The human resources department at a firm developed a multiple regression to predict the success of candidates for available positions. Drawing records of new hires from five years ago, analysts regressed current annual salary on age at the time of hire and score on a personality test given to new hires. The path diagram below summarizes the fitted model. Age is coded in years, the test is scored from 1 to 20, and annual salary is in thousands of dollars ($000).

(a) Write down the equation for the multiple regression model.
(b) Which is larger: the direct or indirect effect of test score?
(c) Find the marginal slope of salary on test score.
(d) If you were a new applicant and could take a special course that in a week€™s time could raise your test score by 5 points, would the course be worth the $25,000 being charged? Which slope is relevant: marginal or partial?

Age 5 $000/year 5 points/ year 2 years/point Salary Test Score 2 s00/point