Vote for me say all political candidates But what combinatio

Vote for me!! say all political candidates. But what combination of policies would win them most votes? Suppose that you are working for one of the presidential campaigns, and need to give advice on how can the candidate adjust his policies to appeal to most voters. In this scenario, you are concerned with their possible position on two key issues: Taxes and Health care: (for Taxes, the candidate could raise taxes on all people (T1), raise taxes on rich only (T2), not change taxes (T3), or lower taxes (T4)); for Health care (the candidate could choose a private system with better access (H1), or a national system (H2)). The response variable is the percentage of [candidate’s] voters who believe the candidate holds a specic position. As both these key issues are part of a candidate’s domestic agenda, it is natural to consider a model with interaction.

There are no data provided for this problem, all your answers should be expressed in terms of model parameters.
(a) Write down a statistical model that relates the average percentage of voters to a candidate’s position on Taxes and Health Care issues, including the interaction between them. Clearly dene any indicator variables you used.

(b) Write down the form of the model for the percentage of voters who are in favor of a national health care system and raise taxes on the rich.

(c) Based on the model in part (5a), compute the difference in the mean percentage of voters in favor of a national health care system vs. those not in favor, assuming all these voters would like to have the taxes on the rich raised. Write your answer in terms of model parameters, and show any work.

(d) Based on the model in part (5a), compute the mean percentage of voters who are in favor of a national health care system. Write your answer in terms of model parameters, and show any work.

Solution

(a) Write down a statistical model that relates the average percentage of voters to a candidate’s position on Taxes and Health Care issues, including the interaction between them. Clearly dene any indicator variables you used.

average percentage = n* p

(b) Write down the form of the model for the percentage of voters who are in favor of a national health care system and raise taxes on the rich.

P = x / n