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# 1 Competitive Auctions on eBay. The file eBayAuctions.xls contains information on 1972 auctions transacted on eBay.com during May-June 2004.

9.1 Competitive Auctions on eBay.com. The file eBayAuctions.xls 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 into 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?