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.

And that would give us the sum of squared residuals.

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

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

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.

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

So let me just graph those.

Lynn example.

59 squared, OK, and finally?

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.

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.

This gives me the multi, the element wise squaring of

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

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

It's going to look like that.

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

And their sum is equal to this up here.

So that's equal to 25.

Or we could write this as x minus 7 squared is equal to 0.

OK, now we can simplify.

And we see here in the graph exactly the behavior that we discussed earlier, which is that the small

I swapped the sides.

Arthur Benjamin

AB 23 squared, OK. Audience

So, sigma squared 1 of course would be equal to 4, for example, as the square of 2.

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.

So 15 squared plus 20 squared is going to be equal to r squared.

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

The square of 5 is 25.

It's 225.

Plus or minus the square root of b squared.

So I can say, Okay, well now how about weight in pounds and height in inches squared? And I have to multiply, right? Because I have to multiply by the conversion.

And that just gives me the center of this distribution. How about sigma squared?

So this expression with the squared here is going to be positive, and you multiply it by 3, and it's going to be positive.

And all that tells us is it the sum of the squares of the shorter sides of the triangle are going to be equal to the square of the longer side.

And now we distribute this minus over this whole expression.

We don't do that. But I did it here just to demonstrate the similarity of some cross products.

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

AB 987 squared is 974,169.