The Variable Loan Type

Indian School of Business

Credit Risk Project, Installment 2

Your answers to the following questions are to be submitted in a single report document. The report file must have a separate cover page that identifies the team (e.g., J-1) and lists the members of the team who are participating in the project. Number the subsequent pages and format them to have 1-inch margins all around. Include only plots that are discussed in your report. Reports are to be submitted via the LMS by 23:55hrs on Monday, May 7th.

As you did for Installment 1, for the sake of checking conditions, assume that the cases represent a simple random sample from the population of loans described in the project description. In these questions if there is a “claim” that you are testing, associate the claim with the null hypothesis. Use only those rows in the data table for which you can calculate a PRSM score.

1. The variable Loan Type indicates a new or repeat customer. It has been claimed that 1/4 of customers who get these loans have had them before. Does that seem to be an appropriate claim about the population based on your data? Offer a brief explanation.

Ans) The concept of testing for a proportion will be applied.

Set “Repeat” loans to 1 and “Original” loans to 0.

Hypothesis: Let HO:  po = ¼ and HA: po ≠ ¼. α = 0.05

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Test mean of Loan.Type.2

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Since the prob > |t| is less than 0.05 we reject null hypothesis.

1. Does the FICO score of the borrower appear to be normally distributed? Justify your answer.
   
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Ans) The distribution is largely normal with some slight skewness on the right side.

1. State the 95% confidence interval for the average FICO score and give a brief interpretation of what this interval means. Be sure to check that it is appropriate to form such a confidence interval for your data.

Ans) For a 95% confidence interval and a near normal distribution

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Therefore, we can be 95% confident that the population mean lies in the interval (572.5, 579.3). We assume an iid sample, with the sample size less than 10% of the population size.

1. A manager at the loan operation claimed that the average age (the Years in Business variable) of all of the businesses served by this firm is less than 8 years. Do you agree, based on your data?  Explain briefly

Ans) Hypothesis: Let HO: µ0 ≤ 8 and HA: µ0 > 8. α = 0.05

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Since t statistic is more than 2 standard deviations, we reject the null hypothesis and conclude that the average age is greater than 8 years.

1. To identify the average PRSM in the population to 2 decimal places (i.e., to have the margin of error less than 0.005), how large a sample would you recommend?

Ans) After correcting the anomaly in one of the data entry, the PRSM scores are normally distributed.
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1. Is the population average PRSM score statistically significantly different from 1?

1. Indicate an answer to the question, with a brief account of your analysis.
2. What are the implications of your answer for the business?

Ans) a) Hypothesis: Let HO: µ0 = 1 & H1: µ0 ≠ 1

Test mean for PRSM distribution and set mean = 1

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Since t statistic is less than -2, we reject the null hypothesis. Hence the average PRSM score is significantly different from 1.

Ans) b) Since the mean of PRSM score (=0.807) is less than 1, loans are recovered slower than expected, which is bad news for the business.  

1. The Chief Risk Officer is particularly concerned about the percentage of loans that have PRSM scores of less than 0.7. What can you tell her about this percentage from your data?1 Approach this question by creating a confidence interval for the proportion of loans in the population that have a PRSM score of 0.7 or less.

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1. To make a dummy variable, add a column and define a formula. In the formula editor select the conditional group from the list of functions, and pick the top item “If”. Define the conditions by picking variables and assigning 0/1 to the alternatives.

Ans) Set PRSM scores above 0.7 as 0 and below or equal to 0.7 as 1. Obtain the 95% confidence interval for the distribution.

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Hence the 95% confidence interval is   0.174 to 0.3237.

1. Do loans from ISO SPS have significantly different average PRSM scores than those from EZCheck?

Ans) Let µ1 = Mean SPS PRSM score and µ2 =  Mean EZCheck PRSM score

HO: µ1 - µ2 = 0 & H1: µ1 - µ2 ≠ 0

Fit Y (PRSM score) by X (ISO.Name) and run a t test.

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Since the t ratio is lower than -2 standard errors, we reject the null hypothesis.