Based on a random sample of voters, you run a regression for Y, the approval rating of the current president's handling of the economy (on a 0 to 100 scale). There are several explanatory variables, including the voter's stated party preference (Republican, Democrat, or Independent). Because this is a text variable, you create three dummy variables: R (1 if Republican, 0 otherwise), D (1 if Democrat, 0 otherwise), and I (1 if Independent, 0 otherwise). Which of the following can you conclude?

a. If you include all three of these dummies in the regression, the sum of their estimated coefficients will have a meaningful interpretation.

b. If you include only the dummies R and I in the equation, and their coefficients are -5.2 and 1.3, this indicates that all else being equal (i.e., all other explanatory variables remaining constant), Democrats have the lowest average approval rating.

c. If you include only the dummies D and I in the equation, and their coefficients are 3.1 and 1.2, this implies that if you reran the same regression, except with only the dummies R and I included, the estimated coefficients of R and I would be -3.1 and 4.3.

d. If you include only the dummies D and R in the equation, and their coefficients are -4.7 and 5.4, this implies that if you reran the same regression, except with only the dummies D and I included, the estimated coefficients of D and I would be -10.1 and -5.4.