33) Professor McTower has made a study of the relationship between the unemploym

Question

33)       Professor McTower has made a study of the relationship between the unemployment rate and the outcomes of 20 presidential elections. Her results are:

V = 51.0 - 2.00 U

(3.5) (4.0)

where

V = percent of vote received by the incumbent party; average value = 53 percent

U = change in the unemployment rate in the year of the election, average value = -1.0.

() = t-values

a) What is her estimate of the effect of unemployment on presidential elections? Is her estimate substantial?

b) What would be a 95 percent confidence interval for her estimate? Is her estimate statistically significant, in that we can reject the hypothesis that there is no effect of unemployment changes on presidential elections?

c) According to her equation, what fraction of the vote will the incumbent party receive if the unemployment rate falls by 15 percent ( U = -15) during the election year? Is there any special statistical reason for caution about such a forecast.

Explanation / Answer

here, the regression equation is given as V = 51.0 - 2.00 U , where U denotes change in the unemployment rate in the year of the election and V denotes percent of vote received by the incumbent party.

a) the regression coefficient of V on U is given by bvu=-2 thus for unit increment in U i.e. unemployment rate, V i.e. the percent of vote recieved is decreased by 2 units.

the t value for U is given as 4 whereas the table value for t19,0.025 is 2.093 which implies that U is significant for estimating V

thus the estimate is substantial.

b) the 95% CI for her estimate can be obtained using the following formula

(bvu_hat- t19,0.025*SE(bvu_hat),bvu_hat+ t19,0.025*SE(bvu_hat))

now, given t value of bvu is 4 and bvu_hat is -2

then SE(bvu_hat)=| bvu_hat| /( t value of bvu )

=2/4=0.5

then the CI is given by (-2-0.5*2.093,-2+0.5*2.093)

=(-3.0465, -0.9535)

c) if the unemployment rate falls by 15% then according to her equation the vote percentage will be=51-2*(-15)=81

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