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

A researcher estimates an unrestricted regression with 5 explanatory variables and an intercept on 124 observations, getting R-squared of 0.55. She then tests 3 exclusion restrictions (three slopes equal to zero), and the restricted model has R-squared of 0.49 with the same dependent variable. What is the F-statistic, to two decimals?

The F-statistic is about 5.24. The fall in R-squared from the restrictions is 0.06, or 0.02 per restriction over 3 restrictions. The unrestricted unexplained share is 0.45 divided by 118 degrees of freedom, which is 0.003814. Dividing 0.02 by that gives 5.24.

  1. A5.24Correct
  2. B5.51
  3. C15.73
  4. D4.63

Explanation

The unrestricted residual df is 124−6=118. F = ((0.55−0.49)/3) / ((1−0.55)/118) = 0.02/0.0038136 = 5.24. Using 124 as the denominator df gives 5.51. Omitting the division by q gives 15.73. Using 1−R² of the restricted model in the denominator gives 4.63.

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