The question concerns data from a case-control study of esophageal cancer in Ile- et-Vilaine, France. The data is distributed with R and may be obtained along with a description of the variables by: > data (esoph) > help (esoph) (a) Fit a binomial GLM with interactions between all three predictors. Use back- ward elimination to simplify the model as far as is reasonable. (b) All three factors are ordered and so special contrasts have been used appro- priate for ordered factors involving linear, quadratic and cubic terms. Further simplification of the model is possible by eliminating some of these terms. Use the unclass function to convert some or all factors to a numerical representa- tion and show how the model may be simplified. (c) Does your final model fit the data? Is the test you make accurate for this data? (d) Check for outliers in your final model. (e) What is the predicted effect of moving one category higher in alcohol con- sumption? (1) Compute a 95% confidence interval for this predicted effect. (g) Bearing in mind that this is a case-control study, what can be said about the predicted probability that a 25-year-old who does not smoke or drink will get esophageal cancer?