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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 = 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 The regression equation is y = 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 x 2

5 Regress y on x 4 The regression equation is y = 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 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 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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