Calculate the variance inflation factors

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Numerical Questions

Answer the following using the R statistical computing platform. Your answer should include the code you wrote, the output of such code, and written, English coding comments where necessary.

The attached data set found in "Topic 7 Assignment Data" shows mile per gallon (variable to be regressed) and the cars' specifications (explanatory) variables.

Does the correlation matrix give any indication of multicollinearity?

Calculate the variance inflation factors and the condition number of X′X. Is there any evidence of multicollinearity?

Find the eigenvectors associated with the smallest eigenvalues of X′X. Interpret the elements of these vectors. What can you say about the source of multicollinearity in these data?

Examine the patient satisfaction data from Topic 2 for multicollinearity. Perform a principle-component regression, and find the variance inflation factors. What can you conclude?

Theoretical Questions

Recall the principal-component regression model y=Zα+?, where Z=XT,α=T^' β,T^' X^' XT=Z^' Z=Λ.

Show that if X'X is in correlation form, Λ is the diagonal matrix of eigenvalues of X'X, and T is the corresponding matrix of eigenvectors, then the variance inflation factors are the main diagonal elements of TΛ^(-1) T'.

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Reference no: EM132963527

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