• VIF - (5 pts.): Review the instructions below for calculating VIF (Variance Inflation Factor). In the full model shown above, the VIF for Shore Excursions is 1.07. Follow the instructions below to calculate it. (Note that Xidenotes a predictor in the original model.) Show the following Minitab output for credit:
• The Coefficients Table and Model Summary for the regression that is needed;
• The calculation of VIF.
• Give a brief interpretation of the VIF for Shore Excursions in the full model.

Calculation and analysis [edit] We can calculate k different VIFs (one for each X) in three steps: Step one (edit) First we run an ordinary least square regression that has X, as a function of all the other explanatory variables in the first equation. If i = 1, for example, equation would be X1 = @o + a2X2 + az X: +...+aXx te where an is a constant and e is the error term. Step two [edit] Then, calculate the VIF factor for B; with the following formula : 1 1- R where is the coefficient of determination of the regression equation in step one, with X, on the left hand side, and all other predictor variables (all the other X variables) on the right hand side. VIF, = Step three [edit] Analyze the magnitude of multicollinearity by considering the size of the VIF(B:). A rule of thumb is that if VIF (@:) > 10 then multicolinearity is high15) (a cutoff of 5 is also commonly used()). Some software instead calculates the tolerance which is just the reciprocal of the VIF. The choice of which to use is a matter of personal preference. Interpretation [edit] The square root of the variance inflation factor indicates how much larger the standard error increases compared to if that variable had correlation to other predictor variables in the model. Example If the variance inflation factor of a predictor variable were 5.27 (v5.27 = 2.3), this means that the standard error for the coefficient of that predictor variable is 2.3 times larger than if that predictor variable had 0 correlation with the other predictor variables. Calculation and analysis [edit] We can calculate k different VIFs (one for each X) in three steps: Step one (edit) First we run an ordinary least square regression that has X, as a function of all the other explanatory variables in the first equation. If i = 1, for example, equation would be X1 = @o + a2X2 + az X: +...+aXx te where an is a constant and e is the error term. Step two [edit] Then, calculate the VIF factor for B; with the following formula : 1 1- R where is the coefficient of determination of the regression equation in step one, with X, on the left hand side, and all other predictor variables (all the other X variables) on the right hand side. VIF, = Step three [edit] Analyze the magnitude of multicollinearity by considering the size of the VIF(B:). A rule of thumb is that if VIF (@:) > 10 then multicolinearity is high15) (a cutoff of 5 is also commonly used()). Some software instead calculates the tolerance which is just the reciprocal of the VIF. The choice of which to use is a matter of personal preference. Interpretation [edit] The square root of the variance inflation factor indicates how much larger the standard error increases compared to if that variable had correlation to other predictor variables in the model. Example If the variance inflation factor of a predictor variable were 5.27 (v5.27 = 2.3), this means that the standard error for the coefficient of that predictor variable is 2.3 times larger than if that predictor variable had 0 correlation with the other predictor variables