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FRM Part I · FRM Exam Part I · Linear Regression

In a simple linear regression of a fund's monthly excess return on the market's excess return using 62 observations, the estimated slope is 1.15 with a standard error of 0.20. Testing H0: slope = 1 against a two-sided alternative, what is the t-statistic and the degrees of freedom?

The t-statistic is 0.75 with 60 degrees of freedom. The estimate minus the hypothesized value of 1 is 0.15, divided by the standard error of 0.20. A simple regression with 62 observations estimates two parameters, leaving n - 2 = 60 degrees of freedom.

  1. At = 0.75 with 60 degrees of freedomCorrect
  2. Bt = 5.75 with 60 degrees of freedom
  3. Ct = 0.75 with 61 degrees of freedom
  4. Dt = 0.75 with 62 degrees of freedom

Explanation

The t-statistic tests against the hypothesized value: (1.15 - 1)/0.20 = 0.75. Degrees of freedom are n - 2 = 60 in a simple regression. Using 5.75 comes from testing against zero (1.15/0.20), which is the wrong null here.

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