Nov 6 2007 ECON 140A 240A 1 Midterm L Phillips Answer all five questions 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 a Do you think this scorecard system adequately discriminates between the two groups b Is the dispersion of scores about the same for the two groups Explain c Of those who repaid and were good risks would less than one quarter have scored below the cutoff d Of those who defaulted and were bad risks would more than one quarter have scored above the cutoff Nov 6 2007 ECON 140A 240A 2 Midterm L Phillips e For which group does this methodology predict better 1 those who repay or 2 those who default 2 15 The following table displays the joint probabilities associated with smoking and lung disease for men ages 60 65 Smokers Lung Disease No Lung Diseas 0 12 0 19 Non Smokers 0 03 0 66 a What percent of men in this age group with lung disease are smokers b What is the joint probability of having lung disease and being a nonsmoker for this age group for men c What percentage of men in this age group are smokers d What is the conditional probability of having lung disease given you are a smoker for men at these ages e What is the conditional probability of having lung disease given you are a non smoker for this age group of men 3 15 Suppose in an unnamed university for every 100 male revelers on Del Playa on a certain holiday night there are 150 females in party costume A professor of Sociology figures out how to take a random sample of ten by recording the gender of the next person to come around a blind corner after his random timer sounds off a What is the probability that seven or more of this random sample of ten will be female b Should you use the normal distribution for this calculation Explain c What distribution should you use 4 15 The Los Angeles Times Bloomberg conducted a poll of 1209 adults The results were reported in the October 25 Business section of the LA Times pp C1C2 One question was How likely is it that the nation could face an economic recession in the next year Sixty five percent of the adults polled said likely Nov 6 2007 ECON 140A 240A 3 Midterm L Phillips a Is this significantly more than half the adult population thinking a recession is likely Hint You can group don t know with not likely so that this is a Bernoulli i e yes no response b On p C2 the poll methodology reported the margin of sampling error for all adults is plus or minus three percent Show how this was calculated You can round to the nearest percent c What size type error is implied by the sampling error reported in part b 5 15 In 1979 the Gann Initiative was placed on the California ballot and was passed by 75 of the voters This legislation attempted to limit the growth of government allowing for inflation and population growth The question is has it worked California General Fund Expenditures in real 2007 08 dollars per capita is plotted against fiscal year in Figure 5 1 for years 1955 56 through 2007 08 Nov 6 2007 ECON 140A 240A 4 Midterm L Phillips a Did the Gann Initiative make a difference Explain Real general Fund Expenditures per capita were regressed against a time index with the value zero in 1978 79 one in 1979 80 and 29 in 2007 08 The results are shown in Table 5 1 b Was there a significant trend in real California General Fund Expenditures per capita after the passage of the Gann initiative Explain Lastly a plot of the dependent variable its fitted value and the residual is shown in Figure 5 3 c Do you see any evidence that one of the assumptions of least squares regression has been violated Explain Nov 6 2007 ECON 140A 240A 5 Midterm L Phillips Table 5 1 Dependent Variable CAGFDEXPC Method Least Squares Sample 1978 2007 Included observations 30 Variable Coefficient Std Error t Statistic Prob TIME C 19 71867 1981 554 4 438117 74 94595 4 443026 26 43977 0 0001 0 0000 R squared Adjusted R squared S E of regression Sum squared resid Log likelihood Durbin Watson stat 0 413496 0 392549 210 4014 1239525 202 0038 0 376228 Mean dependent var S D dependent var Akaike info criterion Schwarz criterion F statistic Prob F statistic 2267 475 269 9560 13 60025 13 69366 19 74048 0 000127 Figure 5 2 Plot of Actual Fitted and Residual from Trend Regression 3000 2800 2600 2400 2200 600 2000 400 1800 200 0 200 400 600 80 85 90 Res idual 95 Ac tual 00 05 Fitted
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