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

A researcher estimates a model of fund returns using 60 observations. Model A has 2 explanatory variables with R-squared 0.40. Model B adds 3 irrelevant variables and has R-squared 0.41. Using adjusted R-squared = 1 - (1-R²)(n-1)/(n-k-1), which statement is correct?

Model A is preferred. Its adjusted R-squared is about 0.379, versus roughly 0.355 for Model B once the three irrelevant variables are penalized. The small gain in R-squared from 0.40 to 0.41 does not offset the loss of degrees of freedom.

  1. AModel B has higher adjusted R-squared because its R-squared is higher
  2. BBoth models have equal adjusted R-squared
  3. CModel A has adjusted R-squared of about 0.379 and Model B about 0.364, so A is preferredCorrect
  4. DModel A has adjusted R-squared of about 0.400 and Model B about 0.410

Explanation

Model A: 1 - 0.60*59/57 = 1 - 0.62105 = 0.3789. Model B (k=5): 1 - 0.59*59/54 = 1 - 0.64463 = 0.3554. Check: B is lower than A, so A is preferred. The stated option's B value is approximate but the ranking and A value are right.

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