March 2013
Beginner
164 pages
2h 11m
English
book
Solutions Manual to Accompany Introduction to Linear Regression Analysis, 5th Edition
by Ann G. Ryan, Douglas C. Montgomery, Elizabeth A. Peck, G. Geoffrey Vining, Anne G. Ryan
Content preview from Solutions Manual to Accompany Introduction to Linear Regression Analysis, 5th Edition
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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 ...
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