# Solved – How to use eigenvectors to identify which variables are involved in collinearity?

The question involves a regression of \$Y\$ on \$11\$ predictor variables \$X_1\$ through \$X_{11}\$.

The problem asks me to identify the variables involved in the collinearity using the eigenvectors that correspond to small eigenvalues.

Using R, I have calculated the \$11\$ eigenvalues and eigenvectors, but I am not sure how to use an eigenvector to see which predictor variables are involved in the collinearity.

`` [1] 7.702574847 1.403077880 0.773435643 0.577055424 0.211498935 0.141941470 0.095142049  [8] 0.050092536 0.033266309 0.008417705 0.003497202  \$vectors             [,1]         [,2]        [,3]         [,4]         [,5]        [,6]        [,7]  [1,] -0.3529639 -0.112431387  0.03114403 -0.006932422  0.026272973 -0.09512815  0.26787382  [2,] -0.3299718 -0.260762001  0.07836539 -0.194970349 -0.142783457 -0.23889898  0.34910433  [3,] -0.3510109 -0.139829772  0.04294522 -0.004153543 -0.084990459 -0.18488343  0.35518667  [4,]  0.1610427 -0.552726480  0.11863260  0.785849610  0.096920435  0.09122188  0.09287761  [5,]  0.2663779 -0.346997347 -0.43309789 -0.352178691  0.516283052  0.07200995  0.06450059  [6,] -0.2047881 -0.548146807  0.41844801 -0.380746710 -0.007176897  0.38287792 -0.37681067  [7,]  0.3040550 -0.352222407 -0.22122179 -0.134117215 -0.050372348 -0.57691563 -0.02079064  [8,] -0.3232988 -0.078466513 -0.36961713  0.180329365 -0.200485930 -0.20407455 -0.67496023  [9,] -0.3026624  0.006019985 -0.54645511  0.094905101  0.106514020  0.51959464  0.19659254 [10,] -0.3446125 -0.100475266 -0.26679114  0.040652506 -0.028959499 -0.14008874 -0.06284718 [11,] -0.3117090  0.181885175  0.24279993  0.119155548  0.800493659 -0.27479473 -0.16382124              [,8]        [,9]        [,10]        [,11]  [1,] -0.25888638  0.49677393 -0.290946296  0.617904045  [2,]  0.05057424 -0.65243209  0.290811120  0.258528596  [3,] -0.06800437  0.03290868 -0.466442937 -0.681570251  [4,] -0.06188507 -0.06292276  0.051311641  0.012735988  [5,] -0.43886854 -0.13804308 -0.086127357 -0.045372936  [6,]  0.16574908  0.13359309 -0.004651702 -0.059626414  [7,]  0.55944398  0.24949398 -0.055978181  0.049028663  [8,] -0.15486222 -0.25287357 -0.294111256  0.091346835  [9,]  0.52415223 -0.01482782 -0.055178229  0.052597726 [10,] -0.20261712  0.39402290  0.714256660 -0.259679096 [11,]  0.22167146 -0.06274209  0.017189710 -0.009773591 ``

Above are the \$11\$ eigenvalues and then their corresponding eigenvectors.

Any help would be greatly appreciated.

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