(3) (10 POINTS) Table 1 contains results for a regression study on the relation
ID: 3048980 • Letter: #
Question
(3) (10 POINTS) Table 1 contains results for a regression study on the relation between po- litical campaign expenditures and vote shares. The population model is where CES measures the share of total campaign expenditures by a candidate, and VS measures the share of the vote he/she won on election day Table 1. Vote Share Regression Results Parameter Parameter Standard Estimate Error 0.0002 0.7871 Campaign Expenditure Share 0.4638 Intercept 26.81 173 SST SSE SSR 48457.25 6970.77 (a) Explain in common terms what the coefficient for "CES" means (b) Construct a test statistic to evaluate the hypothesis that a candidate's expenditure share has no effect on her vote share, against the alternative hypothesis that it does matter in some way (i.e., a two-sided alternative). State the distribution of the test statistic (including degrees of freedom) (c) Using the tables in your book, state an interval which contains the P-value for the test in the previous part. Judging by the P-value, would you reject the null hypothesis that campaign expenditure share doesn't matter at the 1% level? (d) Compute a 90% confidence interval for the intercept term (ie., test the null hypothesis that the population regression line passes through the origin, against a two-sided alternative). Interpret your result. (e) Using the information contained in the table, compute the SSE and the R2 of the re- gression. Interpret your R2 estimate in terms of the percentage of the total variability in VS accounted for by the modelExplanation / Answer
a)
In common terms, coefficient of CES means that for every increase of 1 in CES, vote share would go up by 0.4638.
b)
SST=48457.25, SSR=6970.77, SSE=48457.25-6970.77=41486.48, MSR=6970.77/1=6970.77, MSE=41486.48/171=242.61, F=6970.77/242.61=28.73, Sign F=0.00000027. Hence, reject the null hypothesis. We conclude that CES influences vote share.
c)
Sign F=0.00000027. Considering at the p-value of 0.05, we reject the null hypothesis and conclude that CES influences vote share.
d)
26.81+/-1.6538*0.7871=25.51 to 28.11
e)
SST=48457.25, SSR=6970.77, SSE=48457.25-6970.77=41486.48, r^2=SSR/SST=6970.77/48457.25=0.143854. Around 14.39% of the variability in VS accounted for by CES
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