Recent years have seen the growth of a new crime – identity theft. The theft of an identity is often

Recent years have seen the growth of a new
crime – identity theft. The theft of an identity is often accomplished by
stealing or otherwise acquiring the mail of the intended victim. The criminal
determines a number of critical facts about the victim, including name,
address, Medicare number and credit cards held. With this information the
criminal creates credit cards with the correct name and number. In the past,
financial institutions attempted to prevent credit card fraud by developing a
model that describes how the owner of the card actually uses it. Variations
from this pattern would
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Recent years have seen the growth of a new
crime – identity theft. The theft of an identity is often accomplished by
stealing or otherwise acquiring the mail of the intended victim. The criminal
determines a number of critical facts about the victim, including name,
address, Medicare number and credit cards held. With this information the
criminal creates credit cards with the correct name and number. In the past,
financial institutions attempted to prevent credit card fraud by developing a
model that describes how the owner of the card actually uses it. Variations
from this pattern would alert the bank to the possibility of fraud. However,
these models were rarely successful, missing many frauds and falsely
identifying illegal use by the card’s owner (what statisticians would call Type
I and Type II errors). SCORE has pioneered the use of logistic regression to
help identify the pattern of the fraudulent use of credit cards. The relevant
independent variables are as follows.

• Number of purchases or cash advances
within a three-hour period (a statistic called the velocity) (x1)

• Number of credit card purchases or cash
advances (x2)

• Code representing products purchased or
transactions, where 1 = jewellery or cash advances and 0 = other (x3)
The model is designed to estimate the probability that the use is legal. The
following regression coefficients were computed:

The bank’s computer has just received the
following information from one credit card. There have been four purchases or
transactions over the past three hours, the total amount was $1855, and at
least one transaction was a cash advance. Calculate the probability that the
transactions are fraudulent. How should the estimated probabilities be
employed? Discuss various issues associated with any policy you propose.

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