MPG - VIF and Backward Selection

Now its time to build a model.

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Build a model that contains all your transformed variables and the dummy variables you created in the the dummy vars assignment. 

  •  Is there any multicolinearity issues (Correlation Matrix. VIF)?
  •  Removes a variable one at a time. The one with the highest VIF. Then run the regression without that variable. Recalculate your VIF for the remaining variables. Continue to do this until you have removed multicollinearity from your model.  Remember that we can't just remove one level of a dummy variable from the model. It is all or none. Are you willing to tolerate any multicollinearity in the model?
  • Perform backward elimination on the remaining variables.
  • This again requires removing variables based on P values.
  • Is the model specification different than you anticipated from your EDA?
  • Interpret the model output. 0 What does your ANOVA table tell you?
  • What about the goodness of fit statistics (R, Rsquare, Standard Error)?
  •  interpret your individual parameters... do they make sense in terms of direction and magnitude? They should all be significant or near significant  What is the regression equation for the prediction? 

Submit via canvas. Include all relevant outputs and explanations of what you did and your thinking. This assignment is the culmination of several lectures.