Charisma of top-level leaders. According to a theory proposed in the Academy of Management Journal (August 2015), top leaders in business are selected based on their organizationâ€™s performance as well as the leaderâ€™s charisma. To test this theory, the researchers collected data on 24 U.S. presidential elections from 1916 to 2008. 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. The charisma of both the Democratic and Republican candidates was measured (on a 150-point scale) based on the candidatesâ€™ acceptance speeches at their partyâ€™s national convention. One of the independent variables of interest was the difference (x) between the Democratic and Republican charisma values. These data are listed in the accompanying table.
a. Find the least squares line relating Democratic vote share (y) to charisma difference (x).
b. Graph the least squares line on a scatterplot of the data. Is there visual evidence of a linear relationship between the variables? Is the relationship positive or negative?
c. Interpret, practically, the estimated slope of the line.