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

In a simple linear regression, an analyst increases the sample size while the estimated slope stays the same and the variability of the residuals stays the same. All else equal, the slope's t-statistic most likely:

The t-statistic most likely increases. A larger sample reduces the standard error of the slope coefficient, and with the estimated slope unchanged, a smaller denominator produces a larger t-statistic, making rejection of the null of zero slope more likely.

  1. Adecreases, because degrees of freedom rise
  2. Bincreases, because the standard error of the slope fallsCorrect
  3. Cstays the same, because the estimated slope is unchanged

Explanation

The standard error of the slope falls as the sample grows, because the sum of squared deviations of the independent variable rises. With an unchanged slope estimate, dividing by a smaller standard error increases the t-statistic.

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