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?
Predicted odds will be 98.26 percent less
Predicted odds will be 97.01 percent less
Predicted odds will be 99.15 percent less
Predicted odds would increase
Predicted odds will be 90.37 percent less
To hold LargeTransaction constant, we only need to consider the effect of the SimilarityScore. The coefficient for SimilarityScore is -0.018 in the model.
To compare the predicted odds of purchase fraud for a SimilarityScore of 900 compared to 675, we can calculate the difference in the log-odds:
Difference in log-odds = 0.018 * (900 - 675) = 0.018 * 225 = 4.05
Since the log-odds represent the natural logarithm of the odds, we can calculate the percentage change in odds using the formula:
Percentage change in odds = (e^(Difference in log-odds) - 1) * 100
Plugging in the value of the difference in log-odds:
Percentage change in odds = (e^(4.05) - 1) * 100 ≈ 57.78
Therefore, the predicted odds of purchase fraud for a SimilarityScore of 900 compared to 675 will decrease by approximately 57.78 percent.
None of the given answer choices match this calculation exactly. However, the closest answer choice is "Predicted odds will be 57.78 percent less", which is not provided.