FRM Part I · FRM Exam Part I · Machine-Learning Methods
A ridge regression is fitted with a single standardized predictor and no intercept. The ordinary least squares slope is 0.80, the sum of squared predictor values is 50, and the ridge objective is the residual sum of squares plus lambda times the squared coefficient. For this one-predictor case the ridge estimate equals the OLS estimate multiplied by S/(S + lambda), where S is the sum of squared predictor values. If lambda = 30, what is the ridge slope?
The ridge slope is 0.50. The shrinkage factor is 50 divided by 80, which is 0.625, and multiplying the OLS slope of 0.80 by this factor gives 0.50. The penalty therefore pulls the coefficient toward zero by 37.5 percent.
- A0.30
- B0.50
- C0.60
- D0.48Correct
Explanation
Shrinkage factor = 50/(50+30) = 0.625. Ridge slope = 0.80 × 0.625 = 0.50. Check: 0.50/0.80 = 0.625. Wait, this gives 0.50, so the correct choice is 0.50.
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