More on understanding variance inflation factors (VIFk)

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Presentation transcript:

More on understanding variance inflation factors (VIFk)

Cement example

Pearson correlation of x2 and x4 = -0.973 The regression equation is x4 = 80.4 - 1.05 x2 Predictor Coef SE Coef T P Constant 80.396 3.777 21.28 0.000 x2 -1.04657 0.07492 -13.97 0.000 S = 4.038 R-Sq = 94.7% R-Sq(adj) = 94.2% The regression equation is x2 = 75.3 - 0.905 x4 Predictor Coef SE Coef T P Constant 75.289 2.204 34.16 0.000 x4 -0.90452 0.06475 -13.97 0.000 S = 3.754 R-Sq = 94.7% R-Sq(adj) = 94.2% Pearson correlation of x2 and x4 = -0.973

Regress y on x2 The regression equation is y = 57.4 + 0.789 x2 Predictor Coef SE Coef T P Constant 57.424 8.491 6.76 0.000 x2 0.7891 0.1684 4.69 0.001 S = 9.077 R-Sq = 66.6% R-Sq(adj) = 63.6% Analysis of Variance Source DF SS MS F P Regression 1 1809.4 1809.4 21.96 0.001 Residual Error 11 906.3 82.4 Total 12 2715.8

Regress y on x4 The regression equation is y = 118 - 0.738 x4 Predictor Coef SE Coef T P Constant 117.568 5.262 22.34 0.000 x4 -0.7382 0.1546 -4.77 0.001 S = 8.964 R-Sq = 67.5% R-Sq(adj) = 64.5% Analysis of Variance Source DF SS MS F P Regression 1 1831.9 1831.9 22.80 0.001 Residual Error 11 883.9 80.4 Total 12 2715.8

Regress y on x2 and x4 The regression equation is y = 94.2 + 0.311 x2 - 0.457 x4 Predictor Coef SE Coef T P VIF Constant 94.16 56.63 1.66 0.127 x2 0.3109 0.7486 0.42 0.687 18.7 x4 -0.4569 0.6960 -0.66 0.526 18.7 S = 9.321 R-Sq = 68.0% R-Sq(adj) = 61.6% Analysis of Variance Source DF SS MS F P Regression 2 1846.88 923.44 10.63 0.003 Residual Error 10 868.88 86.89 Total 12 2715.76

Is the variance of b4 inflated by a factor of 18.7? almost ….

Is the variance of b2 inflated by a factor of 18.7? again almost ….

Variance inflation factor VIFk The variance inflation factor quantifies “how much the variance of the estimated regression coefficient is inflated by the existence of multicollinearity.” The theory… The estimate…

Variance inflation factor VIFk To get the theoretical VIF4, , that Minitab reports, we need to multiply the ratio of the variance estimates by

Is the variance of b4 inflated by a factor of 18.7?

Is the variance of b2 inflated by a factor of 18.7?