This, that's the beauty of multiple regression and building a model with multiple predictors, is we can account for more variance with this set of predictors.

That's how we get predicted scores on Y, from a set of values on, set of predictors, X1, X2, and X3.

The model R squared will take into account the entire proportion of var, of variants that's shared with the entire set of predictors.

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

And the columns correspond to individual predictors.

Is that. Putting these two, predictors together.

And we'll predict the outcome variable on the basis of multiple predictors.

With both predictors in it. Is doing better.

And we're just gonna look at two predictors.

We could try and come up with more reliable predictors or just add in more predictors to the model. So we did that.

C. Again, the model R squared, will be the entire area that's overlapping between Y and the set of predictors that are in the model at that step.

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And to see if there's moderation, we just take the product of those two predictors.

So if you put in a lot of predictors, the , eventually they should all suffer.

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

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What we're doing is we're finding the best linear combination of these predictors to explain the outcome.

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There's a new set of values, a new set of things people value.

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

Now, we can get a better correlation because we're adding in multiple predictors.

Now, that doesn't mean that these individual predictors are correlated that strongly, alright?

If you can start to spot patterns in your residuals, then you can start to think about how you can improve your predictors, or you can think of other predictors to add to the regression equation.

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And then, this idea of doing things sort of sequentially or just putting all of the predictors into an equation all at once

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To get a sense for how much each one of these predictors by themselves would explain in faculty salary.

Sometimes it's also called the validation set, instead of cross validation set.

Today, we'll see how multiple regression, multiple regression works where we have multiple predictors.

Now, let's look at what happens when I put both predictors in the model.