Actuarial Notes

CAS Exam MAS-I Spring 2018, Question 34

Study guide: Exam MAS-I

You are estimating the coefficients of a linear regression model by minimizing the sum:

\sum_{i=1}^{n}\left(y_i - \beta_0 - \sum_{j=1}^{p}\beta_j x_{ij}\right)^2 \quad \text{subject to} \quad \sum_{j=1}^{p}\beta_j^2 \le s

From this model you have produced the following plot of various statistics as a function of the budget parameter, s:

Determine which of the following statistics X and Y represent.

  • A) X = Squared Bias, Y = Test MSE
  • B) X = Test MSE, Y = Variance
  • C) X = Training MSE, Y = Squared Bias
  • D) X = Training MSE, Y = Variance
  • E) X = Variance, Y = Training MSE

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