Table gives the level of gross fixed capital formation Y , sales X1, both in thousands of dollars, and a productivity index X2, for 35 firms in an industry. It is expected that Y will be directly related to both X1 and X2. Regress Y on X1 and X2 for (a) the entire sample, (b) the 14 observations with the smallest values of X2 and record ESS1, and (c) the 14 observations with the largest values of X2 and record ESS2. (d) Test for the presence of heteroscedasticity.
Table Gross Fixed Capital Formation, Sales, and Productivity in 35 Firms
|
Firm
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
|
Y
|
30.9
|
31.5
|
43.2
|
36.9
|
44.3
|
30.5
|
32.3
|
42.9
|
31.2
|
39.1
|
35.7
|
40.8
|
|
X1
|
135
|
150
|
300
|
225
|
310
|
105
|
170
|
285
|
145
|
250
|
205
|
275
|
|
X2
|
10.3
|
10.8
|
16.4
|
12.9
|
16.7
|
10.0
|
10.9
|
15.9
|
10.6
|
14.6
|
12.1
|
15.5
|
|
Firm
|
13
|
14
|
15
|
16
|
17
|
18
|
19
|
20
|
21
|
22
|
23
|
24
|
|
Y
|
31.2
|
42.1
|
32.8
|
36.3
|
37.4
|
30.5
|
33.4
|
37.4
|
44.9
|
33.4
|
45.2
|
30.2
|
|
X1
|
140
|
280
|
180
|
215
|
235
|
110
|
190
|
230
|
315
|
195
|
320
|
100
|
|
X2
|
10.5
|
15.6
|
10.9
|
12.5
|
13.8
|
10.0
|
11.1
|
13.1
|
17.1
|
11.3
|
17.3
|
9.9
|
|
Firm
|
25
|
26
|
27
|
28
|
29
|
30
|
31
|
32
|
33
|
34
|
35
|
|
|
Y
|
45.9
|
46.8
|
35.1
|
40.2
|
47.9
|
30.7
|
38.1
|
49.3
|
31.9
|
37.8
|
31.5
|
|
X1
|
330
|
345
|
200
|
260
|
350
|
120
|
250
|
355
|
165
|
245
|
150
|
|
X2
|
17.5
|
17.9
|
11.5
|
14.9
|
18.3
|
10.1
|
14.1
|
18.5
|
10.8
|
13.9
|
10.7
|
(a) Assuming that the error variance is proportional to X2 in Prob. 9.21, (a) correct for heteroscedasticity.
(a) What is the value of the new intercept and the slope coefficients associated with X1 and X2? How do they compare with the corresponding values before the transformation?