[MUSIC] So let's go back to something a little bit more interesting, or hopefully more interesting, I guess more interesting if you're a statistician. Which is our regression model. And in this slide, I'm being very careful about the boldface notation, and you'll see that I'm very careful with this boldface notation throughout this course. So, it's meaningful. Okay, so when we have these multiple inputs, the simplest models we can think of is just assuming that our eye thoughts or vision is just a function directly of the inputs themselves. Not other functions of the inputs just taking number of square feet, number of bathrooms, number of bedrooms and plugging those directly entirely into out linear model. And again, we still have this noise term, epsilon i. So, just to be very explicit about the features associated with this simple hyperplane model, well, the first feature in our model is just this one, this constant feature. The second feature is the first input. For example, number of square feet. The third feature, indexing is weird, but third feature is our second input. For example, number of bathrooms. And this goes on and on till we get to our last input, which is the little d+1 feature. For example may be lot size. For generically, instead of just a simple hyperplane just like we talked about, instead of a single line, you can fit a polynomial. Well instead of just a hyperplane, we can fit some D-dimensional curve. This is capital D-dimensional curve. Because we're gonna assume that there's some capital D different features of this of these multiple inputs. So just as an example, maybe our zero feature is just that one constant term and that's pretty typical. That just shifts up and down where this curve leads in the space and maybe our first feature might be just our first input like in the hyperplane example which is quite fit. And the second feature, it could be the second input like in our hyperplane example, or could be some other function of any of the inputs. Maybe we wanna take log of the seventh input, which happens to be number of bedrooms, times just the number of bathrooms. So, in this case our second feature of the model is relating log number of bathrooms times number, log number of bedrooms times number of bathrooms to the output. And then we get all the way up to our capital D feature which is some function of any of our inputs to our regression model. So this is our generic multiple regression model with multiple features. And again we can take this big sum and represent it with this capita sigma notation. So this formula, Yi, equals the sum of Wj, Hj of X, plus Epsilon i, that is gonna be an equation that we're gonna use a lot. That's why I put this green box around the equation. This is an important equation that's gonna follow us for the rest of this module, and throughout this course. Okay, so just one more slide on notation. We're gonna use capital N to represent the number of observation we have. We're gonna use little d to represent the number of inputs, and we're gonna use capital D to represent the number of features we take of those inputs. [MUSIC]