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?

We can see here that the model with all district has r2=0.535, from that we can say that model is explaining 53.5% of variation in WSV is explained this model so it could be considered as good model.

when we look at the second model which has r2=0.440 which mean model explains only 44% of variation in WSV and third model has r2=0.615 which indicates that it expains 61.5% if variation in WSV.

So, models can be used productively to predict.

From, the model with all district a candidate can get insight that,

Here, both the variable WSTE and WSRV have positive coefficient so we can say that as total share of advertising expenditure and number of registered voters incandidates politicel party increases his share of votes cast will increase.

And if candidate is registering from the incumbent district his share of votes cast will increase.

If the candidate has already dicided to register him self form an incumbent district he can get insight from the model of incumbent disctrict.

This model has positive coefficient for WSTE that concludes that more the candidate expenses for advertising campaign more his share of votes cast will be. and similarly for WSRV also has positive coefficient so more number of registered voter that are registered to his party can also increase the candidate's share of votes casted in the election.

If a candidate decides to register from nonincumbent district he can get insights from model for nonincumbent district.

This model has positive coefficient for WSTE that concludes that if candidate make more expenses for advertising campain more his share of votes cast will be. and similarly WSRV also has positive coefficient so more number of registered voter that are registered to his party can also increase the candidate's share of votes casted in the election.

Overall we could say if a candidate want to win the election he has to more expenses for his advertising campaign and also he to make that he has more proportion of registered voters that are registered to his political party.

I hope this helped !!!