Midterm 2007 key - Nov 6 2007 ECON 140A/240A-1 Midterm L...

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Nov. 6, 2007 ECON 140A/240A- 1 L. Phillips Midterm Answer all five questions. The first is a descriptive statistics question. The second is a conditional probability question given joint probabilities and hence marginal ones. The third is a Binomial distribution problem, the fourth, a rates and proportions problem and the fifth a regression problem. 1. (15) The current sub-prime crisis is causing many home-owners to default and, as a consequence, their banks or lenders are stuck with bad loans that are not being paid off. A bank is evaluating a “scorecard” based on each applicant’s credit history, i.e. information obtained by the bank from credit bureaus. The bank is applying this methodology to two groups: (1) applicants that received loans and later repaid, and (2) applicants who received loans and later defaulted. The cutoff score for an applicant to receive a loan is 650 or better. There are box plots of this retrospective score data for two groups of borrowers from the bank: (1) borrowers who repaid and (2) borrowers who defaulted. The data follow: Repaid Smallest = 546 Q1 = 714 Median = 761 Q3 = 801 Largest = 938 IQR = 87 Outliers: 938, 578, 569, 551, 546, Defaulted Smallest = 436 Q1 = 584.75 Median = 633 Q3 = 670.5 Largest = 790 IQR = 85.75 Outliers: 436, BoxPlot 0 200 400 600 800 1000 BoxPlot 0 200 400 600 800 1000 a. Do you think this scorecard system adequately discriminates between the two groups? Yes, there is a 123 point difference in the medians. b. Is the dispersion of scores about the same for the two groups? Explain. Yes. The inter-quartile ranges are 87 and 85.75, quite close.
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Nov. 6, 2007 ECON 140A/240A- 2 L. Phillips Midterm c. Of those who repaid and were good risks, would less than one quarter have scored below the cutoff? Yes, the first quartile is 714, well above the cutoff of 650.
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