1. For the data of Example, ?nd the variance in?ation factors, and comment on their relative magnitudes.
2. Find the correlation between X1 and X 2 for the data of Example 11-1 pre- sented in Table 11-1. Is multicollinearity a problem here? Also ?nd the variance in?ation factors, and comment on their magnitudes.
3. Regress Y against X1, X 2, and X3 with the following sample data:
|
Y
13.79
|
X1
76.45
|
X2
44.47
|
X3
8.00
|
|
21.23
|
24.37
|
37.45
|
7.56
|
|
66.49
|
98.46
|
95.04
|
19.00
|
|
35.97
|
49.21
|
2.17
|
0.44
|
|
37.88
|
76.12
|
36.75
|
7.50
|
|
72.70
|
82.93
|
42.83
|
8.74
|
|
81.73
|
23.04
|
82.17
|
16.51
|
|
58.91
|
80.98
|
7.84
|
1.59
|
|
30.47
|
47.45
|
88.58
|
17.86
|
|
8.51
|
65.09
|
25.59
|
5.12
|
|
39.96
|
44.82
|
74.93
|
15.05
|
|
67.85
|
85.17
|
55.70
|
11.16
|
|
10.77
|
27.71
|
30.60
|
6.23
|
|
72.30
|
62.32
|
12.97
|
2.58
|
a. What is the regression equation?
b. Change the ?rst observation of X3 from 8.00 to 9.00. Repeat the regres- sion. What is the new regression equation?
c. Compare the old and the new regression equations. Does the comparison prove multicollinearity in the data? What is your suggestion for getting rid of the multicollinearity?
d. Looking at the results of the original regression only, could you have ?g- ured out that there is a multicollinearity problem? How?