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FRM Part I · FRM Exam Part I · Regression Diagnostics

Two models explain bond spread changes using n = 54 observations. Model A has 3 explanatory variables and R-squared of 0.60. Model B adds 2 more explanatory variables and has R-squared of 0.61. Using adjusted R-squared = 1 - (1 - R^2)(n-1)/(n-k-1), which statement is correct?

Model A has the higher adjusted R-squared. Model A gives 1 minus 0.40 times 53/50, or 0.576, while Model B gives 1 minus 0.39 times 53/48, or about 0.569. The small gain in R-squared does not offset the penalty for two extra variables.

  1. AModel A has the higher adjusted R-squaredCorrect
  2. BModel B has the higher adjusted R-squared
  3. CBoth have identical adjusted R-squared
  4. DAdjusted R-squared of Model B is below zero

Explanation

Model A: 1 - 0.40 x 53/50 = 1 - 0.424 = 0.576. Model B: 1 - 0.39 x 53/48 = 1 - 0.43063 = 0.5694. Model A is higher, so the extra variables are not justified. Relying on raw R-squared would wrongly favor B.

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