More on understanding variance inflation factors (VIFk)

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More on understanding variance inflation factors
(VIFk)
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Cement example
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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
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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
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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
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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
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Is the variance of b4 inflated by a factor of
18.7?
almost .
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Is the variance of b2 inflated by a factor of
18.7?
again almost .
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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
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Variance inflation factor VIFk
To get the theoretical VIF4,
, that Minitab reports,
we need to multiply the ratio of the variance
estimates by
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Is the variance of b4 inflated by a factor of
18.7?
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Is the variance of b2 inflated by a factor of
18.7?