In an effort to model executive compensation for the year 1979, 33 firms were selected, and data… 1 answer below »

In an effort to model executive compensation for the year 1979, 33 firms were selected, and data… 1 answer below »

In an effort to model executive compensation for the year 1979, 33 firms were selected, and data were gathered on compensation, sales, profits, and employment. The following data were gathered for the year 1979.

Firm

Compensation, y (thousands)

Sales, x1 (millions)

Profits, x2 (millions)

Employ- ment, x3

1

$450

$4,600.60

$128.10

48,000

2

387

9255.4

783.9

55,900

3

368

1526.2

136.0

13,783

4

277

1683.2

179.0

27,765

5

676

2752.8

231.5

34,000

6

454

2205.8

329.5

26,500

7

507

2384.6

381.8

30,800

8

496

2746.0

237.9

41,000

9

487

1434.0

222.3

25,900

10

$383

$470.60

$63.70

8600

11

311

1508.0

149.5

21,075

12

271

464.4

30.0

6874

13

524

9329.3

577.3

39,000

14

498

2377.5

250.7

34,300

15

343

1174.3

82.6

19,405

16

354

409.3

61.5

3586.0

17

324

724.7

90.8

3905.0

18

225

578.9

63.3

4139.0

19

254

966.8

42.8

6255.0

20

208

591.0

48.5

10,605

21

518

4933.1

310.6

65,392

22

406

7613.2

491.6

89,400

23

332

3457.4

228.0

55,200

24

340

545.3

54.6

7800

25

698

22,862.80

3011.3

337,119

26

306

2361

203.0

52,000

27

613

2614.1

201.0

50,500

28

302

1013.2

121.3

18,625

29

540

4560.3

194.6

97,937

30

293

855.7

63.4

12,300

31

528

4211.6

352.1

71,800

32

456

5440.4

655.2

87,700

33

417

1229.9

97.5

14,600

Consider the model

yi = β0 + β1 ln x1i+ β2 ln x2i

+ β3 ln x3i+ ?i, i= 1, 2, . . . , 33.

(a) Fit the regression with the model above.

(b) Is a model with a subset of the variables preferable to the full model?

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