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

A model with k = 3 regressors on n = 25 observations has R-squared of 0.40. Adding two more regressors raises R-squared to 0.44 with the same sample. What is the change in adjusted R-squared?

Adjusted R-squared falls from about 0.314 to about 0.293, a decrease of roughly 0.02. Although R-squared rises by 0.04, the two extra regressors use up degrees of freedom and the small gain does not compensate, so the adjusted measure declines.

  1. AAn increase of about 0.04
  2. BA decrease of about 0.02Correct
  3. CA decrease of about 0.04
  4. DNo change

Explanation

Original: 1 - 0.60 × 24/21 = 1 - 0.6857 = 0.3143. New with k = 5: 1 - 0.56 × 24/19 = 1 - 0.7074 = 0.2926. Change = -0.0217, about -0.02. The increase of 0.04 mistakes the R-squared change for the adjusted change.

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