Question

Another researcher, after viewing the puny value of adjusted R-square in Exercise 4, suggests that another variable—whether individuals are liberal or conservative—may shape evaluations of the Republican Party. This researcher defines a dummy variable, “conservative,” which is coded 1 for self-described conservatives and 0 for nonconservatives. The regression to be estimated: y = a+b₁ (owner)+b₂ (conservative), where “owner” is the gun owner/nonowner dummy and “conservative” is the conservative/nonconservative dummy .

Here are the results (the standard errors for the regression coefficients are in parentheses):

y = 30.0+7.2(owner)+24.8(conservation)(.70)(.67)    

Adjusted R² = .23

Type-in your responses to a-g in the box below:

a) (i) What is the partial effect of gun ownership on ratings of Republicans, controlling for conservative beliefs? (ii) Is it reasonable to infer that, in the population, gun owners give the Republicans higher ratings than do nonowners? (iii) Explain.

B) (i) What is the partial effect of conservatism on the dependent variable, controlling for differences between gun owners and nonowners? (ii) Is it reasonable to infer that, in the population, conservatives give the Republicans higher ratings than do nonconservatives? (iii) Explain.

c) (i) Based on this regression, what is the mean Republican rating for gun-owning conservatives? (ii) For gun-owning nonconservatives?

d) The adjusted R² value is .23. This means that ______________ percent of the variation in Republican ratings is explained by both variables in the model. It also means that ____________ percent is explained by variables not in the model.

e) When owner is used as the sole predictor of Republican ratings (Exercise 5), it has a regression coefficient equal to 11.5. In this exercise, when conservative is added to the regression model, the effect of owner drops to 7.2. Explain why the effect is weaker in the multiple regression model than in the bivariate regression model.

f) The correlation between owner and conservative is equal to .17. (i) Is multicollinearity as problem in this regression model? (ii) Explain how you know.

G) (i) Name one other variable that may account for differences in the dependent variable. (ii) Briefly describe why you think this variable may contribute to the explanation of Republican ratings.

Answer 1