2x squared.

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

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

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

And that would give us the sum of squared residuals.

OK, now we can simplify.

Lynn example.

I swapped the sides.

Arthur Benjamin

AB 23 squared, OK. Audience

So that is going to be one over 2M of, my usual cost function.

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.

AB 987 squared is 974,169.

57,683 squared.

The taxi picked up two passengers.

It's going to look like that.

It's worth twice as much.

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.

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.

Computer script errors by, you know, taking the difference between your predictions and the y values and taking the element of y squaring and then finally computing the cost function J. And Octave knows that J is a value I want to return because J appeared here in the function definition.

I'm think about standard deviations, but the formula on the previous 5 actually gave the estimates of the squares of theses things, so sigma squared 1 and sigma squared 2.

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

So let's take the x squared terms first.

And their sum is equal to this up here.

10 for v.

So that's equal to 25.

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

I'm going to break the problem down into three parts.

Gaussian distribution with some parameter Mu and some parameter sigma squared.

The problem with parameter estimation is, given my data set I want to figure out, I want to estimate, what are the values of Mu and sigma squared.

Of theta one x I minus y I and if you simplify this turns out to be. That. Zero

And now we distribute this minus over this whole expression.

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

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

So let's substitute that here.

Not minus x squared plus 3, but just x squared plus 3.

And again it is right there in the math, you should feel comfortable with this mathematically it's the deviation scores square them, sum square deviation scores, that's the sum squares, if you divide by n, that's the mean squares.

So, just be careful whether you are using sigma 1, sigma 2, or sigma squared 1 or sigma squared 2.

So if I look at my outcome measure Y, I can sort of parse the variants into two pieces.

The square of 5 is 25.