Data 2.9 on page 103 introduces data on the approval rating of an incumbent US president and the margin of victory or defeat in the subsequent election (where negative numbers indicate the margin by which the incumbent president lost the re-election campaign). The data are reproduced in Table 9.5 and are available in Election Margin.

Table 9.5

Computer output for summary statistics for the two variables and for a regression model to predict the margin of victory or defeat from the approval rating is shown:

Use values from this output to calculate and interpret the following. Show your work.
(a) A 95% confidence interval for the mean margin of victory for all presidents with an approval rating of 50%
(b) A 95% prediction interval for the margin of victory for a president with an approval rating of 50%.
(c) A 95% confidence interval for the mean margin of victory if we have no information about the approval rating.

Data 2.9 on page 103

When a US president runs for re-election, how strong is the relationship between the president€™s approval rating and the outcome of the election? Table 2.29 includes all the presidential elections since 1940 in which an incumbent was running and shows the presidential approval rating at the time of the election and the margin of victory or defeat for the president in the
election. The data are available in ElectionMargin.

Table 2.29

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Approval Margin 70 57 31 57 18.2 55 8.5 39 -5.5 49 2.4 62 50 4.5 67 48 10.0 22.6 -9.7 15.4 23.2 -2.1 Variable N Mean StDev 53.18 Approval Margin 11 11.54 11 7.95 11.17 The regression equation is Margin = - 36.5 + 0.836 Approval Predictor Coef SE Coef т Constant -36.483 8.855 -4.12 0.003 Approval 0.8356 0.1631 5.12 0.001 S= 5.95019 R-Sq = 74.5% R-Sq(adj) = 71.6% Analysis of Variance Source DF MS Regression 929.74 929.74 26.26 0.001 Residual Error 318.64 35.40 Total 10 1248.39