A car manufacturer conducts a survey to see how appealing its new model is to its existing customer base. It selects current customers at random, and gives them a new vehicle with two different car setups, a conventional city setup (A) and a sporty setup (B) and, following a period of one month, asks them to rate the vehicle's performance on a scale of LO (not satisfied) to L3 (very satisfied). The data is provided in the file market.csv. a) State why a proportional odds model is appropriate for these data. Fit a proportional odds model to the data, both with a logit link and a probit link and comment on the respective fits. Use the polr function in the MASS package for fitting the model. (2 marks) b) From now on consider only the proportional odds model with the logistic link. Use the estimated 8 parameters to find the probability of a male rating L2 or less with the sporty setup. Verify your results using the predict function. (Note: polr assumes a model of the form g(x) =Boj - 11ii - 12:32 - ...). c) What are the odds of a male rating L2 or less with the sporty setup? (2 marks) (2 marks) d) Using the estimated parameters, compute the odds of a female rating L2 or less with the city setup relative to those of a male rating L2 or less with a sporty setup. Verify your answer by computing the probabilities (and from those the odds) using the predict function. (2 marks) e) By exponentiating confidence intervals on a linear combination of the parameters, provide 99% confidence intervals for the odds ratio in 1d) (Hint: Use the function vcov to get the covariance matrix of the 3 parameters). Is the observed odds ratio significant? setup sex response frequency 1 A male LO 45 2 A male L1 28 3 A male L2 29 4 A male L3 26 5 A female LO 12 6 A female L1 4 7 A female L2 5 8 A female L3 2 9 B male LO 20 10 B male L1 20 11 B male L2 41 12 B male L3 44 13 B female LO 7 14 B female L1 12 15 B female L2 3 16 B female L3 1