Assume a $10 cost for soliciting a non-responder and a $200 profit for soliciting a responder. The logistic regression model gives a probability score named P_R on a SAS data set called VALID. The VAL

Question

Options

• Adata VALID; set VALID; Profit = (P_R > .05)Purch200 - (P_R > .05)*(1 - Purch)*10; run;
• Bdata VALID; set VALID; Profit = (P_R <= .05)Purch200 - (P_R > .05)*(1 - Purch)*10; run;
• Cdata VALID; set VALID; if P_R > .05; Profit = (P_R > .05)Purch200 - (P_R > .05)*(1 - Purch)*10; run;
• Ddata VALID; set VALID; if P_R > .05; Profit = (P_R > .05)Purch200 + (P_R <= .05)*(1 - Purch)*10; run;

• A
  70% (30)
• B
  9% (4)
• C
  16% (7)
• D
  5% (2)

Explanation

Option A correctly models the profit for every customer in the dataset. In SAS, a boolean expression like (P_R > .05) evaluates to 1 when true and 0 when false, acting as a selector. The formula awards +$200 when a customer is solicited (P_R > .05) and responds (Purch=1), subtracts $10 when solicited and doesn't respond (1-Purch=1), and yields $0 for anyone not solicited - which is exactly the business logic described.

Option B is wrong because its first term uses (P_R <= .05) instead of (P_R > .05), meaning it mistakenly assigns the $200 profit to unsolicited responders rather than solicited ones. Option C is wrong because the bare if P_R > .05; (without then) is a SAS subsetting IF - it silently drops all records where P_R ≤ 0.05 from the output, so customers who weren't solicited get no profit row at all, instead of a $0 row. Option D fails for the same subsetting IF reason as C, and also uses + instead of - before the cost term, turning the $10 cost into a phantom gain.

Memory tip: Think "selector × outcome × value" - every term in the profit formula must use (P_R > .05) as the solicitation gate, Purch (or 1-Purch) as the response gate, and the sign distinguishes profit (+200) from cost (-10). Any option that flips the inequality in a profit term or uses a bare if without then is a trap.

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