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# 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 ...

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