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

An analyst tests whether a stock's beta exceeds 1.0 using a one-tailed test at the 5% level. The regression has 32 observations, an estimated slope of 1.35 and a slope standard error of 0.20. The one-tailed critical t-value with 30 degrees of freedom is 1.697. The analyst most likely concludes that the:

The beta is significantly greater than 1.0. The t-statistic is (1.35 − 1.0) divided by 0.20, or 1.75, which exceeds the one-tailed critical value of 1.697, so the null hypothesis that beta is at most 1.0 is rejected at the 5% level.

  1. Abeta is significantly greater than 1.0, because the t-statistic of 1.75 exceeds 1.697Correct
  2. Bbeta is not significantly greater than 1.0, because the t-statistic of 1.75 is below the two-tailed critical value of 2.042
  3. Cbeta is significantly greater than 1.0, because the t-statistic of 6.75 exceeds 1.697

Explanation

The statistic is (1.35 − 1.0)/0.20 = 1.75. With a one-tailed test the relevant critical value is 1.697, and 1.75 exceeds it, so the null that beta ≤ 1.0 is rejected. Using the two-tailed value of 2.042 applies the wrong test, and 6.75 tests against zero.

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