Homework 5

1) Go over the regression example handout.  No thinking here, but try to understand what the windows do, and what the various forms are.

2) Analyze the "cars" data.  You can find this in the Vista folder, under Data: Regres.   Your goal is to find the best possible linear model to predict mpg (miles per gallon).  You should justify why your model is appropriate.  Also, you should interpret the model (what do the coefficients mean)?  Here's a plan of attack:

    Describe the relations of the predictors to the response.  Do they look linear, quadratic?  (You can add quadratic terms, or rather, convert linear terms into quadratic terms, by using the box-cox slider under the "Transform" menu.  Other packages let you add a new variable x^2.)
    Fit all of the variables.  Which look significant, which do not? Any surprises?   Examine the diagnostic plots (Visualize Model).  What do you learn?
    Fix any deviations from normality, or add squared terms, or do any necessary transformation.  Fit model again.
    Choose a set of predictors that you think "best".
 

Note: The ViSta philosophy, apparently excludes adding quadratic (or higher) powers of variables.  There is sound reason for this: these powers will be correlated with the lower powers and this correlation contradicts some of the assumptions of the regression.  (Multicollinearity.)  On the other hand, this can still provide a useful model in some situations.  Still, you can often avoid adding quadratic powers by transforming the variables appropriately, and the box-cox slider will help you do this.