Do gun owners give the Republican Party higher ratings than people who do not ow

Question

Do gun owners give the Republican Party higher ratings than people who do not own guns? To find out, a researcher tests a regression model in which the dependent variable, y, is a feeling thermometer scale of the Republican Party. Respondents can give the Republican Party ratings that range from 0 (cold or negative) to 100 (warm or positive). The researcher creates a dummy variable, named “owner,” coded 1 for respondents who own a gun and 0 for respondents who do not. Owner is the independent variable, x. Here are the regression results:

y = 40.2 + 11.5(owner)

Standard error of b = .76

Adjusted R2 = .04

A. Based on these findings, the researcher concludes: “People who do not own guns rated the Republicans at 40.2, on average. However, among gun owners the Republicans averaged only 11.5 on the scale. Therefore, people who do not own guns are more pro-Republican than are people who own guns.” Is this inference correct? Why or why not?

B. Another conclusion reached by the researcher: “The independent variable has a statistically significant effect on the dependent variable.” Is this inference correct? Why or why not?

C. Yet another of the researcher’s conclusions: “The independent variable explains very little of the variation in the dependent variable.” Is this inference correct? Why or why not?

Explanation / Answer

(A)

“People who do not own guns rated the Republicans at 40.2, on average. However, among gun owners the Republicans averaged only 11.5 on the scale. Therefore, people who do not own guns are more pro-Republican than are people who own guns.” This statement is incorrect because among gun owners, the Republicans averaged (40.2+11.5)=51.7 and not 11.2

(B)

“The independent variable has a statistically significant effect on the dependent variable.” This statement is incorrect because the standard error of b is high and Adjusted R2 is low.

(C)

“The independent variable explains very little of the variation in the dependent variable.” This statement is correct because Adjusted R2 says that only 4% of variation is explained

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