Looking at the 955 counties in the US that have a population over 50,000 people (total of 955 counties).

Model how the county voted in the 2016 presidential election.

The response variable how the county voted (variable is Vote_Ordered), which has 4 values:

Value Label Vote Percent for Democrat

1 Rep Strong Less than 40%

2 Rep Weak 40% - 50%

3 Dem Weak 50%-60%

4 Dem Strong More than 60%

The two explanatory variables we will use are:

Region of the US (z): (MW/NE/S/W, 4 levels)

College (x): Percentage of people that attended at least some college - 5 # summary = {26, 52, 59, 65, 86}

1. We will start with a baseline logistic regression model with "Rep Strong" be the baseline category.

a. Write out the three logit models that model will fit, not including the linear predictor component.

b. The R output below shows the additive model. Interpret the effect of a county being in the West rather than the South and voting Rep Strong vs Dem Strong

call :multi nom(formula= Vote_Type Region + collage data = counties2)

coefficients :

(Intercept) Regionw RegionMW RegionS college

Rep_Weak-3.75-0.369 -0.532-1. 38 0.0627

Dem_weak-6.68 -0.478-1.156 -1.91 0.1103

Dem_strong-7.00-0.180-1.717 -1.40 0.1123

Std. Errors:

(Intercept) RegionW RegionMW RegionS college

Rep_weak0.6250. 3190.2640.258 0.0104

Dem_weak 0.7690. 3340.2990.297 0.0125

Dem_Strong 0.793 0. 337 0.3530.291 0.0128

Residual Deviance: 2077.324

AIC: 2107.324

c. Interpret the effect of College between "Dem Weak" vs "Rep Weak"

d. For a county in the Northeast with a college percentage of 70, find all four estimated probabilities.

e. What does the intercept term for Dem_Strong indicate about how a county votes?

f. The deviance of a model that includes the interaction terms between College and Region is 2049.9. Find the test statistic, df, p-value, and state the conclusion of a hypothesis test to determine if the interaction terms improve the fit of the model.

g. If we drop Region from the model, the estimates are shown below. Explain a plot of the probabilities of how a county votes as College changes (range from 26% to 86%). Make sure the plot clearly indicates which line corresponds to which Vote Type.

coefficients :

(Intercept) college

Rep_weak -4. 78 0.0671

Dem_weak -7.99 0.1137

Dem_strong -8. 13 0.1146