Answer the following using the R statistical computing platform.

mile per gallon (variable to be regressed) and the cars' specifications (explanatory) variables.

1.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 ofX?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?

Fuel-Efficiency-(g/km) Cetane-Number Density Viscosity Initial-Boiling-Pt Final-Boiling-Pt Flash-Pt Total-Aromatics 343 52.8 811.7 2.11 220 261 87 1.8 356 52.8 811.7 2.11 220 261 87 1.8 344 50 821.3 2.11 223 260 87 16.6 356 50 821.3 2.11 223 260 87 16.6 352 47.2 832 2.09 221 261 92 23 361 47.2 832 2.09 221 261 92 23 372 47 831.3 2.26 190 323 75 25.1 355 47 831.3 2.26 190 323 75 25.1 375 48.3 836.8 2.47 180 364 71 26.1 359 48.3 836.8 2.47 180 364 71 26.1 364 44.7 808.3 1.41 180 300 64 20 357 44.7 808.3 1.41 180 300 64 20 368 55.7 808.7 1.44 176 299 64 20.5 360 55.7 808.7 1.44 176 299 64 20.5 372 52.8 813.2 1.96 175 301 75 17.3 352 52.8 813.2 1.96 175 301 75 17.3

Fuel-Efficiency-(g/km) Cetane-Number Density Viscosity Initial-Boiling-Pt Final-Boiling-Pt Flash-Pt Total-Aromatics 343 52.8 811.7 2.11 220 261 87 1.8 356 52.8 811.7 2.11 220 261 87 1.8 344 50 821.3 2.11 223 260 87 16.6 356 50 821.3 2.11 223 260 87 16.6 352 47.2 832 2.09 221 261 92 23 361 47.2 832 2.09 221 261 92 23 372 47 831.3 2.26 190 323 75 25.1 355 47 831.3 2.26 190 323 75 25.1 375 48.3 836.8 2.47 180 364 71 26.1 359 48.3 836.8 2.47 180 364 71 26.1 364 44.7 808.3 1.41 180 300 64 20 357 44.7 808.3 1.41 180 300 64 20 368 55.7 808.7 1.44 176 299 64 20.5 360 55.7 808.7 1.44 176 299 64 20.5 372 52.8 813.2 1.96 175 301 75 17.3 352 52.8 813.2 1.96 175 301 75 17.3Satisfactic Age Severity Anxiety 68 55 50 2.1 77 46 24 2.8 96 30 46 3.8 80 35 48 4.5 43 59 58 2 41 61 65 5.1 26 74 60 5.5 88 39 42 3.2 75 82 42 3.1 57 27 50 2.4 56 51 38 2.2 88 53 30 2.1 88 41 31 1.9 102 37 34 3.1 88 24 30 3 70 27 48 4.2 82 50 61 4.6 43 58 71 5.3 46 60 62 7.2 56 62 38 7.8 59 68 41 7 26 70 66 6.2 52 79 37 4.1 73 39 42 3.5