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IAI Actuarial Core Principles · Actuarial Statistics · Linear regression models

In a simple linear regression fitted to n = 12 observations, the estimated slope is 2.50 with standard error 0.80. For a test of H0: slope = 0 against H1: slope ≠ 0, what is the value of the test statistic and its degrees of freedom?

The test statistic is 2.50 divided by 0.80, which equals 3.125, compared with a t distribution on n minus 2, so 10, degrees of freedom, because two parameters (intercept and slope) are estimated in simple linear regression.

  1. At = 3.125 with 10 degrees of freedomCorrect
  2. Bt = 3.125 with 11 degrees of freedom
  3. Ct = 3.125 with 12 degrees of freedom
  4. Dt = 0.320 with 10 degrees of freedom
  5. t = 1.953 with 10 degrees of freedom

Explanation

The statistic is the estimate divided by its standard error: 2.50/0.80 = 3.125. Simple linear regression estimates two parameters, so the degrees of freedom are n - 2 = 10. Using 11 or 12 ignores the two estimated parameters, and 0.320 inverts the ratio.

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