And so welcome again to the third lecture in my own series about statistics for user

studies.

Again, this is part of empirical research methods in medical engineering.

And so since both last lectures were used to talk about significant tests, effect sizes,

co-hands D and stuff like that.

And this lecture is going to be a little compressed.

I'm going to talk about correlation and regression.

And then I have a couple of exercises on the so-called ANOVA, so the analysis of variance.

Now, this is a quite fat lecture, so bear with me.

And so correlation and regression, that's a very, very interesting topic.

Actually it extends much further, much beyond statistics, in my opinion.

So first of all, correlation.

Correlation is a close keen to regression, but I'm not really interested in exploring

the relationship between the first and the second.

There's a clear relationship and you already saw something about that in the theory lecture

before.

So I'm going to talk about correlation and show you a couple examples of linear and nonlinear

correlation, because there is no linear correlation, although not very many people know about that,

but it's very useful.

And then we're going to have a short philosophical talk about causation in relation to correlation.

And then we're going to talk about regression.

So evaluating it in practice, in end dimensions should be D dimensions here, that would be

much better to let me correct this on the spot.

It should be, I usually use the letter D rather than N to denote the dimensions of my input

space.

So let's be coherent here and keep on talking about D, small D actually.

And then we'll try to make correlation nonlinear.

And turning linear regression, which is still called linear regression into a universal

approximator, so something which you can use to approximate any kind of function with

no limit to an arbitrary degree of precision.

And of course, in that case, you have to be careful that you don't overfit, but that's

not rush.

So number one, correlation.

correlation is turning to pin myself, and I won't see my face ever again, that's it.

Okay, so correlation is, my perspective on it is two things going up and down at the

same time, synergistically, synchronously.

So one goes up, the other goes down, and vice versa.

That would be positive correlation.

If this thing is the other way around, so one goes down and the other goes up, so there

are sort of out of phase, that's negative correlation, but still it's a relationship between one

variable and the other.

So first of all, check how to graphically recognize it, although you see in a couple of

cool examples of stuff, which seems correlated and it is not, or they don't seem correlated,

but then the evaluation gives you correlation, then how to evaluate it numerically and also

nonlinearly.

And then, couple of questions about correlation and causation.

So as usual, you have on the student, you have my call advice, just in case you're interested,

should download, then try and execute them, and then try to execute the tasks I place

in them for you.

So let's start with correlation, in the simplest form.