Suppose you are examining how age and year of birth are related to the tendency

Question

Suppose you are examining how age and year of birth are related to the tendency to vote Republican because you believe that when you were born affects your political attitudes and that people become more conservative with age. Let Yi be year of birth, Ai be age in years, and let Vi be the share of offices on the ballot for which person i votes Republican.

a.) If you regress Vi on Yi and a constant, what is the interpretation of the coefficient on Yi ?

b.) If you now add Ai to be specification in part a. and estimate. What is the interpretation now of the coefficient on Yi in this multivariate regression?

c.) Suppose you have a sample of voters and their votes for all offices on the ballot in one election in the year 2000. What will happen if you try to estimate the model in part b. with these data? Why?

d.) Suppose you now have data for two election years, 2000 and 2004 and estimate the model in part b. What will happen?

e.) Suppose you think the country is becoming more Republican over time to you add another variable, Ei , the year of the election. What will happen now if you regress Vi on your three independent variables? Why?

Explanation / Answer

Here dependent variable (Vi) = share of offices on the ballot for which person i votes Republican.

And independent variables are Yi = year of birth and

Ai = age in years

a.) If you regress Vi on Yi  and a constant, what is the interpretation of the coefficient on Yi ?

If we regress Vi on Yi then the regression equation is of the form,

Vi = a + b*Yi

where a is intercept and

b is slope.

The coefficient of Yi is b which is interpreted as one unit change in Yi (year of birth) will be b unit increase in Vi (share of offices on the ballot for which person i votes Republican).

b.) If you now add Ai to be specification in part a. and estimate. What is the interpretation now of the coefficient on Yi in this multivariate regression?

If we regress Vi on Yi and Ai then the regression equation is of the form,

Vi = a + bYi + cAi

where a is intercept and

b is coefficient of Yi

c is coefficient of Ai.

If we fixed variable Ai then one unit change in Yi will be b unit increase in Vi and if we fixed Yi then one unit change in Ai will be c unit increase in Vi.

c.) Suppose you have a sample of voters and their votes for all offices on the ballot in one election in the year 2000. What will happen if you try to estimate the model in part b. with these data? Why?

If we regress Vi on Yi and Ai in the year 2000 then the regression equation is of the form,

Vi(2000) = a + bYi + cAi

where 2000 is the year

where a is intercept and

b is coefficient of Yi

c is coefficient of Ai.

If we fixed variable Ai then one unit change in Yi will be b unit increase in Vi and if we fixed Yi then one unit change in Ai will be c unit increase in Vi.

Here all the results for year 2000.

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