Solutions Manual to Accompany Introduction to Linear Regression Analysis, 5th Edition

Chapter 9

Multicollinearity

9.1 a. The correlation between x₁ and x₂ is .824.

b. The variance inflation factors are 3.1.

c. The condition number of X′X is κ = 40.68 which indicates that multicollinearity is not a problem in these data.

9.3 The eigenvector associated with the smallest eigenvalue is

Eigenvector

−0.839

0.081

0.437

0.117

0.289

All four factors contribute to multicollinearity.

9.5 There are two large condition indices in the non-centered data. In general, it is better to center.

9.7 a. The correlation matrix is

which indicates that there is a potential problem with multicollinearity.

b. The variance inflation factors are

Regressor	VIF
x1	117.6
x2	33.9
x3	116.0
x6	4.6
x7	5.4
x8	18.2
x9	7.6
x10	78.6
x11	5.1

which indicates there is evidence of multicollinearity.

9.9 The condition indices are

1.00 9.65 61.93 126.11 2015.02 5453.08 44836.79 85564.32 5899200.59 8.86 × 1012

which indicate a serious problem with multicollinearity.

9.11 The condition number is κ = 24,031.36 which indicates a problem with multicollinearity. The variance inflation factors shown below indicate evidence of multicollinearity.

Regressor	VIF
x1	3.67
x2	7.73
x3	19.20
x4	7.46
x5	4.69
x6	7.73
x7	1.12

9.13 The condition number is κ = 12400885.78 ...