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

Which statement about the ordinary least squares (OLS) estimation of a simple linear regression is most accurate?

OLS minimizes the sum of the squared vertical distances between the observed and fitted values of the dependent variable, known as the sum of squared errors. It does not maximize residual correlation with X, which is zero by construction, nor minimize deviations of X from its mean.

  1. AIt maximizes the correlation between the residuals and the independent variable.
  2. BIt minimizes the sum of the squared vertical distances between observed and fitted values of the dependent variable.Correct
  3. CIt minimizes the sum of the absolute differences between the observed values of the independent variable and their mean.

Explanation

OLS chooses the intercept and slope that minimize the sum of squared residuals, which are the vertical differences between actual and fitted values of Y. As a result, the residuals are uncorrelated with X rather than maximally correlated, and absolute deviations around the mean of X are unrelated to the criterion.

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