Problem Set #5 Assume you want to predict the Percent of Votes that Donald Trump won...

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Problem Set #5 Assume you want to predict the Percent of Votes that Donald Trump won in a county in 2016, PercentTrump. You include the county's median income in $1,000s, MedianIncome, the percent of the county's population that has a bachelor's degree or higher, Percent Bachelorsor Higher, the percent of the population considered living in poverty, PercentInPoverty, the percent of the population that is white, Percent White, a dummy variable for whether the county was Rural, and a dummy variable for whether their unemployment was greater than 6%, HighUnemp. PrecentTrump = Po + BMedianIncome + 2 Percent BachelorsorHigher + 3 PercentInPoverty + 4PercentWhite + 5Rural +B6HighUnemp+ Assume that you believe there is a different effect of high unemployment, HighUnemp, for Rural vs. Non-Rural counties. Include an interaction term between the two. 1. When all other variables are equal to 0 what is the predicted PercentTrump for a Rural county with High Unemployment? (2 POINTS) 2. What is the marginal effect of a county having High Unemployment for a Rural vs. Non-Rural county? Is this difference statistically significant at the 10% level, and why? (4 POINTS) 3. What is the predicted percent of the county that votes for Trump when all other variables are equal to zero for a county that is Rural and has High Unemployment? What is the predicted percent of the county that votes for Trump when all other variables are equal to zero for a county that is NOT Rural and has Low Unemployment? (3 POINTS) Assume that instead of the previous interaction term, you use all variables above, but also a dummy variable, RedCounty, for whether the county is a "Red County" or had more republican votes than democrat votes in 2012. ("Blue State" would refer to when the democratic candidate is greater than the republican.) You believe the Median Income of the county, MedianIncome, has a different effect in counties considered Red States. 4. What is the predicted change in the Percent of votes for Trump from a $1,000 increase (one unit) in Median Income for a Red County, and is this statistically different than the effect for a Blue State (Non-Red County) and why? (3 POINTS) 5. What Median Income represents the turning point" for the marginal effect of being a Red County? Does this turning point exist in the actual data, provide evidence why or why it does not? (4 POINTS) 6. Discuss two reason that indicate why the interaction term should be included in your regression. (2 POINTS) Assume that instead of the previous interaction terms, you run the following regression, but also include an interaction between the Median Income of the county and the Unemployment Rate of the county: Percent Trump = Bo+ BMedianIncome + B2Percent BachelorsorHigher + 3 PercentInPoverty + 4PercentWhite + 5Rural +B6UnemploymentRate + 7. Holding all other factors constant, is the marginal effect of a $1,000 increase in the Median Income of a county statistically significant at the 10% level and why. Is the marginal effect of a $1,000 increase in Median Income statistically different when the Unemployment rate is higher and why? (3 POINTS) 8. What is the Median Income representing the "turning point" for the marginal effect of a change in the Unemployment Rate, and what Unemployment Rate represents the "turning point" for the marginal effect of a change in Median Income? Do you see those values in the actual data set, provide evidence for either why or why not? (3 POINTS) Problem Set #5 Assume you want to predict the Percent of Votes that Donald Trump won in a county in 2016, PercentTrump. You include the county's median income in $1,000s, MedianIncome, the percent of the county's population that has a bachelor's degree or higher, Percent Bachelorsor Higher, the percent of the population considered living in poverty, PercentInPoverty, the percent of the population that is white, Percent White, a dummy variable for whether the county was Rural, and a dummy variable for whether their unemployment was greater than 6%, HighUnemp. PrecentTrump = Po + BMedianIncome + 2 Percent BachelorsorHigher + 3 PercentInPoverty + 4PercentWhite + 5Rural +B6HighUnemp+ Assume that you believe there is a different effect of high unemployment, HighUnemp, for Rural vs. Non-Rural counties. Include an interaction term between the two. 1. When all other variables are equal to 0 what is the predicted PercentTrump for a Rural county with High Unemployment? (2 POINTS) 2. What is the marginal effect of a county having High Unemployment for a Rural vs. Non-Rural county? Is this difference statistically significant at the 10% level, and why? (4 POINTS) 3. What is the predicted percent of the county that votes for Trump when all other variables are equal to zero for a county that is Rural and has High Unemployment? What is the predicted percent of the county that votes for Trump when all other variables are equal to zero for a county that is NOT Rural and has Low Unemployment? (3 POINTS) Assume that instead of the previous interaction term, you use all variables above, but also a dummy variable, RedCounty, for whether the county is a "Red County" or had more republican votes than democrat votes in 2012. ("Blue State" would refer to when the democratic candidate is greater than the republican.) You believe the Median Income of the county, MedianIncome, has a different effect in counties considered Red States. 4. What is the predicted change in the Percent of votes for Trump from a $1,000 increase (one unit) in Median Income for a Red County, and is this statistically different than the effect for a Blue State (Non-Red County) and why? (3 POINTS) 5. What Median Income represents the turning point" for the marginal effect of being a Red County? Does this turning point exist in the actual data, provide evidence why or why it does not? (4 POINTS) 6. Discuss two reason that indicate why the interaction term should be included in your regression. (2 POINTS) Assume that instead of the previous interaction terms, you run the following regression, but also include an interaction between the Median Income of the county and the Unemployment Rate of the county: Percent Trump = Bo+ BMedianIncome + B2Percent BachelorsorHigher + 3 PercentInPoverty + 4PercentWhite + 5Rural +B6UnemploymentRate + 7. Holding all other factors constant, is the marginal effect of a $1,000 increase in the Median Income of a county statistically significant at the 10% level and why. Is the marginal effect of a $1,000 increase in Median Income statistically different when the Unemployment rate is higher and why? (3 POINTS) 8. What is the Median Income representing the "turning point" for the marginal effect of a change in the Unemployment Rate, and what Unemployment Rate represents the "turning point" for the marginal effect of a change in Median Income? Do you see those values in the actual data set, provide evidence for either why or why not? (3 POINTS)