Election Research, a marketing research firm specializing in political campaigns

Question

Election Research, a marketing research firm specializing in political campaigns, did an analysis on the 1996 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 regression runs (the numbers in parentheses are the t-values):

All districts:

WSV = 0.240 + 0.174WSTE(4.82)

            + 0.414WSRV(4.60) + 0.751(7.01)

    r2 = 0.535

     N = 72

Incumbent districts:

WSV = 0.329 + 0.157WSTE(3.67)

        + 0.409WSRV(6.07)

      r2= 0.440

N= 55

Nonincumbent districts:

WSV = 0.212 + 0.234WSTE(3.39)

        + 0.399WSRV(3.21)

       r2= 0.615

       N= 17

Where:

WSV= winner's share of total votes cast

WSTE= winner's share of total advertsing 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 districtand I = 0 for a nonincumbent district.

Question Two:

Explain exactly what the t-value means. Determine the p-value associated with each. Interpret r2. Why is r2 different for each equation?

Explanation / Answer

Solution

The t value is the t-score or the critical value for the given specific probability. It is same like the z-score for the given distribution. The t-value for the variable all districts WSTE is given as 4.82 and the associated p-value is given as 0.0000039513. The t-value associated with the variable all districts WSRV is given as 4.6 and the associated p-value is given as 0.00000898. The value for the R square or the coefficient of determination is given as 0.535 which means about 53.5% of the variation in the dependent variable is explained by the independent variables WSTE and WSRV.

The t-value for the variable incumbent districts WSTE is given as 3.67 and the associated p-value is given as 0.000278. The t-value associated with the variable incumbent districts WSRV is given as 6.07 and the associated p-value is given as 0.00000006583. The value for the R square or the coefficient of determination is given as 0.44 which means about 44% of the variation in the dependent variable is explained by the independent variables WSTE and WSRV.

The t-value for the variable non-incumbent districts WSTE is given as 3.39 and the associated p-value is given as 0.001869. The t-value associated with the variable non- incumbent districts WSRV is given as 3.21 and the associated p-value is given as 0.002731. The value for the R square or the coefficient of determination is given as 0.615 which means about 61.5% of the variation in the dependent variable is explained by the independent variables WSTE and WSRV.

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