A large bank is interested in identifying the probability of fraudulent online purchases. The model below uses a variable, SimilarityScore, which considers similarity with past purchases, and an indicator variable for large transaction amounts. LargeTransaction (coded 1 if a transaction is greater than $1,000 and coded 0 if not) to explain the log-odds of fraudulent purchases (coded 1 if the transaction is fraudulent and coded 0 if not)

Question

A large bank is interested in identifying the probability of fraudulent online purchases. The model below uses a variable, SimilarityScore, which considers similarity with past purchases, and an indicator variable for large transaction amounts. LargeTransaction (coded 1 if a transaction is greater than $1,000 and coded 0 if not) to explain the log-odds of fraudulent purchases (coded 1 if the transaction is fraudulent and coded 0 if not)

Ln(odds of purchase fraud) = 12 - 0.018*Similarity + 0.4*LargeTransaction

Holding LargeTransaction constant, how will the predicted odds of purchase fraud change for a purchase with a SimilarityScore of 900 compared to 675?

Answer 1

To determine how the predicted odds of purchase fraud will change for a purchase with a SimilarityScore of 900 compared to 675 while holding LargeTransaction constant, we can look at the coefficient of the SimilarityScore variable.

According to the given model, the coefficient for SimilarityScore is -0.018.

The predicted odds of purchase fraud for a purchase with SimilarityScore of 675 can be calculated as follows:

Ln(odds of purchase fraud) = 12 - 0.018 * 675 + 0.4 * LargeTransaction

To hold LargeTransaction constant, we assume that the value of LargeTransaction is the same for both cases.

Now, let's calculate the predicted odds of purchase fraud for a purchase with SimilarityScore of 900:

Ln(odds of purchase fraud) = 12 - 0.018 * 900 + 0.4 * LargeTransaction

Comparing the two equations, we can see that the only difference is the coefficient for SimilarityScore:

For SimilarityScore of 675: -0.018 * 675
For SimilarityScore of 900: -0.018 * 900

Since the coefficient is negative, we can infer that as the SimilarityScore increases, the predicted odds of purchase fraud decrease. Thus, the predicted odds of purchase fraud would be lower for a purchase with a SimilarityScore of 900 compared to a purchase with a SimilarityScore of 675 while holding LargeTransaction constant.