Statistics Scatterplots

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Today we are going to be talking about scatterplots.0002

First we are going to talk about how scatterplots are different from previous visualization.0007

Because of that I will go over a little bit about what the previous visualizations all have in common.0013

Then I will compare and contrast this with scatterplots.0018

Finally we are going to go on to describing the different aspects of scatterplot versus other distributions we have been talking about before.0023

The previous distributions we are talking about have largely been about frequency distributions.0030

and here we are talking about the one continuous variable like height or age or number of friends on www.facebook.com.0039

We are asking how frequent is this value?0049

How frequent is that to have 200 friends on www.facebook.com?0052

How frequent is it to be 6 feet tall?0057

Now the frequency distribution looks like there are two variables because the x-axis and y-axis.0061

But it is one variable height and the frequency which is just another variable for counting how many you have.0069

We have looked at some cases where we compare two different variables, but usually it might be comparing two groups on some continuous variables.0080

We might compare male and female heights, but we are only looking at one continuous variable height.0091

The other variable is a categorical variable, the two groups.0099

That is how we get the two groups like gender.0103

Although we have that still the fundamental basis is that we only been looking at one continuous variable at a time.0107

Now these frequency distribution we have drawn like histograms and different beings, they often look like this is and they are summarized by shape, center, and spread.0116

Usually by center we mean something like mean and by spread we mean something like standard deviation.0129

Now that is going to be sort of the past.0140

Now we are moving on to scatterplots.0144

Here is how scatterplots are different.0148

Instead of having one continuous variable we have two continuous variables.0150

That is the big key difference.0155

And because of that one axis is going to have variable 1 and instead of putting frequency here we are going to put variable 2 here.0157

Some frequency distributions we had variable 1 here and we have that frequency of variable 1 here.0172

Notice here there is no explicit representation of frequency.0179

There is no number that we are planning to represent frequency and each axis is going to represent the variable.0182

We are summarizing these distributions by shape, strand and strength.0193

Here it can be called a scatterplot because each case is now going to appear as a dot.0201

Each case, for instance each person on www.facebook.com might have variable 1, number of friends, as well as variable 2.0210

How many photos they have uploaded?0220

Each dot represents one person, but 2 values within that person.0223

And because of that, it is called the scatterplot because it looked like somebody just scattered a bunch of dots on this graph.0232

It makes sense that it is called the scatterplot and notice that here it does not quite seem like we are really interested in the center of one dimension.0242

We are interested in the center of two dimensions.0254

Because of that trend is going to be sort of like center and strength is going to be a lot of like spread.0258

These concepts are concepts you have got about before but we are translating them from one dimension to 2 dimensions.0273

Spread used to be something like this but now we are talking about spread in 2 dimensions.0284

That is going to look a little bit different.0291

Let us talk about these particular summary values of shape, center, and spread.0296

Remember frequency distributions are always what we call univariate in terms of continuous variables.0301

It might have 2 variables but one will probably be categorical.0309

When we talk about shape we talked about being like unimodal, symmetric, asymptote.0315

Those are common features that we are looking for.0329

Is it normal, uniform?0332

Those are words that we are buzzed when we talked about shape in frequency distributions.0336

In scatterplot we are largely interested in putting different shapes.0342

One shape might be that the dots sort of fall in a line.0347

Is it a linear scatterplot?0353

Another potential distribution is that the dots might fall in a curve.0358

Is it curvilinear?0366

It is a shape that we are interested in is that there is just sort of no shape, and it sort of the love like or cloudlike.0370

This is not the cloud may be one way of thinking about it.0383

Those are different shapes that we are interested in.0391

How linear is it? Is it curvilinear, is it cloud?0397

Let us talk about center.0403

The way we talked about center before was that we are interested in things like the mean, median, and mode.0404

A lot of times we used mean.0413

Either signified by mu or ex-bar , depending on whether you are in the population or sample.0415

Trend has sort of the same idea as center.0426

You could think about this as a version of center, except the center of two variables not just one.0432

Here it is not useful to have a center of just dot because that is what we had before.0444

We had point mean.0455

It was like a particular point, but now what we are interested in it is let us say we have a whole bunch of dot scattered here.0457

What we might be more interested in is a line of some sort that describes the relationship between all these points on these two variables.0466

Here we are not just interested in a pointcenter, we are interested in a line center.0478

I’m goingto adjust these to be lines center rather than a point center.0486

That line is going to be called the official term for that is regression.0493

That is going to be the regression line.0500

The final idea that we talk about here is strength and I want to tie that to the idea of spread that we talked about.0504

One important idea of spread that we frequency talked about with standard deviation expressed as sigma or expressed as S.0517

Those are two ways we have talked about spread before and that gives you a one-dimensional spread,0536

but what might be more useful here is something like two-dimensional spread.0542

Here we have our dots, we have our line, but now we are interested in how spread out these dots are.0549

You could think about it at all these little distances away from the line.0560

What is that is spread away from the line like?0568

You want to think of this as a multidimensional spread.0573

It is not just the one-dimensional spread, it is a two-dimensional spread.0576

You can think about this as spread around line.0582

Before this was spread around the points, but now it is spread around the whole line.0591

We are going to call that correlation.0598