A study on U.S. Army soldiers investigated the preference for black olives as a function of the soldiers’ origin. N = 644 male subjects were randomly selected from the Rural and Urban locations from each of three U.S. regions: Midwest (MW), Northeast (NE), and Southwest (SW), for a total of six groups. Each individual rated a preference for olives on a six-category original scale: A=extremely, B=dislike very much or moderately, C=dislike a little or neutral, D=like slightly, E=like moderately, F=like very much or extremely like. The data are in the belowA. Fit a statistical model for preference as a function of location, region, and an interaction. Make sure that you check model assumptions (e.g. proportional odds).B. Simplify your model, if possible, by eliminating effects or combining categories of the predictors. C. Using your final model, write a short summary for the client that describes the differences in preferences by location and region. As part of this summary make some very specific statements about what your model says about how the odds or probability of liking olives, versus not liking them (i.e., categories A through C, versus D through F.) depends on location and/or region.data olive;input type $ region $