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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Elementary principles of machine learning

A regression model is evaluated on a test set of 4 observations with actual values 10, 12, 14, 20 and predicted values 11, 10, 14, 16. What are the mean squared error (MSE) and the mean absolute error (MAE)?

The errors are -1, 2, 0 and 4. The squared errors sum to 21, giving MSE = 21/4 = 5.25. The absolute errors sum to 7, giving MAE = 7/4 = 1.75. Hence MSE is 5.25 and MAE is 1.75.

  1. AMSE = 5.25, MAE = 1.75Correct
  2. BMSE = 5.25, MAE = 2.25
  3. CMSE = 21, MAE = 7
  4. DMSE = 4.25, MAE = 1.75
  5. MSE = 5.25, MAE = 1.25

Explanation

Errors are -1, 2, 0, 4 (actual minus predicted: -1, 2, 0, 4). Squares are 1, 4, 0, 16, total 21, so MSE = 21/4 = 5.25. Absolute errors are 1, 2, 0, 4, total 7, so MAE = 7/4 = 1.75. Option 3 gives the totals without dividing by 4.

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