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In the last two movies, we've looked at ways to take output from SPSS and reformat it by pasting it into a spreadsheet and working with it to get it so it's clear, simpler, and easier to communicate. In the first movie, we looked at formatting a table of descriptive statistics. In the second one, we looked at how to deal with a correlation matrix. In this third one, I want to show you how to take the results of a multiple regression and compare them with the results of correlation coefficients, as a way of communicating the different perspectives that these analyses can give you and to make it clearer how to interpret them in a meaningful way.
To do this, I'm going to be using the same data sets, Google searches, and the same variables that I used in the last two examples. I need to get a linear regression output. To do this, I come up to Analyze and go to Regression, to Linear. I need to take my dependent variable. That's my outcome variable or the thing I'm trying to predict. That's SPSS and I put that into Dependent. Then I take all the variables that I want to use as my predictors, the things that I think will explain interest in SPSS.
And in this case, I'm going to be using the same ones that was used before, searches for Business Intelligence, searches for Data Visualization. And then I'm going to come down to the degree, Percentage of a state population with Bachelors Degree or more, the Median Age, and then my three dichotomous indicators for Region. Now I've mentioned before that Region has four categories and the reason we used three indicator variables for this is because the fourth category, which would be West, is implied by 0s in all of these.
In the other analyses, it's okay to have a fourth indicator for West, but in linear regression it's not. That introduces something called multicolinearity and it can really wreak havoc with the result if you have variables that are correlated entirely with each other. So that's why we don't do that. Now to make this one simple, I'll leave it as Enter. That means it's going to give me a regression coefficient for all of these at once. I just leave everything at the default and I press OK. And I have a number of statistics here. The one I'm going to go to right now is this one that says Coefficients.
Really there is one column here that's of most interest. it's the one that says Standardized Coefficients Beta. It's third from the right. There's an inferential statistic next to it, the TTest, and then there's a Significant value next to that. What I really want is the Beta Coefficients, because those are the ones that are most comparable to correlation coefficients. And then I'm going to indicate the statistical significance by highlighting the ones that are significant. I'm also going to use some of the information from the two tables above that, the Model Summary and the ANOVA.
I'll show you those in a moment. So what I'm going to do is I'm going to rightclick on my Coefficients table, copy it, and I'm going to go to the same Excel spreadsheet that I used for modifying the correlation coefficients, except for this moment I'm going to start with the second sheet. I'll go to B1 and paste the results in. Again, because that allows me to put in a column, so I can reconstitute the order if I need to. And then I'm going to start getting rid of some information. I don't need this merged cell that says Coefficients on the top.
I don't need this giant merged cell that says Model here on the side. And then I don't need this one that says t and I don't need the Unstandardized Coefficients. So these are the ones in the original metric, but I'm just going to leave those out for right now, because the standardized coefficients, which are also called the Beta Weights, are the ones that are most easily compared with the correlation coefficients. Now the Constant, the Intercept term, doesn't have a standardized regression Beta Weight.
That's fine, so we can just leave that out. And in fact, what I'm going to going to do is I'm going to put here Predictor, Beta, and then I'm going to put p right here, and I don't need one for the Intercept. That way I can delete these merged cells up here and I have just these ones left. I don't need to worry too much about the formatting of the labels here, because I'm going to use the ones on the other page.
In the last one, I highlighted everything that was statistically significant in the 05. I'm also going to highlight the ones here that are statistically significant. An easy way to do that is to come in here to the p values and sort. And so now all the small p values, the ones that are statistically significant, are right here. And then I can highlight those and then if all goes well, I can sort them again. Now I can delete the p values. All I need are these ones, and I'm going to copy those and I'm going to go to the first page where I have my correlation coefficients.
And I just want to make sure that everything is in the same order. It is. These I need to say are correlations and these are beta coefficients. A beta coefficient is a standardized regression coefficient, and then here I've got Predicting SPSS. And so now what I have, I'm going to remove the borders that I actually put in earlier, and I'll get those all centered.
Here's an interesting thing. The correlations and the beta coefficients, I'm going to change the decimal places here, are approximately the same thing. Now what's interesting about putting the correlation coefficients in one column and the beta coefficients next to them is you can see actually that there's a huge contrast between the two of these. In the correlations, we had three variables that individually had high correlations with the relative interest in SPSS as a Google search term. They were Business Intelligence, Data Visualization, and the proportion of a state's population that had degrees.
All three of those are significantly and positively correlated, and the age and the region variables were not. However, when we go over to the regression results, we get a very different pattern. For one thing, Business Intelligence is no longer significantly correlated, where there's gone negative but it's not significant, so we'll treat it as functionally 0. Degree has also gone negative, but it's not significant. Data visualization on the other hand is still statistically significant and it has actually gone much, much higher.
Beta coefficients are like correlations and that they go from 0 to 1. They can be positive or negative. This is almost as strong as it can be. Data Visualization becomes a huge predictor. And then what's really shocking is that this three region variables, which individually had no correlation with interest in SPSS, all three of them had become statistically significant in the regression coefficient. What this lets us know is that region as a whole does matter and mostly because the three of these are contrasting with the West, we would want to look at the relative interest of SPSS in the four regions.
The other thing to keep in mind is that the correlation coefficients are valid individually. The correlation of Business Intelligence to SPSS of .49 is calculated on its own. The next one down between Data Visualization and SPSS, where we have a correlation of .60, that's correlated on its own. However, for the regression the seven beta coefficients are calculated simultaneously. If we removed any one of these, all of the others would change. They're taken as a combination and their values and their probability values are only valid when taken as a group.
And so that's one of the reasons why I can get very different patterns when you put in a linear regression result versus a correlation. Now there's one other thing I want to add for the linear regression. And that is this thing up here, under Model Summary where it gives the R Squared. And that is an indication of the proportion of variance in the outcome variable, which is SPSS searches that can accurately be predicted by the combination of the other variables. And what we have here is an R Squared of .589 and what that means is that nearly 60% of the variance in SPSS and just can be predicted by these other seven variables collectively.
So I'm going to take that .589, I'm just going to insert a row, and I'll label it R Squared, and I'm going to put down the .589. I'll just round it off right now and you can actually put that down as a percentage. And I'm going to leave it highlighted, I'll change that one to a percentage, and I'm going to leave it highlighted in yellow, because it is statistically significant. What that means is it's different from the 0 and the way I can tell that is by the result in the next table of the Analysis of Variance table where the model as a whole has a significant value of less than .000 here, but .001.
And so I know that that R Squared value of .589 is statistically significant. What I have here is a result that says that those seven variables collectively predict a lot of the interest in SPSS as a Google search term. What's funny about it is that the pattern from the individual correlations to the combined regression coefficient changes dramatically. And it's not the case that one of these is accurate and the other is inaccurate. They are both accurate; they are just very different perspectives on the issue, the individual versus the group predicting.
Anyhow, this can be one step in trying to tell an analytic story about your data. It can get complicated. it can require some insight and some judgment in how best to interpret it. But this is a way of taking a huge amount of numbers and a huge number of tables and boiling them down to a very small concise way of presenting the results that I think it makes it much easier for you to articulate your story, your vision of your data analysis.
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