Election Research, a marketing research firm specializing in political campaigns, did an analysis on the 2016 California state legislature elections. Data were obtained for 72 districts and included the total number of registered voters by district, their party affiliation, the number of votes received by each candidate, the campaign expenditures of each candidate, and the identity of the incumbent, if one existed. Of the 72 districts used, 27 had Republican winners and 45 had Democratic winners. There were 55 incumbent winners and 17 nonincumbent winners. The winners received an average of 66.6 percent of the votes cast and incurred 63.2 percent of the advertising expenses. The winner's advertising expenditure averaged $18,031 per district ($22,805 without an incumbent and $10,710 with an incumbent) The following are the results of three regress: runs (the numbers in parentheses are the t-values): All districts: WSV 0.240+0.174WSTE(4.82)+ 0.414WSRV(4.60) + 0.751 I (7.01) r2 = .535 N=72 Incumbent districts: WSV = 0.329 + 0.157WSTE(3.67)+ 0.409WSRV(6.07) r2 440 N= .55 Nonincumbent districts: NSV 0.212 + 0.234WSTE(3.39)+ 0.399WSRV(3.21) r2 .615 N 17 where WSV = winner's share of total votes cast WSTE winner's share of total advertising expenditures WSRV = proportion of registered voters that are registered to the winner's political party I = winner's incumbency dummy variable. A dummy variable is a 0-1 variable. In this case I = 1 for an incumbent dis 0 for a no cumbent district ct and Please answer the following questions: 1. Interpret the regression coefficients. For all districts, what exactly does the coefficient 0.174 mean? Interpret the coefficients 0.414 and 0.75 as well. Why is the coefficient for the WSTE variable different in the three equations?
2. Explain exactly what the t-value means. Determine the p-value associated with each. Interpret r2 Why is r2 different for each equation?
3. Why does the incumbency dummy variable appear only in the first equation?
4. Could this model be used productively to predict? What insights could a candidate get from the model?