Let me take a corn example. So, it's called sigma y, x.

Covariance of y with x is this. Summation Pi (yi - y bar) (xi - x bar),

right? It's very important to take deviations

from normal behavior. That's why I said, when I smile, it's,

what is my normal behavior? No smile, right?

Okay that's, that's [unknown]. And the probabilities are in there, right?

Look, what will, what will happen to this? Right now, I had this in bushels, if I

believe, yep. And I had this rainfall in inches.

Could I change this number, and suppose this number was 55, whatever, can I make

this number larger Just, without changing anything dramatically fundamental?

Answer is yes. Start measuring your rainfall instead of

inches, in millimeters. What will happen?

This number will become big. Because there are a lot more millimeters

in an inch, right? So, it does, it doesn't have magnitude.

It doesn't tell me anything. The only thing that's good is, it's

telling sign is okay. But magnitude is not reflective of

strength or weakness. The second tragedy with it is this, it is

unit-dependent. So, what are the units of covariance?

The units of the covariance are the units of both the things being measured,

alright? [laugh] In, when we do return analysis,

both the returns are measured in percentage.

So, it's not a big deal, but I wanted that's why to show you, why Statistics is

so awesome and why you have to deal with things which are more difficult than in

finance? So, bushel inches, what it is suppose to

mean? I mean, it shouldn't be.

An ideal measure of relationship shouldn't have units.

So, how can I compare bushel inches with, say, the productivity of people and

whether they have had a school education or not.

That units are totally different, correlation, it, the measurement, the

relationship should be comparable across different phenomena.

So, here's the tragedy of covariance. Though it's trying to measure the right

thing, its magnitude doesn't mean much and it's unit-dependent.

So, what did we do? What does the, the statisticians do?

A very little about this to talk about that's important to us, but this one is

extremely important. So, we took covariance of y and x, which

units was what? Bushels, four inches.

And magnitude was what? Didn't affect much, but sign was okay.

In other words, the, that it's positive or negative relationship is being reflected

because you're taking deviations from the mean and then multiplying.

So, what did we do? We came up with a measure called

correlation. And what is correlation?

Correlation simply takes sigma yx. Remember, what are the units?