equation as follows.

Those are the coefficients that go into the regression equation.

Here I've, I've summarized the regression equation at the top.

Now that we're in regression I want to present this with respect to the unstandardized regression coefficient, B, in the regression equation.

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

It was just that equation with one regression coefficient in it.

Here's our regression equation. We have the intercept and the slope.

So, here's a simple regression equation, or, a simple path model.

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

So, that whole regression equation is represented in this simple path model.

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

Consider the regression coefficient for the equation y bx a and the correlation coefficient.

Up to this point, I've been saying that one regression equation is one model.

And with the second regression equation, what I'm showing you is picking off this piece.

In a sequential regression, we as the researchers or as the experimenters, we will decide how to enter the predictor's into the regression equation.

So then in the third segment, we'll take a closer look again at the regression equation and talk about how those regression coefficients are estimated.

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

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, if you run this in R, this is the regression equation that you get out, and

The regression equation is just the model. You'll see that our, our models will get more complex.

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.

So to wrap up this segment, the most important things to take away are what is the regression equation, it's just at this point and simple regression, it's just the equation for a line, we have intercept and slope.

linear regression.

logistic regression.

logistic regression.

And again, remember that in the simple regression equation, B1 is the slope relating X to Y. But beware.

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Regression is continuous.

Then we walked through the matrix algebra that allowed us to estimate the regression coefficients with multiple predictors in one equation.

Here's the regression equation from R. It looks a little weird, doesn't it? 282 (1044)X. Why is that so weird?

So in the last lecture, we walked through multiple regression, the regression equation, how the regression coefficients are estimated, and I showed you a little bit of matrix algebra so you could see how they're calculated if you wanted to do that by hand.

So you may see the regression equation presented, if you just Google regression, if you get the Wikipedia look up regression you may see just the formula for a line which is Y m bX where m is the intercept, b is the slope.

The important concepts to take away from this segment are, again, understanding the equation and the components of the equation, how to interpret the, both the unstandardized and the standarized regression coefficients.

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