Exercise 2: Choosing a model and using it The HR director of an industrial group would like to construct a model explaining the monthly salary of all employees. Using data collected from a random sample of 36 employees, he tests two explanatory variables that he deems relevant: the number of years of graduate studies (X1) and the number of years of service (X2). You can find below results from three regression models he tested using Excel. 1) For each of the three suggested models: a. Calculate the coefficient of determination r b. Conduct the Student tests for the explanatory variables. 2) Can you help the HR director choose the most suitable model? a. Using the information provided, which model would you suggest to use? Justify your choice. b. Estimate the parameters of the chosen model. 3) Pierre Durand, an employee of this group, is 38 years old, with 10 years of service and 4 years of graduate studies. His monthly salary is 2050 Euros and he thinks he is underpaid. Calculate a 95% confidence interval for the mean salary of an employee with Pierre Durand's profile. If you were the HR director of that firm, what would you tell Pierre Durand about his salary? Variable Y Mean 1850 X1 3.5 X2 4.17 Sample standard deviation* 795.88 2.40 2.15 * Reminder: this is the value of the unbiased point estimate (coefficient 1/n-1) Regression of Y w.r.t X ANALYSIS OF VARIANCE Regression Residual Total Sum of Squares ? 694 925 22 170 000 Coefficients Standard- error Constant Variable X 706 326.9 10.08 3