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e. The accompanying table is the correlation matrix for the three variables. As you can see, all three are highly correlated with one another. If we look at the intersection of each pair of variables, the number next to "Pearson correlation" is the correlation coefficient. For example, the correlation between "Anxiety year 1" and "Depression year 1" is .549. Which two variables show the strongest correlation? How might this explain the fact that depression at year 1 seems to be a better predictor when it's the only independent variable than when anxiety at year 1 also is included? What does this tell us about the importance of including third variables in the regression analyses when possible? f. Let's say you want to add a fourth independent variable. You have to choose among three possible independent variables: (1) a variable highly correlated with both independent variables and the dependent variable, (2) a variable highly correlated with the dependent variable but not correlated with either independent variable, and Correlations 16.48 Anxiety, depression, and multiple regression: We conducted a second regression analysis on the data from Exercise 16.47. In addition to depression at year 1, we included a second independent variable to predict anxiety at year 3. We also included anxiety at year 1. (We might expect that the best predictor of anxiety at a later point in time is one's anxiety at an earlier point in time.) Here is the output for that analysis. Coefficients(a) Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta (Constant) 17.038 1.484 11.482 .000 Depression Year 1 -.013 .055 -.019 -.237 .813 Anxiety Year 1 .307 .056 .442 5.521 .000 a. Dependent Variable: Anxiety Year 3

e. The accompanying table is the correlation matrix for the three variables. As you can see, all three are highly correlated with one another. If we look at the intersection of each pair of variables, the number next to "Pearson correlation" is the correlation coefficient. For example, the correlation between "Anxiety year 1" and "Depression year 1" is .549. Which two variables show the strongest correlation? How might this explain the fact that depression at year 1 seems to be a better predictor when it's the only independent variable than when anxiety at year 1 also is included? What does this tell us about the importance of including third variables in the regression analyses when possible?
f. Let's say you want to add a fourth independent variable. You have to choose among three possible independent variables: (1) a variable highly correlated with both independent variables and the dependent variable, (2) a variable highly correlated with the dependent variable but not correlated with either independent variable, and
Correlations
16.48 Anxiety, depression, and multiple regression: We conducted a second regression analysis on the data from Exercise 16.47. In addition to depression at year 1, we included a second independent variable to predict anxiety at year 3. We also included anxiety at year 1. (We might expect that the best predictor of anxiety at a later point in time is one's anxiety at an earlier point in time.) Here is the output for that analysis.
Coefficients(a)
Unstandardized Coefficients Standardized Coefficients t Sig.
B Std. Error Beta
(Constant) 17.038 1.484 11.482 .000
Depression Year 1 -.013 .055 -.019 -.237 .813
Anxiety Year 1 .307 .056 .442 5.521 .000
a. Dependent Variable: Anxiety Year 3

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