According to a theory proposed in the Academy of Management Journal (August 2015), top leaders in business are selected based on their organization's performance as well as the leader'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 candidates' acceptance speeches at their party'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.

Transcribed Image Text:

Vote Share Year Charisma Difference 1916 51.68 -6.0 1920 36.15 -60.0 18.0 1924 41.74 1928 41.24 4.0 59.15 -22.0 1932 1936 62.23 -14.5 1940 54.98 -7.5 1944 53.78 -10.0 1948 52.32 -10.5 1952 44.71 2.0 1956 42.91 0.0 50.09 61.20 1960 -34.5 1964 -29.0 1968 49.43 -20.5 1972 38.21 -6.0 1976 51.05 14.0 1980 44.84 -12.0 -42.0 1984 40.88 46.17 53.62 54.74 1988 -34.0 18.5 1992 1996 -16.5 -2.5 2000 50.26 2004 48.77 53.69 48.5 13.5 2008