1 Competitive Auctions on eBay.com. The eBayAuctions contains information on 1972 auctions transacted on eBay.com during May-June 2004. The goal is to use these data to build a model that will classify competitive auctions from noncompetitive ones.

A competitive auction is defined as an auction with at least two bids placed on the item auctioned. The data include variables that describe the item (auction category), the seller (his/her eBay rating), and the auction terms that the seller selected (auction duration , opening price, currency, day-of-week of auction close). In addition, we have the price at which the auction closed. The goal is to predict whether or not the auction will be competitive.

Data Preprocessing. Create dummy variables for the categorical predictors. These include Category (18 categories), Currency (USD, GBP. Euro), EndDay (Monday- Sunday), and Duration (1, 3, 5, 7, or 10 days). Split the data in to training and validation datasets using a 60% : 40% ratio.

a. Fit a classification tree using all predictors using the best pruned tree. To avoid overfitting, set the minimum number of observations in a leaf node to 50. Also. set the maximum number of levels to be displayed at seven (the maximum allowed in XLMiner). To remain within the limitation of 30 predictors, combine some of the categories of categorical predictors. Write down the results in terms of rules.

b. Is this model practical for predicting the outcome of a new auction?

c. Describe the interesting and uninteresting information that these rules provide.

d. Fit another classification tree ( using the best-pruned tree, with a minimum number of observations per leaf node = 50 and maximum
allowed number of displayed levels), this time only with predictors that can be used for predicting the outcome of a new auction. Describe the resulting tree in terms of rules. Make sure to report the smallest set of rules required for classification.

e. Plot the resulting tree on a scatterplot: Use the two axes for the two best (quantitative) predictors. Each auction will appear as a point, with coordinates corresponding to its values on those two predictors. Use different colors or symbols to separate competitive and noncompetitive auctions. Draw lines (you can sketch these by hand or use Excel) at the values that create splits. Does this splitting seem reasonable with respect to the meaning of the two predictors? Does it seem to do a good job of separating the two classes?

f. Examine the lift chart and the classification table for the tree. What can you say about the predictive performance of this model?

g. Based on this last tree, what can you conclude from these data about the chances of an auction obtaining at least two bids and its relationship to the auction settings set by the seller (duration, opening price. ending day, currency)? What would you recommend for a seller as the strategy that will most likely lead to a competitive auction?

9.2 Predicting Delayed Flights. The file FlightDelays.xls contains information on ail 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.

Classification and Regression Tree

Data Processing. 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.

a. Fit a classification tree to the flight delay variable using all the relevant predictors. Do not include DEP_TI ME (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 number levels to be displayed = 6".
• Use the best pruned tree without a limitationon the minimum number of observations in the final nodes.

Express the resulting tree as a set of rules.

b. 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?

c. 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.

i. How is this tree used for classification? (What is the rule for classifying?)
ii. To what is this rule equivalent?
iii. Examine the full tree. What are the top three predictors according to this tree?
iv. Why, technically, does the pruned tree result in a tree with a single node?
v. What is the disadvantage of using the top levels of the full tree as opposed to the best pruned tree?
vi. Compare this general result to chat from logistic regression in the example in Chapter 10. What are possible reasons for the classification tree's failure to find a good predictive model?

9.3 Predicting Prices of Used Cars (Regression Trees). The file ToyotaCorolla.xls contains the data on used cars (Toyota Corolla) on sale during late summer of 2004 in The Netherlands. It has 1436 observations containing details on 38 attributes, including Price, Age, KM, HP, and other specifications. The goal is to predict the price of a used Toyota Corolla based on its specifications. (The example in Section 9.8 is a subset of this dataset.)

Data Preprocessing. Create dummy variables for the categorical predictors (Fuel Type and Color). Split the data into training (50%), validation (30%), and test (20%) datasets.

a. Run a regression tree (RT) using the prediction menu in XLMiner with the out- put variable Price and input variables Age_08_0-L KM, FueLType, H

P, Automatic, Doors, Quarterly_ Tax, Mfg_Guarantee, Guarantee _ Period, Airco, Automatic_Airco, CD_ Player, Powered _ Windows, Sport_ Model, and Tow_ Bar. Normalize the variables. Keep the minimum number of observations in a terminal node to 1 and the scoring option to Full Tree, to make the run least restrictive.

b. Which appear to be the three or four most important car specifications for predicting the car's price?