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. Since the data are ordinal, we can use cumulative logistic regression to estimate the probabilities of the counties falling into one of the 4 voting types: RS, RW, DW, DS.

call:

polr(formula = Vote_Type ~ Region * college, data = counties2, Hess = T)

coeffients :

value std. Error t value

RegionW 4.1347 1.4631 2 . 826

RegionMW 1. 3162 1. 3935 0.945

RegionS 1.2543 1. 3005 0.964

College 0.1263 0.0179 7 .040

RegionW: college -0.0702 0.0237 -2.968

RegionMW: College -0.0381 0.0229 -1. 665

Regions : College -0.0429 0.0217 -1.977

Intercepts :

value std. Error t value

Rep_strong | Rep_weak 6. 6921.072 6.240

Rep_weak | Dem_weak 7.806 1.081 7.220

Dem_weak I Dem_Strong 8. 890 1.091 8. 148

Residual Deviance: 2088. 544

AIC: 2108.544

a. Calculate the probability a county in the West is in the "Weak Dem" category if it has a college percentage of 58%.

b. The deviance for the model without interaction terms is 2097.67. Calculate the test statistic, df, p-value, and state the conclusion if the interaction term should be kept in the model.

c. An additive model (no interaction) was fit with non-parallel slopes and has a deviance of 2066.6. Is there evidence that the proportional odds assumption is not true for the data? Calculate the test statistic, df, p-value, and state the conclusion.