FRM Part I · FRM Exam Part I · Machine-Learning Methods
A ridge regression with one standardized predictor and no intercept has the OLS slope estimate of 1.20, where the predictor's sum of squares is 20. The ridge penalty is lambda times the squared coefficient, minimizing SSR + lambda*b^2. With lambda = 5, what is the ridge slope estimate?
The ridge slope is 0.96. The OLS slope of 1.20 with a sum of squares of 20 implies sum xy equals 24. Ridge divides by sum of squares plus lambda, so 24 divided by 25 equals 0.96, a shrinkage from 1.20.
- A0.96Correct
- B0.60
- C1.00
- D1.20
Explanation
For a single predictor with no intercept, ridge b = (sum xy)/(sum x^2 + lambda). OLS b = sum xy/20 = 1.20, so sum xy = 24. Ridge b = 24/(20+5) = 0.96. Dividing 24 by 40 gives 0.60 by wrongly doubling lambda.
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