 Before you take the results of your linear regression and you go running off to market and making massive changes, you do want to make sure that you actually dotted your eyes and crossed your T's and you want to make sure that your data met the assumptions that the model has and that your data is leading you in the right direction. This becomes a matter of checking what are called regression diagnostics, a number of statistical and graphical methods for looking at how well your data fits the model. Now I'm going to do this by coming back to the same model and data that we used before where we're looking at variables to predict the openness of people on a state-by-state basis and I'm going to click on this model right here and what I'm going to do is I'm going to come back not to model builder although that is where I specified the blocks that I was going to use but I'm going to come down a little further to assumption checks and this is where the most important things are going to happen. Now there are a few here that are particularly important. If you have data that's measured repeatedly over time like quarter one quarter two quarter three results then you're going to need to deal with autocorrelation to see how much a carryover effect there is from one time to another. We don't have that right here so I'm not going to deal with that but we do need to be worried about colinearity or multi-colinearity and that's what happens when your variables that you're using to predict the outcome are correlated with each other. Now really the easiest way to check that is to get a correlation coefficient and look at the associations between your various predictor variables but the statistics that are specific to colinearity within linear regression also tell you important things. We come down here it's giving us two measures in particular and we're looking at model two that's the one I have selected. The first is VIF which stands for the variance inflation factor and the second one is tolerance and there's a correlation or an association between those and what they're both referring to in different ways is the association of each of these variables with the other predictors in the model and I can tell by looking at these that we do have some crossover between them. The actual ways that they operate gets a little complicated and that's beyond what I'm trying to do here. Mostly I want you to know that Jmovi is able to do this for you and you can interpret the results in ways that are going to make your model more robust. You can also do the QQ plot of residuals. I've demonstrated that elsewhere and it's relevant here too. The residuals or the leftovers from predictions based on your model need to be approximately normally distributed and they need to not flare out on one end of the model or the other. Now I do see that there's one down here dipping kind of low. The rest are basically on the line and we come off a little bit. It's not horrible though you may want to do a little more of a drill down analysis to see what's happening in this particular data set. There are two ways you can do that. One is with the residual plots and that's going to do separate plots for each of the predictor variables that we have in the model and so it's going to take a moment to catch up with all of those and the other one is what's called Cook's distance and that's going to give you a measure of the influence of specific cases. Now because we have only 48 cases in our data, it's the 48 continental United States, that's not such a horrible idea. Here we have the plots that we're looking at. We see for instance with openness there's this pattern in the residuals that we don't have in other things and so that's an issue we may be concerned about. I'll click on Cook's distance as well and Cook's distance actually shows up above the charts that we have right here and it's simply giving us the mean, the median standard deviation and the range of these and so you can look at the individual scores that you have and try to find out what's going on in the residual spots to see if there's something that is deviating really sharply from your expectations or the assumptions of the modeling technique. I do want to finish with one other thing and that is the estimated marginal means. Now this will be more helpful in some situations than in others but what you can do here is you can actually try to get a chart that shows you how these variables predict your outcome. So I can take governor which is an easy one because there's only two categories there and that's going to make a chart. It'll be down here at the bottom. This simply gives me the mean level of openness for the states with Democrat governors and the mean level of openness for states with Republican governors and you can actually see while the means are a little different this dot is a little lower than this dot the confidence intervals overlap substantially and you can do this with other terms if you want we can take for instance modern dance here and we can put that in and it's going to be a little different because this is a quantitative or continuous predictor whereas the governor was a dichotomous nominal variable and we'll scroll down a little bit and what it is is kind of like a scatterplot but there's no data points on here and instead we're looking at a regression line with a confidence interval around it at the association between the two as how modern dance predicts the expected levels of openness and you see as the relative interest in modern dance goes up to about a level of four point something that the average level of openness for this state goes up as well and so this can be a way of also seeing how well your data match the assumptions and fit in with the approach of linear aggression which after all is one of the most common and most powerful methods of using data to model specific outcomes and something that Jamovia makes incredibly easy to do and to interpret