# More on understanding variance inflation factors (VIFk)

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More on understanding variance inflation factors (VIFk)

Cement example

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 =

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

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

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

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?