And, if X and Y overlap, if they co vary.

So, you might think well, this is just like what we did in correlation.

Treat their measurement with the thermometer as variable x2.

That's a rather negative association.

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

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

And looked at the correlations among their scores in those different disciplines.

What effect size tells you is what was the magnitude of the effect?

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

Statistics one. In the last lecture, we talked about correlations.

This is, again, keep it simple, stupid.

The important topics to take away from this segment are validity and reliability.

Not in a measurement sense, but just with respect to correlations and, and correlation based arguments.

To sum up this segment, what I want you to take away is just the concept of correlation, what their used for, and how we use scatter plots to evaluate correlations and see where correlations, might be going wrong or where they, where the strength is coming from.

A way to quantify this is to follow the 2 point correlation function.

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

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

So I'm still perplexed about what the true meaning of technology is as it relates to humanity, as it relates to nature, as it relates to the spiritual.

We forgot about the entire chain around us.

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

I must confer with my colleagues on the matter.

Just run the correlation between X1 and X2, and that provides you with a reliability estimate.

I have mixed feelings about this.

Now, let's move to the very different looking wall in the Alhambra.

How do we compute such statistical correlations?

So say we observe a correlation of like.7, which was the correlation between on base percentage and runs scored.

Then we came to the meat of the unit.

There must be some single factor that caused.

And what's the correlation between runs scored and on base percentage?

Again, think about, think that through for a second if and only correlates with itself is 0.34.

If we just have one predictor then beta will equal R. They will be the same as the correlation co efficient.

In the middle of this distribution. What that means is if I did the study over, and over, and over again.

And this network of relations is ever evolving.

Which I haven't really explained yet.

It's very tempting to just omit this from your data, and if you do, you might find correlations in this case, a positive correlation between the hospital and death, that have nothing to do with the way things are being caused, and as a result, those correlations don't relate at all to what you should do.

The general expectation is that clustering has to get stronger in time or conversely, it'll be weaker at higher redshifts.

It is no longer the case.

That's called a Bayesian approach, and we'll get to that at the very end of the semester.

So again remember the idea of mediation.

And here's the output from that script.

What about causality?

In MCMC, that's not true.

Throughout this whole thing, making toys,

The universality, to repeat, is us that we are the city.

And it's wonderful, wonderful work.