Aa Aa E. 8. Logistic regression Credit card fraud is fraud perpetrated through s

Question

Aa Aa E. 8. Logistic regression Credit card fraud is fraud perpetrated through stolen credit cards or credit card information. For years, credit card issuers have been using data mining and statistical tools to detect fraud. Citibank reported that knowing the type of product or service bought, frequency of purchases, and size and location of transaction can significantly reduce fraud. (Source: Jesus Mena, Investigative Data Mining for Security and Criminal Detection, Butterworth-Heinemann, pp. 250-251) A data-mining analyst at a major credit card company would like to construct and test a simple logistic regression model for detecting credit card fraud using data on card transactions classified as either fraudulent or non-fraudulent. The dependent variable for the model is: 1 if the transaction is due to credit card fraud; 0 if the transaction is not due to credit card fraud The independent variables for the model are chosen from the following: dollar amount of the transaction number of transactions in the preceding 12 hours X2 1 if the Standard Industry Code (SIC) forthe produ ct or service bought never appeared the card owner's X3 transaction history; 0 if otherwise 1 if the ZIP code of the transaction never appeared in the card owner's transaction history; 0 if otherwise X4 The analyst would like to test a logistic regression model that predicts credit card fraud using the dollar amount of the transaction, the number of transactions in the preceding 12 hours, and the indicator variable for whether the ZIP code of the transaction never appeared in the card owner's transaction history. (Note: Actual fraud-detection models used by credit card companies are much more complicated than the above, including up to hundreds of independent variables.) The logistic regression equation for the above model is: O E(y) exp(Bo B3x3 B4x4) [1 exp(Bo B3x3 B4x4)] O E(y) exp (Ao B1x1 B2x2 B4x4) [1 exp(Bo B1x1 B2x2 B4x4)] O E(y) B o B1x1 B2x2 B4x4 O E(y) B o B3x3 B4x4 59 Timeout

Explanation / Answer

The logistic regressesion equation that better fits to the model is f) E(y)=B0+B3X3+B4X4

Because is only d) and f) are linear equations, we can only select from those. We chose F) becasuse f) only takes into account X3 and X4, those variables are bionomial, meaning that they can only have 0 or 1 as parameters, meaning that is both variables are 0, we will have only E(y) =B0, excluding the other variables to decide if the transaction is fraudulent or not when E(y) = 1. Then...

If X4 =1,the mean of the dependet variable y is the probability that the transaction is fraudulent when the ZIP code of the transaction has not apperared in the card owner's transactions history , for given values X1 and X2.

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