Predicting Delayed Flights. The file FlightDelays.xls contains information on all commercial flights departing the Washington, D.C., area and arriving at New York during January 2004. For each flight there is information on the departure and arrival airports, the distance of the route, the scheduled time and date of the flight, and so on. The variable that we are trying to predict is whether or not a flight is delayed. A delay is defined as an arrival that is at least 15 minutes later than scheduled. Data Preprocessing. Create dummies for day of week, carrier, departure airport, and arrival airport. This will give you 17 dummies. Bin the scheduled departure time into 2-hour bins (in XLMiner use Data Utilities > Bin Continuous Data and select 8 bins with equal width). After binning DEP_TIME into 8 bins, this new variable should be broken down into 7 dummies (because the effect will not be linear due to the morning and afternoon rush hours). This will avoid treating the departure time as a continuous predictor because it is reasonable that delays are related to rush-hour times. Partition the data into training and validation sets. Fit a classification tree to the flight delay variable using all the relevant predictors. Do not include DEP_TIME (actual departure time) in the model because it is unknown at the time of prediction (unless we are doing our predicting of delays after the plane takes off, which is unlikely). In the third step of the classification tree menu, choose “Maximum # levels to be displayed = 6”. Use the best pruned tree without a limitation on the minimum number of observations in the final nodes. Express the resulting tree as a set of rules. If you needed to fly between DCA and EWR on a Monday at 7 AM, would you be able to use this tree? What other information would you need? Is it available in practice? What information is redundant? Fit another tree, this time excluding the day-of-month predictor. (Why?) Select the option of seeing both the full tree and the best pruned tree. You will find that the best pruned tree contains a single terminal node. How is this tree used for classification? (What is the rule for classifying?) To what is this rule equivalent? Examine the full tree. What are the top three predictors according to this tree? Why, technically, does the pruned tree result in a tree with a single node? What is the disadvantage of using the top levels of the full tree as opposed to the best pruned tree?