Another researcher working with the American National Election Study wants to investigate the relationship between age and feeling thermometer ratings of the Supreme Court. He conducts a bivariate regression between the two variables.

a. The slope for age in the bivariate regression is 0.08. What does this slope mean, in words? Based on the slope, how does the relationship between age and ratings of transgender people (Problem 8) compare to the relationship between age and ratings of the Supreme Court?

b. The researcher decides to add respondents’ party affiliation as an additional independent variable. The variable, Democrat, measures whether the respondent identifies as a Democrat (1) or another party (0). The slope for Democrat is 3.23. Explain what the slope for the Democrat variable means here.

c. The researcher’s statistical software program produces an F-statistic of 25.68 for the model and standard errors of 0.016 and 0.647 for the slopes of age and party affiliation, respectively. All three of these statistics are associated with p-values less than 0.001. Would we be better off using this regression equation to predict Supreme Court ratings than using the sample mean ratings as the predicted rating for all respondents? Which statistic answers this question?

d. The researcher wants to know the standard error of the estimate for the regression equation. He knows that the sum of squared residuals—Σ(y – yˆ)2—

equals 1,338,728 and the sample size is 3,593. Use this information to calculate the standard error of the estimate. Explain what it means in words.

e. The researcher wants to know the r2 value for the regression equation. He knows that the sum of all squared deviations of the mean Supreme Court rating from the predicted value for each respondent is 19,149.5. He knows that the sum of squared deviations of the mean Supreme Court rating from the actual rating for each respondent is 1,357,877.5. Find r2 and explain what it means in words.

f. Compare the tests of inference described in Part c (standard errors of the slopes and F-statistic) and the goodness-of-fit measures (standard error of the estimate and r2) that you calculated for Parts d and

e. What can you conclude about the statistical significance compared to the substantive importance of the effects of age and party affiliation on thermometer ratings of the Supreme Court?