Correlation

So the important topics to take away from this segment.

And that's true of any sample statistic.

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

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

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

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

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

How strong is the relationship?

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.

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.

In summary, you really learned about correlation coefficients.

How do we compute such statistical correlations?

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.

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

What about causality?

This is supposed to be a constant

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

Throughout this whole thing, making toys,

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.

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.

2nd derivative r squared.

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.

But let's look at on base percentage.

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

Asking for the standardized. Coefficients.

In MCMC, that's not true.

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

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

Though there's plenty who would.

Just a final note on correlations, I'm,

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?

The raw data matrix, the, The subjects and their scores.