Two congressional scholars are discussing the extent to which members of the U.S. House of Representatives stay in touch with the voters in their states.

Problem 1
Two congressional scholars are discussing the extent to which members of the U.S. House of Representatives stay in touch with the voters in their states.

Scholar 1: “When members of Congress vote on important public policies, they are closely attuned to the ideological make-up of their states. Members from states having lots of liberals will tend to cast votes in the liberal direction. Representatives from states with mostly conservative constituencies, by contrast, will take conservative positions on important policies."


Scholar 2: “You certainly have a naive view of congressional behavior. Once they get elected, members of Congress adopt a `Washington D.C., state of mind,' perhaps voting in the liberal direction on one policy and in the conservative direction on another. One thing is certain: The way members vote has little to do with the ideological composition of their states."


A) Think about an explanatory variable that measures the percentage of self-described “conservatives" among the mass public in a state, with low values indicating low percentages of conservatives and high values indicating high percentages of conservatives. And consider an outcome variable that gauges the degree to which the state's delegation to the U.S. House of Representatives votes in a conservative direction on public policies. Low scores on this variable would indicate that the delegation tends to vote in a liberal direction, and high scores say that the delegation tends to vote in a conservative direction. What would you expect the relationship between these two variables to look like (positive vs. negative) if Scholar 1 is correct? What if Scholar 2 is correct?


B) The states dataset contains the variable conpct_m, the percentage of the mass public calling themselves conservative. This is the explanatory variable. The data also contain cons_hr, a measure of conservative votes by the delegation to the U.S. House of Representatives. Scores on this variable can range from 0 (low conservatism) to 100 (high conservatism). This is the outcome variable. Run a regression of cons_hr on conpct_m. Using the notation from lecture. Interpret the values of β ̂_0 and β ̂_1. What are the values of σ ̂_β0 and σ ̂_β1 and to what do they refer? What does the p -value for β ̂_1 mean?


C) 46.84% of Mississippians identify themselves as conservative. Based on your regression estimates, what is your prediction for the conservatism score of the state's delegation to the U.S. House of Representatives? What is the value of the residual for Mississippi?


D) Create a nicely formatted graph of the regression line.


E) Based on your inspection of the data and regression line, which congressional scholar do you think is more correct? Why?