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

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

That's the way to interpret the regression coefficients when there are multiple predictors in the model.

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

We, just ran a multiple regression analysis.

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.

And what's new is doing multiple regression analysis, asking for standardized regression coefficients.

How do we do that in multiple regression?

Particularly when we do things like multiple regression.

That's the beauty of doing multiple regression analysis.

We're just gonna do a multiple regression analysis.

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.

You can do a multiple regression analysis by hand.

Well, let's see that in a multiple regression analysis.

And today, I'd like to introduce you to multiple regression.

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

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

To see how we get those. Multiple, regression coefficients estimated.

But first lets just start with basic multiple regression analysis.

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

We're in the second segment of lecture nine on multiple regression analyses in R. So in the last segment we ran one multiple regression analysis, and in this segment what I'd like to do is run it again, but now get standardized regression coefficients, and compare the results of multiple models, and we'll do that through model comparison.

And today we're going to do multiple regression analysis in R.

You'll have to write a script that does multiple regression analysis.

For such situations there is a model called logistic regression, which uses a slightly more complicated model than linear regression, which goes as follows .

Regression co efficients, in a multiple regression, using matrix algebra and last week, you didn't even know matrix algebra.

So in the first segment, we'll run a first multiple regression analysis.

last segment demonstrating the use of multiple regression analysis to test mediation.

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

So, a better approach would be to have multiple models, multiple regression models, and test them against each other.

In the last few lectures we have covered in detail multiple regression analysis.

So, here, to summarize is the final script for that multiple regression analysis.

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.

We'll do a multiple regression analysis again just like the last segment, but we'll get standardized regression coefficients, and that's real easy.

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

In the previous video, we talked about the form of the hypothesis for linear regression with multiple features or with multiple variables.

This model is called linear regression or this, for example, is actually linear regression with one variable, with the variable being x.

lecture eight, you'll see in multiple regression, it gets a little more difficult than that.

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

Because what these estimates represent, and this is the most important thing to take home from multiple regression analysis, is remember how to interpret these regression coefficients when there are multiple predictors in the equation.

In particular let's talk about how to use gradient descent for linear regression with multiple features.

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

So, I'll start out in the first segment just by introducing you to the multiple regression equation, and I'll present an example so you can get a flavor for how to interpret multiple regression coefficients in one example.

And then, I'll talk about the difference between what I'll call a standard multiple regression, where we enter all predictors in together, and what I call a sequential multiple regression, where we enter predictors in a particular order.

So, to avoid confusion because we have multiple regression equations going into this model, let's just label the paths and this is again is a common technique in path analysis and modelling.