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 lnx1i+β2 lnx2i
+β3 lnx3i+ ?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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