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What happens when more predictor variables are added?
When predictor variables are correlated, the precision of the estimated regression coefficients decreases as more predictor variables are added to the model. Here’s the relevant portion of the table:
Now, here’s where you have to turn on your imagination. The primary characteristic of the data — because the predictors are perfectly uncorrelated — is that the predictor values are spread out and anchored in each of four corners, providing a solid base over which to draw the response plane.
The regression of the response y = BP on the predictors x 2 = Weight and x 3 = BSA (in that order): yields the estimated coefficients b 2 = 1.039 and b 3 = 5.83, the standard errors se ( b 2) = 0.193 and se ( b 3) = 6.06, and the sequential sum of squares SSR ( x 3 | x 2) = 2.814.
How to find the best fitting plane for a predictor?
Upon regressing the response y on the uncorrelated predictors x 1 and x 2, Minitab (or any other statistical software for that matter) will find the “best fitting” plane through the data points: Click on the Best Fitting Plane button in order to see the best fitting plane for this particular set of responses.
How is attendance used as a predictor variable?
In order to gain baseline data that can be used to create her program, Mia decides to conduct a study. Mia wants to know if a relationship exists between first generation college students’ attendance and grade point average. More specifically, she wants to test her hypothesis that attendance can be used to predict grade point average.
It appears as if, when predictors are highly correlated, the answers you get depend on the predictors in the model. That’s not good! Let’s proceed through the table and in so doing carefully summarize the effects of multicollinearity on the regression analyses.