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FRM Part I · FRM Exam Part I · Machine Learning and Prediction

An analyst uses ridge regression with one predictor and no intercept, where the predictor has been scaled so that the sum of x squared equals 50 and the sum of x times y equals 40. The ridge objective is the sum of squared residuals plus lambda times beta squared. With lambda = 30, what is the ridge coefficient estimate?

The ridge coefficient is 0.50. With one predictor and no intercept, beta equals the sum of xy divided by the sum of x squared plus lambda, so 40 divided by 80 gives 0.50. The OLS estimate of 0.80 ignores the penalty and is therefore too large.

  1. A0.50Correct
  2. B0.80
  3. C0.67
  4. D1.33

Explanation

The ridge estimate is beta = Sxy / (Sxx + lambda) = 40 / (50 + 30) = 0.50. The OLS estimate is 40/50 = 0.80, which is the unpenalized answer. Using lambda in the numerator or subtracting it (40/20 = 2.0) are errors.

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