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

An analyst regresses monthly excess returns of a fund on the market excess return and a size factor using 62 observations. The estimated size-factor coefficient is 0.45 with a standard error of 0.18. Testing H0: coefficient = 0 against a two-sided alternative, what is the t-statistic and the degrees of freedom?

The t-statistic is the coefficient divided by its standard error, 0.45/0.18 = 2.50. Degrees of freedom equal observations minus estimated parameters including the intercept: 62 - 3 = 59. So the test uses t = 2.50 with 59 degrees of freedom.

  1. At = 2.50 with 59 degrees of freedomCorrect
  2. Bt = 2.50 with 62 degrees of freedom
  3. Ct = 0.40 with 59 degrees of freedom
  4. Dt = 2.50 with 60 degrees of freedom

Explanation

t = 0.45/0.18 = 2.50. With n = 62 and k = 2 slope coefficients, the regression has 3 estimated parameters including the intercept, so df = 62 - 3 = 59. Using 60 would ignore the intercept; 0.40 inverts the ratio.

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