A company gives prospective managers four separate tests for judging their potential. For a sample of 30 managers, the test scores and the subsequent job effectiveness ratings (Rating) given one year later are listed in the file P11_52.xlsx.
a. Look at scatter plots and the table of correlations for these five variables. Does it appear that a multiple regression equation for Rating, with the test scores as explanatory variables, will be successful? Can you foresee any problems in obtaining accurate estimates of the individual regression coefficients?
b. Estimate the regression equation that includes all four test scores, and find 95% confidence intervals for the coefficients of the explanatory variables. How can you explain the negative coefficient of Test3, given that the correlation between Rating and Test3 is positive?
c. Can you reject the null hypothesis that these test scores, as a whole, have no predictive ability for job effectiveness at the 1% level? Why or why not?
d. If a new prospective manager has test scores of 83, 74, 65, and 77, what do you predict his job effectiveness rating will be in one year? What is the standard error of this prediction?