1. The human resources manager of RataCom has hired you to help predict and explain the annual salaries of employees at the company. The dataset DataCom contains details of the data and the data. (30 points) (a) Estimate a multiple linear regression using all the data provided. Ignore the p-values for this question, even if they're large. If needed, use the Engineering Department has the reference group in the model. State your final model from the computer output and write the p-values in parentheses below each coefficient. (b) Interpret the Years Employed and Number Supervised coefficients in one sentence each. (c) Is there a difference in salaries between male and female employees? If so, how much? (d) Compare the salaries of employees in each of the four departments using the regression coefficients and rank order them from the lowest mean salary to the largest mean salary. (e) Using the model, predict the salary for an employee with the following characteristics. Female; Worked in a similar department at another company for 10 years; Years of education after high school is four years from a business school, that is, you will use four as the value for the Years Education variable; Supervises 12 members in her team; Works in Purchasing; Has been at DataCom for five years. (f) Provide an approximate 95% prediction interval for the prediction you obtained in part d and interpret it.Salary Number Supervised Employee Years Previous Experience Years Employed Years Education Gender | Department 0 27 12 1 44 $65,487 4 $46,184 20 $32,782 $54,899 $34,869 6 $35,487 $26,548 8 $32,920 $29,548 10 $34,231 11 $23,654 12 $39,331 13 $36,512 14 $35,467 15 $68,425 16 $35,468 OUT A H DO UI O A UI N CI O W O N OL 17 $36,578 18 $39,828 19 $36,487 20 $37,548 21 $31,528 22 $34,632 23 $46,211 O H O O N A N N A H A N A W O U D J H W U N U M O O OR W UT OO UT H W N H N W O A N N POOH HHHOOOH POP POP BOO OOO OOO H HOOOOHOHOHYAHOOHOPPPOO N O U CA O NA O U G A D N O O U J O O DA W O A WA NU OANDA OOOH DONADVA 24 $29,876 25 $43,674 26 $38,985 27 $53,234 A H W N N W N N A A W A H A A A H H A W H N N A A H W A H W N A NAD WALL 28 $51,698 29 $41,889 30 $38,791 31 $69,246 32 $48,695 33 $34,987 34 $28,985 35 $35,631 W N O W H U O A A O W A H O WO W A O O O VDC 36 $54,679 37 $39,743 38 $41,255 39 $36,431 40 $26,578 41 $47,536 42 $36,571 43 $56,326 44 $31,425 45 $24,749 46 $26,452