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More on understanding variance inflation factors (VIF k )

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Presentation on theme: "More on understanding variance inflation factors (VIF k )"— Presentation transcript:

1 More on understanding variance inflation factors (VIF k )

2 Cement example

3 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

4 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 x 2

5 Regress y on x 4 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

6 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 Regress y on x 2 and x 4

7 Is the variance of b 4 inflated by a factor of 18.7? almost ….

8 Is the variance of b 2 inflated by a factor of 18.7? again almost ….

9 Variance inflation factor VIF k 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…

10 Variance inflation factor VIF k To get the theoretical VIF 4,, that Minitab reports, we need to multiply the ratio of the variance estimates by

11 Is the variance of b 4 inflated by a factor of 18.7?

12 Is the variance of b 2 inflated by a factor of 18.7?


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