Special-purpose transformations: for a study of congressional elections, you would like a measure of the relative amount of money raised by each of the two majorparty candidates in each district....

Special-purpose transformations: for a study of congressional elections, you would like a measure of the relative amount of money raised by each of the two majorparty candidates in each district. Suppose that you know the amount of money raised by each candidate; label these dollar values D_i
and R_i. You would like to combine these into a single variable that can be included as an input variable into a model predicting vote share for the Democrats.

(a) Discuss the advantages and disadvantages of the following measures:

• The simple difference, D_i
− R_i

• The ratio, D_i/R_i

• The difference on the logarithmic scale, log D_i
− log R_i

• The relative proportion, D_i/(D_i
+ R_i).

(b) Propose an idiosyncratic transformation (as in the example on page 65) and discuss the advantages and disadvantages of using it as a regression input.