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11.15. Table 11.7 gives data on 81 cars about MPG (average miles per gallons), HP (engine horsepower), VOL (cubic feet of cab space), SP (top speed, miles per hour), and WT (vehicle weight in 100 lb).
TABLE 11.7 PASSENGER CAR MILAGE DATA
|
Observation |
MPG |
SP |
HP |
VOL |
WT |
Observation |
MPG |
SP |
HP |
VOL |
WT |
|
1 |
65.4 |
96 |
49 |
89 |
17.5 |
42 |
32.2 |
106 |
95 |
106 |
30.0 |
|
2 |
56.0 |
97 |
55 |
92 |
20.0 |
43 |
32.2 |
109 |
102 |
92 |
30.0 |
|
3 |
55.9 |
97 |
55 |
92 |
20.0 |
44 |
32.2 |
106 |
95 |
88 |
30.0 |
|
4 |
49.0 |
105 |
70 |
92 |
20.0 |
45 |
31.5 |
105 |
93 |
102 |
30.0 |
|
5 |
46.5 |
96 |
53 |
92 |
20.0 |
46 |
31.5 |
108 |
100 |
99 |
30.0 |
|
6 |
46.2 |
105 |
70 |
89 |
20.0 |
47 |
31.4 |
108 |
100 |
111 |
30.0 |
|
7 |
45.4 |
97 |
55 |
92 |
20.0 |
48 |
31.4 |
107 |
98 |
103 |
30.0 |
|
8 |
59.2 |
98 |
62 |
50 |
22.5 |
49 |
31.2 |
120 |
130 |
86 |
30.0 |
|
9 |
53.3 |
98 |
62 |
50 |
22.5 |
50 |
33.7 |
109 |
115 |
101 |
35.0 |
|
10 |
43.4 |
107 |
80 |
94 |
22.5 |
51 |
32.6 |
109 |
115 |
101 |
35.0 |
|
11 |
41.1 |
103 |
73 |
89 |
22.5 |
52 |
31.3 |
109 |
115 |
101 |
35.0 |
|
12 |
40.9 |
113 |
92 |
50 |
22.5 |
53 |
31.3 |
109 |
115 |
124 |
35.0 |
|
13 |
40.9 |
113 |
92 |
99 |
22.5 |
54 |
30.4 |
133 |
180 |
113 |
35.0 |
|
14 |
40.4 |
103 |
73 |
89 |
22.5 |
55 |
28.9 |
125 |
160 |
113 |
35.0 |
|
15 |
39.6 |
100 |
66 |
89 |
22.5 |
56 |
28.0 |
115 |
130 |
124 |
35.0 |
|
16 |
39.3 |
103 |
73 |
89 |
22.5 |
57 |
28.0 |
102 |
96 |
92 |
35.0 |
|
17 |
38.9 |
106 |
78 |
91 |
22.5 |
58 |
28.0 |
109 |
115 |
101 |
35.0 |
|
18 |
38.8 |
113 |
92 |
50 |
22.5 |
59 |
28.0 |
104 |
100 |
94 |
35.0 |
|
19 |
38.2 |
106 |
78 |
91 |
22.5 |
60 |
28.0 |
105 |
100 |
115 |
35.0 |
|
20 |
42.2 |
109 |
90 |
103 |
25.0 |
61 |
27.7 |
120 |
145 |
111 |
35.0 |
|
21 |
40.9 |
110 |
92 |
99 |
25.0 |
62 |
25.6 |
107 |
120 |
116 |
40.0 |
|
22 |
40.7 |
101 |
74 |
107 |
25.0 |
63 |
25.3 |
114 |
140 |
131 |
40.0 |
|
23 |
40.0 |
111 |
95 |
101 |
25.0 |
64 |
23.9 |
114 |
140 |
123 |
40.0 |
|
24 |
39.3 |
105 |
81 |
96 |
25.0 |
65 |
23.6 |
117 |
150 |
121 |
40.0 |
|
25 |
38.8 |
111 |
95 |
89 |
25.0 |
66 |
23.6 |
122 |
165 |
50 |
40.0 |
|
26 |
38.4 |
110 |
92 |
50 |
25.0 |
67 |
23.6 |
122 |
165 |
114 |
40.0 |
|
27 |
38.4 |
110 |
92 |
117 |
25.0 |
68 |
23.6 |
122 |
165 |
127 |
40.0 |
|
28 |
38.4 |
110 |
92 |
99 |
25.0 |
69 |
23.6 |
122 |
165 |
123 |
40.0 |
|
29 |
46.9 |
90 |
52 |
104 |
27.5 |
70 |
23.5 |
148 |
245 |
112 |
40.0 |
|
30 |
36.3 |
112 |
103 |
107 |
27.5 |
71 |
23.4 |
160 |
280 |
50 |
40.0 |
|
31 |
36.1 |
103 |
84 |
114 |
27.5 |
72 |
23.4 |
121 |
162 |
135 |
40.0 |
|
32 |
36.1 |
103 |
84 |
101 |
27.5 |
73 |
23.1 |
121 |
162 |
132 |
40.0 |
|
33 |
35.4 |
111 |
102 |
97 |
27.5 |
74 |
22.9 |
110 |
140 |
160 |
45.0 |
|
34 |
35.3 |
111 |
102 |
113 |
27.5 |
75 |
22.9 |
110 |
140 |
129 |
45.0 |
|
35 |
35.1 |
102 |
81 |
101 |
27.5 |
76 |
19.5 |
121 |
175 |
129 |
45.0 |
|
36 |
35.1 |
106 |
90 |
98 |
27.5 |
77 |
18.1 |
165 |
322 |
50 |
45.0 |
|
37 |
35.0 |
106 |
90 |
88 |
27.5 |
78 |
17.2 |
140 |
238 |
115 |
45.0 |
|
38 |
33.2 |
109 |
102 |
86 |
30.0 |
79 |
17.0 |
147 |
263 |
50 |
45.0 |
|
39 |
32.9 |
109 |
102 |
86 |
30.0 |
80 |
16.7 |
157 |
295 |
119 |
45.0 |
|
40 |
32.3 |
120 |
130 |
92 |
30.0 |
81 |
13.2 |
130 |
236 |
107 |
55.0 |
|
41 |
32.2 |
106 |
95 |
113 |
30.0 |
|
|
|
|
|
|
|
Note: |
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VOL = cubic feet of cab space HP = engine horsepower
MPG = average miles per gallon SP = top speed, miles per hour
WT = vehicle weight, hundreds of pounds
Observation = car observation number (Names of cars not disclosed)
Source: U.S. Environmental Protection Agency, 1991, Report EPA/AA/CTAB/91-02.
a. Consider the following model:
MPGi = β1 + β2SP + β3HP + β4WT + ui
Estimate the parameters of this model and interpret the results. Do they make economic sense?
b. Would you expect the error variance in the preceding model to be het- eroscedastic? Why?
c. Use the White test to find out if the error variance is heteroscedastic.
d. Obtain White’s heteroscedasticity-consistent standard errors and t
values and compare your results with those obtained from OLS.
e. If heteroscedasticity is established, how would you transform the data so that in the transformed data the error variance is ho- moscedastic? Show the necessary calculations.