Another way of visualizing two-way relationship is called correlation. Let's go back and see how to get this. So if you go to Rattle, which is where we are, let's go back to data and I do want crime. I don't want to ignore it. I'll have median value, I'll have tax, I have age, and I have five variables, maybe I'll ignore it. So how do you get that nice little graph I just showed you? So you go to Explore and you go to Distributions. Okay. Don't select anything. Don't select the histogram, don't select the box plot. Don't select anything. The other thing is Settings, I need advanced graphics, and now you execute. Now you've got it. Okay. So remember, I had switched the advanced graphics off, now I have it on. Okay. Now you see the zoom. Now not only does it do the correlations which is that given on the top, it also plots 2 by 2 plots between these variables. So let's understand what this means. So going back to the PowerPoint, which is that I want to switch. So in this graph, you can see the correlation. So this tells you the correlation between crime and the fraction of industries is 40 percent. This tells you the correlation between crime and tax is 57 percent. This says the correlation between crime and the median value is minus 0.4. So what is correlation? Correlation has no matrix like kilometers or grams, it has no dimensions. It is usually between minus one and one. The sign of the correlation tells you whether the two variables move in the same direction or not. If it is negative, they move in opposite directions. If it is positive, they move in the same direction. You probably know that already. The closer the value is to plus one or minus one, the stronger the correlation. So zero means they are not probably correlated, they are not associated. Okay. So you can see here that crime and industry, they are correlated and what's the connection you'd think? Well, population probably? You can also see that tax and the value of the house are negatively correlated. That makes sense in a place where the taxes are high, the house values should be lower, whereas if the taxes are lower, the host values will be higher. So this is an analysis we often do to make sure that the data is telling us the story we want it to say. Here is another way of doing correlation and I will not spend too long about it. If you just use the Correlation button which is right here on your distribution, you can get the correlation but it gives you a different kind of plot. But the only difference is the visual it creates, nothing more. The bigger the circle, the more the correlation. That's all it means and that's a simple thing. Here at the bottom, it gives you the correlation between these variables. If somebody said the states you already know how to look at it. Before we do the model, one last thing I want you to be aware of, that there must be sufficient variation in the data. If that is not sufficient variation in your independent-independent, in your response and explanatory variables, you can't fit a model because what is there to fit if all I have is the same value. So if I have a value of 1,000 and all the explanatory variables lets say one, two, and one there's no model you can fit. So you need a reasonable amount of variability to be able to fit any kind of model. So when people say I want more data, probably they're saying I want more variation in the data and that might surprise you for the first time you look at it but variation as data is absolutely necessary.
