Correlation

And that's true of any sample statistic.

So the important topics to take away from this segment.

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

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,

Which I haven't really explained yet.

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.

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 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

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

But let's look at on base percentage.

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

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

Asking for the standardized. Coefficients.

2nd derivative r squared.

So I can just rewrite that as A so now A is not a function anymore, it's just a number A times the second derivative of y, with respect to x, plus B times the first derivative, plus C times y.

So the higher the value in 1 diagonal and the lower the value in the other diagonal, the stronger the correlation.

In statistics, we call this a confounding variable.

What about the second assumption?

And now the data sits, a square in which data is uniformly arranged, correlated, yes or no?