Then we'll talk about the idea of estimation of regression coefficients.

Just like the sum of square, sum of deviation squares. So we'll square them.

X and Y, we are still assuming that X and Y are both continuous, both normal and there's a linear association between them and we will move beyond those assumptions

How does R, or how if we want to calculat e this by hand, how do we come up with these estimates?

And that would give us the sum of squared residuals.

What we're going to do is apply gradient descent to minimize our squared error cost function.

So, we wanna minimize the difference between the observed scores on Y and predicted scores on Y, predicted by the model.

Again his average 22.7, standard deviation of 9.6, and variance of 92.

Now if I want to take this objective function and multiply it by 10, so here my minimization problem is minimum of u of 10, u minus 5 squared plus 10.

So we think of Ci as picking the cluster centroid with the smallest squared distance to my training example Xi.

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

It actually changes the way people think.

In the next video, we're going to take the function J, and set that back to be exactly linear regression's cost function.

For this data set an observation of 0, 0 for x and y, of 1, 2, and of 2, 2, what is the least squares regression using the equation y bx a.

59 squared, OK, and finally?

2x squared.

This is an interesting one where we seem to have a linear relationship that is flatter than the linear regression indicates, but there is one outlier.

Again, there's variance in the population, sigma squared.

So let me just graph those.

Multiplication

We only have 1x squared terms, so let's write that down.

But for the sake of this class, let's just care about it.

Look what's in the numerator, sum of cross products.

But of course minimizing squared distance, and minimizing distance that should give you the same value of Ci, but we usually put in the square there, just as the convention that people use for K means.

So let's think about what that number is, and there's two ways of coming up with that what we could call a least common multiple, the smallest multiple of both 9 and 12 that is common.

OK, now we can simplify.

Lynn example.

I swapped the sides.

Arthur Benjamin

AB 23 squared, OK. Audience

Here is what I mean, to give you a concrete example, suppose I had a minimization problem that you know minimize over a real number u of u minus 5 squared, plus 1, right.

So the standard deviation is one half and the variance sigma squared would therefore be the square of 0.5 would be 0.25.

So we put in one density.

Much richer than you might have initially had intuition for.

First I'm gonna bring your attention to this RSS column.

For an unordered list, it's actually quite a bit easier. Well, let's stick with ordered list for a moment.

AB 987 squared is 974,169.

57,683 squared.

The taxi picked up two passengers.

It's going to look like that.

This gives me the multi, the element wise squaring of

I'll assume that these events are independent.

And I think you're familiar with what that looks like.

Minus 2 and minus 2 is minus 4.

No, that's not it.