FRM Part I · FRM Exam Part I · Machine-Learning Methods
A logistic regression for default has the form ln(p/(1-p)) = -3.0 + 0.5 x, where x is the debt-to-income ratio expressed in percentage points. For a borrower with x = 4, what is the predicted probability of default, to two decimals? (Use e^1 = 2.718.)
The predicted default probability is about 0.27. The log-odds equal -3.0 plus 0.5 times 4, which is -1.0. Converting with the logistic function gives 1 divided by (1 plus e to the power 1), roughly 1/3.718, or 0.27.
- A0.27Correct
- B0.73
- C0.50
- D0.12
Explanation
Log-odds = -3.0 + 0.5*4 = -1.0. Odds = e^-1 = 0.368, so p = odds/(1+odds) = 0.368/1.368 = 0.27. The 0.73 option is 1-p, from inverting the odds. Check: 1/(1+e^1) = 1/3.718 = 0.269.
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