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
Which of the following statements best explains how changes in SimilarityScore affect predictions of a purchase being fraudulent?
Increasing SimilarityScore by one decreases the predicted odds of a purchase being fraudulent by 54.88 percent, holding the transaction amount constant.
Increasing SimilarityScore by one decreases the predicted odds of a purchase being fraudulent by 1.78 percent, holding the amount of the transaction constant.
Increasing SimilarityScore by one increases the predicted odds of a purchase being fraudulent by 54.88 percent, holding the transaction amount constant.
Increasing SimilarityScore by one decreases the predicted odds of a purchase being fraudulent by half, holding the transaction amount constant.
The correct statement is:
Increasing SimilarityScore by one decreases the predicted odds of a purchase being fraudulent by 1.78 percent, holding the amount of the transaction constant.
This is because the coefficient for SimilarityScore is -0.018, indicating that for each unit increase in SimilarityScore, the odds of a purchase being fraudulent decrease by (0.018 * 100) = 1.78 percent.