a. For the OA fraud questions, identify the 16 variables that have the strongest correlation (in absolute value) with whether or not a company was involved in fraudulent activities (use Excel’s CORREL(), ABS(), and RANK() functions). Using the regression approach to 2-group discriminant analysis, use these 16 variables to develop a rule for predicting whether or not a company is involved in fraud.

a. What is your decision rule?

b. Develop a confusion matrix showing how accurate this decision rule is for the given data.

b. For the TML fraud questions, identify the 16 variables that have the strongest correlation (in absolute value) with whether or not a company was involved in fraudulent activities (use Excel’s CORREL(), ABS(), and RANK() functions). Using the regression approach to 2-group discriminant analysis, use these 16 variables to develop a rule for predicting whether or not a company is involved in fraud.

a. What is your decision rule?

b. Develop a confusion matrix showing how accurate this decision rule is for the given data.

c. Suppose OATML wants to use both fraud detection instruments and combine their individual results to create a composite prediction. Let D1 represent the discriminant score for a given company using the OA fraud detection instrument and D2 represent the same company’s discriminant score using the TML instrument. The composite score for the company might then be defined as C = w1D1 + (1 - w1)D2 where 0 ≤ w1 ≤ 1. A decision rule could then be created where we classify the company as non-fraudulent if C is less than or equal to some cut-off value, and is otherwise considered fraudulent. Use Solver’s evolutionary optimizer to find the optimal value of w1 and the cut-off value that minimizes the number of classification errors for the data given.

d. Of the two fraud detection instruments, which would you recommend that OATML implement?

e. What other techniques can you think of for combining OA’s and TML’s fraud detection questionnaires that might be beneficial to OATML?

Following the Enron scandal in 2002, two public accounting firms, Oscar Anderson (OA) and Trice-Milkhouse-Loopers (TML) merged (forming OATML) and are reviewing their methods for detecting management fraud during audits. The two firms had each developed their own set of questions that auditors could use in assessing management fraud.

To avoid a repeat of the problems faced by Enron’s auditors, OATML wants to develop an automated decision tool to help auditors predict whether or not their clients are engaged in fraudulent management practices. This tool would basically ask an auditor all the OA or TML fraud detection questions and then automatically render a decision about whether or not the client company is engaging in fraudulent activities.

The decision problem OATML faces is really twofold:

1) Which of the two sets of fraud detection questions are best at detecting fraud?

2) What’s the best way to translate the answers to these questions into a prediction or classification about management fraud?

To help answer these questions, the company has compiled an Excel spreadsheet (Fraud.xls) that contains both the OA and TML fraud detection questions and answers to both sets of questions based on 382 audits previously conducted by the two companies (see sheets OA and TML, respectively). (For all data 1=yes, 0=no). For each audit, the last variable in the spreadsheet indicates whether or not the respective companies were engaged in fraudulent activities (i.e., 77 audits uncovered fraudulent activities, 305 did not).