Question 11.97

11.97 The multiple regression results do not tell the whole story.

We use a constructed data set in this problem to illustrate this point.

dsetb

  1. Run the multiple regression using and to predict . The test and the significance tests for the coefficients of the explanatory variables fail to reach the 5% level of significance. Summarize these results.
  2. Now run the two simple linear regressions using each of the explanatory variables in separate analyses. The coefficients of the explanatory variables are statistically significant at the 5% level in each of these analyses. Verify these conclusions with plots and correlations.
  3. What do you conclude about an analytical strategy that looks only at multiple regression results?

11.97

(a) The multiple regression equation is: . Likewise, neither predictor tests significant when added last: . The data do not show a significant multiple linear regression between and the predictors and . (b) For and : . For and . Both and are significant in predicting in a simple linear regression. (c) An insignificant multiple regression test doesn’t necessarily imply that all predictors are not useful; we should explore other strategies and/or tests to verify that none of the predictors are useful in different models/settings. In this case, and are highly correlated and likely their tests will be insignificant when they are used in the same model together.