15-1. The following output is associated with a multiple regression model with three independent variables: df...

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15-1. The following output is associated with a multiple regression model with three independent variables: df ss MS F Significance F Regression 3 16,646.091 5,548.697 5.328 0.007 Residual 21 21,871.669 1,041.508 Total 24 38,517.760 Coefficients Standard Error t Stat p-value Intercept 87.790 25.468 3.447 0.002 21 -0.970 0.586 -1.656 0.113 22 0.002 0.001 3.133 0.005 23 -8.723 7.495 -1.164 0.258 Lower 95% Upper 95% Lower 90% Upper 90% Intercept 34.827 140.753 43.966 131.613 21 -2.189 0.248 -1.979 0.038 22 0.001 0.004 0.001 0.004 x3 -24.311 6.864 -21.621 4.174 a. What is the regression model associated with these data? b. Is the model statistically significant? c. How much of the variation in the dependent variable can be explained by the model? d. Are all of the independent variables in the model significant? If not, which are not and how can you tell? e. How much of a change in the dependent variable will be associated with a one-unit change in x? In x3? f. Do any of the 95% confidence interval estimates of the slope coefficients contain zero? If so, what does this indicate? The following correlation matrix is associated with the same data used to build the regression model in Exercise 15-1 y 23 22 21 1 y 21 -0.406 1 0.459 0.051 1 22 -0.244 0.504 23 0.272 1 Does this output indicate any potential multicollinearity problems with the analysis? 15-1. The following output is associated with a multiple regression model with three independent variables: df ss MS F Significance F Regression 3 16,646.091 5,548.697 5.328 0.007 Residual 21 21,871.669 1,041.508 Total 24 38,517.760 Coefficients Standard Error t Stat p-value Intercept 87.790 25.468 3.447 0.002 21 -0.970 0.586 -1.656 0.113 22 0.002 0.001 3.133 0.005 23 -8.723 7.495 -1.164 0.258 Lower 95% Upper 95% Lower 90% Upper 90% Intercept 34.827 140.753 43.966 131.613 21 -2.189 0.248 -1.979 0.038 22 0.001 0.004 0.001 0.004 x3 -24.311 6.864 -21.621 4.174 a. What is the regression model associated with these data? b. Is the model statistically significant? c. How much of the variation in the dependent variable can be explained by the model? d. Are all of the independent variables in the model significant? If not, which are not and how can you tell? e. How much of a change in the dependent variable will be associated with a one-unit change in x? In x3? f. Do any of the 95% confidence interval estimates of the slope coefficients contain zero? If so, what does this indicate? The following correlation matrix is associated with the same data used to build the regression model in Exercise 15-1 y 23 22 21 1 y 21 -0.406 1 0.459 0.051 1 22 -0.244 0.504 23 0.272 1 Does this output indicate any potential multicollinearity problems with the analysis?