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**More on understanding variance inflation factors (VIFk)**

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Cement example

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**Pearson correlation of x2 and x4 = -0.973**

The regression equation is x4 = x2 Predictor Coef SE Coef T P Constant x S = R-Sq = 94.7% R-Sq(adj) = 94.2% The regression equation is x2 = x4 Predictor Coef SE Coef T P Constant x S = R-Sq = 94.7% R-Sq(adj) = 94.2% Pearson correlation of x2 and x4 =

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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 x S = R-Sq = 66.6% R-Sq(adj) = 63.6% Analysis of Variance Source DF SS MS F P Regression Residual Error Total

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**Regress y on x4 The regression equation is y = 118 - 0.738 x4**

Predictor Coef SE Coef T P Constant x S = R-Sq = 67.5% R-Sq(adj) = 64.5% Analysis of Variance Source DF SS MS F P Regression Residual Error Total

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**Regress y on x2 and x4 The regression equation is**

y = x x4 Predictor Coef SE Coef T P VIF Constant x x S = R-Sq = 68.0% R-Sq(adj) = 61.6% Analysis of Variance Source DF SS MS F P Regression Residual Error Total

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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?**

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