X1 through X M, we then fit the parameters, mu 1 through mu n, and sigma squared 1 through sigma squared n, and so these were the formulas similar to the formulas we have in the previous video, that we're going to use the estimate each of these parameters, and just to give some interpretation, mu J, that's my average value of the j feature.

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?

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.

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

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.

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.

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

AB 987 squared is 974,169.

57,683 squared.

The taxi picked up two passengers.

It's going to look like that.

We could trade off the relative way between how much we want to fit the training set well, as minimizing A, versus how much we care about keeping the values of the parameters small.

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.

I peed twice.

Min

Min.

min

Min

Layer Opacity

Minimum

Minimum

Well this is a plus here, so the parenthesis really don't matter.

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