Question

Do gun owners give the Republican Party higher ratings than do 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 11.5 on the scale. Therefore, people who do not own guns are more pro-Republican that are people who own guns." Is this inference correct? Why or why not?

Answer 1

No, the inference is not correct. The first inference is correct that 40.2 is the intercept of regression line which means people who do not own the gun rated the Republicans at 40.2 however those who own gun rated Republicans 40.2 + 11.5*1 which equals to 51.7. Hence the conclusion should be that people who own the gun are pro Republican.

One more point to note here is standard error of b which is .76 (lower is better) however the value of adjusted R2 is 0.04 which is very low and means that number of samples are not enough to have higher confidence level from the research. Adjusted R2 ranges from 0 to 1.