(3) (10 POINTS) Table 1 contains results for a regression study on the relation

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 model

Explanation / Answer

(a) Here coefficient for "CES"' is 0.4638, it means that if we increase the share of total campaign expenditures by candidate by 1 unit will increase the value of the share of the vote he/she won on election day by 0.4638.

(b) Here null hypothesis is

H0 : 1 = 0

Ha : 1 0 where 1 is the slope coefficient of relation betwen CES with VS.

Here the distribution of the test statistic with degrees of freedom (n-2) = 171

(c) Here test statistic

t = 1^/se(1) = 0.4638/0.0002 = 2319

p - value = Pr(t > 2319 ; 171) = 0.000 as this value is very less than 0.001.

Here we can reject the null hypothesis at 1% level. and say that campaign expenditure matters in affecting vote share.

(d) Here 90% confidence level for intercept = 0^ +- t171,0.10 se(0)

= 26.81 +- 1.6538 * 0.7871

= (25.5083, 28.1117)

Doesn't consist the value of zero so the population regression line doesn't passes through the origin.

Here we can interpret the result as that that there is 90% probability that if there is no campaign expenditure share, then the market share he/she holds is in between 25.51% to 28.11%.

(e) SSE = SST - SSR = 48457.25 - 6970.77 = 41486.48

R2 = 1 - SSE / SST = 1 - 41486.48/48457.25 = 0.1439

Here now we can interpret that the 14.39% variabiity in VS is accounted by the variation in CES or say the model.

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