Refer to the Academy of Management Journal (August, 2015) study of the charisma of top leaders in business, Exercise 12.76. The researchers analyzed data collected for 24 U.S. presidential elections where the dependent variable of interest was Democratic vote share (y), measured as the percentage of voters who voted for the Democratic candidate in the national election. One potential quantitative predictor of vote share was the difference (x1) between the Democratic and Republican candidates' charisma values. (Recall that charisma was measured on a 150-point scale based on the candidates' acceptance speeches at their party's national convention.) One potential qualitative predictor was whether or not the election was affected by a World War: x2 = {1 if war, 0 if not}.
a. Propose a model that describes the relationship between Democratic vote share (y) and charisma difference (x1) as two nonparallel straightlines, one for each level of World War status (x2).
b. In terms of the β's of the model, part a, what is the slope of the line relating Democratic vote share (y) to charisma difference (x1) for election years affected by a World War?
c. In terms of the β's of the model, part a, what is the slope of the line relating Democratic vote share (y) to charisma difference (x1) for election years not affected by a World War?
d. In terms of the β's of the model, part a, what is the effect of a World War on mean Democratic vote share, E(y), for all election years when there is no charisma difference (i.e., x1 = 0)?
e. In terms of the β's of the model, part a, what is the effect of a World War on mean Democratic vote share, E(y), for all election years when there the charisma difference is x1 = 50?
f. Fit the model, part a, to the data in the file. Is there sufficient evidence to indicate that the linear effect of the charisma difference on mean Democratic vote share depends on World War status? Test using α = .10.