Researchers at the University of West Florida used regression analysis to build a model for predicting the outcome of presidential elections (Political Analysis, Vol. 17, 2009). The dependent variable of interest was Yt = percentage of the two-party vote won by the incumbent party's candidate in election year t. Independent variables included in the model are similar to those listed below.
Fiscal policy of incumbent party in election year t: X1t = {1 if expansion, 0 if not}
Duration of incumbent party: X2t = number of consecutive terms served prior to election year t
Party of incumbent in election year t: X3t = {1 if Democrat, 0 if Republican}
GDP trend in election year t: X4t = number of quarters of the previous administration where the GDP 7 3.2%
GDP growth rate: X5t = growth rate of the GDP in the first three quarters of election year t
a. Write a first-order regression model for E(Yt) as a function of the five independent variables.
b. The model, part a, was fit to data collected for n = 24 election years (from 1916 to 2008). The coefficient of determination was reported as R2 = .91. Interpret this result, practically.
c. Use the value of R2 to compute the F-statistic for testing the global adequacy of the model. Carry out the test using α = .05.
d. The estimated b for X1t was reported as -4.08 (p-value 6 .05). Interpret this result, practically.
e. The estimated b for X2t was reported as -3.41 (p-value 6 .05). Interpret this result, practically.
f. The estimated b for X3t was reported as -4.84 (p-value 6 .05). Interpret this result, practically.
g. The estimated b for X4t was reported as .92 (p-value 6 .05). Interpret this result, practically.
h. The estimated b for X5t was reported as .66. Interpret this result, practically.
i. The standard deviation of the model was reported as s = 2.36. Interpret this result, practically.
j. Do you recommend that the researchers use the model to predict the outcome of a future presidential election? Explain.