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FRM Part I · FRM Exam Part I · Regression with Multiple Explanatory Variables

Model A has k = 2 regressors and R-squared of 0.500. Model B adds 3 more regressors (k = 5) and has R-squared of 0.530. Both use n = 31 observations. Which statement is correct?

Model A's adjusted R-squared is 0.4643 versus 0.4360 for Model B, so Model A is preferred. The R-squared rise from 0.500 to 0.530 is too small to offset the penalty for three additional regressors with only 31 observations.

  1. AAdjusted R-squared favors Model B because 0.530 exceeds 0.500
  2. BAdjusted R-squared is 0.4643 for A and 0.4360 for B, favoring Model ACorrect
  3. CAdjusted R-squared is 0.4643 for A and 0.4360 for B, favoring Model B
  4. DAdjusted R-squared is equal for both models

Explanation

Model A: 1 - 0.5 × 30/28 = 1 - 0.53571 = 0.4643. Model B: 1 - 0.47 × 30/25 = 1 - 0.564 = 0.4360. Model A has the higher adjusted R-squared, so the small gain in R-squared does not justify three extra variables.

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