EXAMPLE 2 Presidential elections, the Reagan years

Republican Ronald Reagan was elected president twice, in 1980 and in 1984. His economic policy of tax cuts to stimulate the economy, eventually leading to increases in tax revenue, was still advocated by some Republican presidential candidates in 2015. Figure 15.2 plots the percentage of voters in each state who voted for Reagan’s Democratic opponents: Jimmy Carter in 1980 and Walter Mondale in 1984. The plot shows a positive straight-line relationship. We expect this because some states tend to vote Democratic and others tend to vote Republican. There is one outlier: Georgia, President Carter’s home state, voted 56% for the Democrat Carter in 1980 but only 40% Democratic in 1984.

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We could use the regression line drawn in Figure 15.2 to predict a state’s 1984 vote from its 1980 vote. The points in this figure are more widely scattered about the line than are the points in the fossil bone plot in Figure 15.1. The correlations, which measure the strength of the straight-line relationships, are r = 0.994 for Figure 15.1 and r = 0.704 for Figure 15.2. The scatter of the points makes it clear that predictions of voting will be generally less accurate than predictions of bone length.