Reconsider Problem 2.9. Using the data on the Clean Data worksheet tab, partition the historical records into a training partition (60 percent of the records) and a validation partition (the remaining 40 percent of the records). 

a. Searching over values of k from 1 to 9, find the best value for k in the KNN algorithm when it is used to classify applicants from the validation partition as likely to graduate (or not). 

b. Using the best value for k determined in part a, determine the accuracy, sensitivity, and specificity for the algorithm. 

c. Using the best value for k determined in part a, generate the lift chart for the algorithm

Data from Problem 2.9

Pathfinder College is a small liberal arts college that wants to improve its admissions process. In particular, too many of its incoming freshmen have failed to graduate for a variety of reasons, including dropping out, or transferring to another college, or failing to satisfy the graduation standards. Therefore, the admissions office wants to have a better method of predicting whether an applicant would succeed in graduating. The college primarily uses two predictor variables for evaluating an applicant, namely, the high school grade point average and the SAT score. If either is sufficiently high (either a GPA ≥ 3.30 or an SAT score ≥ 1,200), the applicant is immediately accepted. Such applicants who accept admission usually do well until successfully graduating. However, the admissions office needs to go deeper into its applicant pool to fill up its freshman class. The question is how to predict which of these other applicants are the better bet for successfully graduating. The admissions office wishes to consider an applicant for admission only if the prediction is that the applicant is more likely than not of successfully graduating. (Qualitative information about the applicant also will be considered before making the final admission decision, but the focus of this problem is on how to use the GPA and SAT scores.) The admissions office has randomly selected 800 students that were previously admitted and enrolled but did not meet the criteria for immediate acceptance. All have now had sufficient time to graduate. The data for these historical records, including their graduation status, are provided in the spreadsheet file titled Pathfinder College Data available in www.mhhe.com/Hillier7e. The original data (on the Original Data worksheet tab) needs to be cleaned. Perform the following data cleaning tasks.