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CFA Level I · CFA Level I Exam · Applications of Simple Linear Regression in Finance

In a simple linear regression with 27 observations, the estimated slope is 0.80 and its standard error is 0.30. The two-tailed critical t-value at the 5% significance level with 25 degrees of freedom is 2.060. For the null hypothesis that the slope equals zero, the analyst most likely:

The analyst rejects the null hypothesis. The t-statistic is 0.80 divided by 0.30, or 2.67, which is larger than the critical value of 2.060 at 25 degrees of freedom. The slope is therefore significantly different from zero at the 5% level.

  1. Arejects the null hypothesis, because the t-statistic of 2.67 exceeds 2.060Correct
  2. Bfails to reject the null hypothesis, because the t-statistic of 2.67 is below 2.060
  3. Cfails to reject the null hypothesis, because the t-statistic of 0.375 is below 2.060

Explanation

Degrees of freedom are n − 2 = 25. The t-statistic is 0.80/0.30 = 2.67, which exceeds 2.060, so the null is rejected. The 0.375 figure comes from inverting the ratio (0.30/0.80).

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