1. More on understanding variance inflation factors (VIFk)

2. Cement example

3. 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 =

4. 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

5. 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

6. 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

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

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

9. 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…

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

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

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