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

In a simple linear regression estimated by OLS that includes an intercept, which statement about the fitted regression line is most accurate?

The OLS line with an intercept always passes through the point of sample means of X and Y, because the intercept is computed as mean Y minus slope times mean X. It does not generally pass through the origin, and the slope equals correlation only when standard deviations are equal.

  1. AIt always passes through the point defined by the sample means of X and Y.Correct
  2. BIt passes through the origin when the slope is positive.
  3. CIt has a slope that equals the correlation between X and Y.

Explanation

Because intercept = mean Y − slope × mean X, the line satisfies mean Y = intercept + slope × mean X, so it passes through the means. Passing through the origin requires a zero intercept. The slope equals correlation only when both variables have equal standard deviations.

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