So the important topics to take away from this segment.

Which I haven't really explained yet.

Just a final note on correlations, I'm,

Correlation

Or we could calculate the Spearman rank correlation, if they're both, ordinal, or rank variables.

And that's true of any sample statistic.

And that gives me sum of cross products. Analogous to sum of squares.

But let's look at on base percentage.

But again, now that we're in multiple regression, this is not the same as the correlation coefficient.

It's smaller than 0 if the relationship is negative.

It's 1. Again, 2 18 gives us 36. Square root is 6.

And, I'll show you the correlation matrix in a moment.

And how they can tell us a lot about what's going on in our data.

Remember that was just calculating sum of cross products relative to sum of squares and X and Y. So, that's

Cumulative 0 calculates the density function cumulative 1 calculates the distribution.

How strong is the relationship?

I am just gonna pause for a moment to let you think about that.

But there is zero correlation between IQ and emotional empathy, feeling with the other person.

To remind you, this describes the following linear relationship between x and y.

So, if I go to another sample. And measure the same two variables.

In summary, you really learned about correlation coefficients.

And then in the second segment we'll take a more mathematical approach.

If you look at that data between axes x and y,

So instead of reporting just the point estimate, what is the mean, what is the correlation, what is the regression coefficient.

What about causality?

And we want to come up with a correlation between coverage on one side, and outcome of the run on the other side.

And what you see is a nice positive correlation between runs and batting average.4.

It was just that equation with one regression coefficient in it.

How do we compute such statistical correlations?

So then, if I, if I elaborate this first formula.

That's just like variance except it's the sum of cross products over N. And correlation is just standardized co variance.

In MCMC, that's not true.

Throughout this whole thing, making toys,

So it's the area from minus infinity to x of our probability density function.

So these T values, the P values, the R squared, those things don't change.

So one one one, multiply that by r, then you just get r. That's why, the standardized regression c oefficient is so easy.

Though there's plenty who would.

Unfortunately, it's not, because I would like to be taller, but I'm not.

The answer is yes clearly for different values of A, I get different values of B.

That is, to send more winged queens and males to that year's mating flight.

This is supposed to be a constant

Let's implement this in our code.

If we double our y's, we always double b.

That assumes we have two variables, x and y, that are continuous.

One way, if you did want to memorize it, you said, OK, the integration by parts says if I take the integral of the derivative of one thing and then just a regular function of another, it equals the two functions times each other, minus the integral of the reverse.