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

A regression with k = 4 explanatory variables is estimated on n = 41 observations and produces an R-squared of 0.60. What is the adjusted R-squared?

Adjusted R-squared equals 1 minus (1 - R-squared) times (n - 1) divided by (n - k - 1). With R-squared 0.60, n = 41 and k = 4, this is about 0.556, so the closest option is 0.550. Adjusted R-squared is below R-squared.

  1. A0.600
  2. B0.550Correct
  3. C0.500
  4. D0.575

Explanation

Adjusted R² = 1 - (1 - R²)(n - 1)/(n - k - 1) = 1 - 0.40 × 40/36 = 1 - 0.4444 = 0.5556, which is approximately 0.556. Hmm, the closest listed value is 0.550. Check: 0.40 × 40/36 = 0.4444, so the adjusted value is 0.5556, closest to 0.550. Using n - k instead of n - k - 1 gives 1 - 0.4 × 40/37 = 0.5676, near 0.575, which is the wrong denominator.

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