 Perhaps the simplest way of looking at the association between variables is with the correlation coefficient, specifically the Pearson product moment correlation coefficient, usually just called R. And it's a great way of looking at the association between two quantitative or continuous variables, although it's actually much more flexible than that. And I want to take a moment to show you how we can do correlations and correlation matrices and scatterplot matrices in Jmovi. Now to do this, I'm bringing in a new data set, and it's called state data. And it's based on a little bit of information that I've compiled from different sources. One is the name of the state, its code, the region it's from. I looked up whether their current governor is Republican or Democrat. From a few years ago, a study done on categorizing states by their personality characteristics, putting them as temperamental or friendly and relaxed or traditional, another study that classified the states by their big five personality characteristics, extraversion, agreeableness, conscientiousness and so on. And then here at the end, I went to Google correlate and I got state by state data on how common certain search terms are in each state. These are Z scores. So they tell you how many standard deviations above or below that state is from the national average. And I put in some that I felt were at least kind of relevant to the big five personality characteristics, I have some social media ones. I put in some business he wants entrepreneur GDPR stands for the general data privacy regulation that the European Union just put in it's a big deal if you're in e commerce. Then we have universities and then mortgage and then volunteering and museums and scrapbook and my favorite one modern dance. And let's take a look at some of the associations between a few of these variables. And then we'll explore some of the other associations as we go through this chapter on regression in Gemobi. Okay, so the first thing I'm going to do is I'm going to pick a small number of variables. When you go to regression, your first choice here is correlation matrix. And, you know, truthfully, you could put in 100 variables, you just end up with this absolutely gargantuan matrix and not be able to make sense of it. I'm going to be a little more selective and pick just a few right now. I'm going to pick one of our personality characteristics here extraversion. So really how outgoing social person is versus being introverted. And I'm going to pick just a few other things to go with it. So maybe extroverted people might be on social media more. So we'll pick Facebook. And they may or may not be concerned about privacy. Let's see what that looks like. And then how about volunteering. So are they offering to do things for free to help people in their community? Okay, so I put those in there and you see that this table builds up and it fills in almost immediately. What we have are the correlation coefficients arranged in the top right diagonal of the table. There's nothing in the bottom left because those two are mirror images there because the association between extraversion and Facebook is the same as the association between Facebook and extraversion down the diagonal are just these lines because that's each variable with itself. And that's always a perfect correlation, but it doesn't really mean anything. So what we have in this are two things we first have the piercings are this is the product moment correlation coefficient, it goes from negative one, which indicates a perfect negative linear association through zero, which indicates no linear relationship whatsoever to plus one, which indicates a perfect positive linear relationship. And we also have the p value, which is used for the statistical hypothesis testing. And we're looking for a number there that is less than oh five. Now, it's going to be easier to see what's going on if we come over here and click flag significant correlations, it'll put asterisks next to them, which makes it a little easier to find instead of having to compare each number in your own head. And so we see, for instance, that we have three significant correlations out of six. So it turns out extraversion is not associated with any of these things, which is kind of surprising. But states that search for Facebook more on Google search less for privacy, they also search less for volunteering, and then states that search more for privacy search more for volunteering. These are pretty good correlations. And again, it's on a state by state level, it's not a person by person level, it's on the states. By the way, the data set only includes 48 states, it doesn't include Alaska or Hawaii, or the District of Columbia, Washington DC. That's because that's what was included in the one that categorized the states by personalities. And so this gives you something to look at. Now, one interesting option that Jim Ovie gives you is to do confidence intervals. And so we click on that, and it will expand this table and give us a 95% confidence interval, you can change it to something else if you want. And I'll give you the upper bound and the lower bound. So for instance, you can see that this one goes on either side of zero. So it's this and this here, however, this association between Facebook and volunteering as statewide search terms, we go from negative 0.451 to negative 0.789. So it may be that you want confidence intervals for your correlations, it makes for a busy matrix, but they're available. The other thing I want to mention is this, it's always nice to have a graph. And I actually would have called this a scatterplot matrix as opposed to a correlation matrix. But either one works. And what it is is it's a similar rows and columns. But this time it has separate scatterplots for each of the associations. And they get kind of busy, but you can see that we've got a strong negative association, a strong positive association. And some others that are pretty close to zero, it's set up a little bit differently. Here we have stuff on the bottom left diagonal, as opposed to the top right diagonal, but again, it's symmetrical. We can also get the density charts on the diagonal. So we know what the distribution looks like for each variable. And from that, you can see that extraversion and Facebook are kind of normal, we got a peculiar shape here with privacy, because we have outliers and volunteering is bimodal. And then also we can get statistics that'll give us the actual correlation coefficients displayed on the upper right side of the diagonal in the scatterplot matrix. See these numbers correspond to what we have up here, there's the point 036 and there's the same thing down here. And so we have both a numerical summary of the correlations, the associations between these variables, as well as a graphical summary. That's generally how you want to do it anyhow. And so correlations are a fabulous first step at looking at the association between variables, especially when they are quantitative or continuous variables. Again, it's more flexible than that. But that's the canonical usage of correlations in Jmovi and elsewhere.