Question: 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.

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. Consider the model

(a) Fit the regression with the model above.

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

Compen- sation, y Sales, 1 Profits, Firm (thousands) (millions) (millions) $4, 600.6

Compen- sation, y Sales, 1 Profits, Firm (thousands) (millions) (millions) $4, 600.6 9, 255.4 Employ- iment, T3 $450 $128.1 48, 000 55. 900 13. 783 27, 765 34, 000 26. 500 30. 800 41.000 25. 900 8.600 21.075 6,874 39, 000 34, 300 19.405 3.586 3.905 4, 139 6. 255 10,605 65, 392 89, 400 387 783.9 3 368 1,526.2 136.0 179.0 4 277 1,683.2 676 2. 752.8 231.5 454 2.205.8 329.5 2. 384.6 2,746.0 1, 434.0 470.6 1.508.0 464.4 9.329.3 2, 377.5 1.174.3 409.3 724.7 578.9 966.8 591.0 4, 933.1 7, 613.2 3, 457.4 545.3 22, 862.8 2,361.0 2,614.1 507 381.8 496 237.9 487 383 311 222.3 63.7 149.5 30.0 577.3 250.7 82.6 61.5 10 11 12 13 271 524 498 343 354 324 225 254 208 14 15 16 17 18 19 20 90.8 63.3 42.8 48.5 310.6 21 518 22 406 491.6 23 332 228.0 54.6 55, 200 24 340 698 7,800 337, 119 25 3011.3 26 306 203.0 52. 000 613 27 50, 500 201.0 121.3 28 302 1,013.2 18, 625 97, 937 12, 300 71.800 4, 560.3 29 540 194.6 63.4 352.1 30 31 293 528 855.7 4,211.6 87. 700 14,600 5. 440.4 32 456 655.2 417 33 1.229.9 97.5

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