Another researcher, after viewing the puny value of adjusted R-square in Exercis
ID: 3361054 • Letter: A
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 non-conservatives. The regression to be estimated: y = a + b1 (owner) + b2 (conservative), where “owner” is the gun/nonowner dummy and “conservative” is the conservative/non-conservative dummy. Here are the results (the standard errors for the regression coefficients are in parentheses):
y = 38.7 + 6.4 (owner) + 20.1 (conservative)
(1.2) (1.2)
Adjusted R2 = .16
A. What is the partial effect of gun ownership on ratings of Republicans, controlling for conservative beliefs? Is it reasonable to infer that, in the population, gun owners give the Republicans higher ratings than do nonowners? Explain
B. What is the partial effect of conservatism on the dependent variable, controlling for differences between gun owners and nonowners? Is it reasonable to infer that, in the population, conservatives give the Republicans higher ratings than do non-conservatives? Explain
C. Based on this regression, what is the mean Republican rating for gun-owning conservatives? For gun-owning non-conservatives?
D. The Adjusted R2 value is .16. 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. Name one other variable that may account for differences in the dependent variable. Briefly describe why you think this variable may contribute to the explanation of Republican ratings
Explanation / Answer
(A) The partial effect of gun ownership is that if some person owns a gun, then it increase the ratings of republicans by 6.4 points. We can infer that gun owners give the Republicans higher ratings than do nonowners. We can check its significance by dividing regression coefficient 1 by standard error.
t = 6.4/1.2 = 5.33 which given p - value in around less than 0.01 so we can say that there is significance effect of gun ownership on higher ratings on Republicans.
(B)
The partial effect of coservatism is that if some person is conservative in nature , then it increase the ratings of republicans by 20.1 points. We can infer that conservative people give the Republicans higher ratings than do nonowners. We can check its significance by dividing regression coefficient 2 by standard error.
t = 20.1/1.2 = 16.75 which gives p - value in around less than 0.01 so we can say that there is significance effect of conservatism on higher ratings on Republicans.
(c) what is the mean Republican rating for gun-owning conservatives
y = 38.7 + 6.4 (owner) + 20.1 (conservative)
y (gun owner - conservative) = 38.7 + 6.4 + 20.1 = 65.2
y(no gun not conservative) = 38.7
(D) R2 = 0.16
THis means that 16% of the variation in Republicans ratings is explained by both variables in the model. It also means that 84% is explained by variables not in the model.
(E) Normaly working class and rural people vote for republicans. So, rural and urba class dummy variables can be used alongwith the income group.