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

In a simple linear regression of an asset's excess return on the market's excess return, the ordinary least squares (OLS) estimates of the slope and intercept are chosen to minimize the:

OLS chooses the slope and intercept that minimize the sum of squared residuals, meaning the squared vertical gaps between observed and fitted values of the dependent variable. It does not use horizontal distances, and the residuals sum to zero by construction, so that sum cannot be minimized.

  1. Asum of the squared vertical distances between observed and fitted values of the dependent variableCorrect
  2. Bsum of the absolute horizontal distances between observed and fitted values of the independent variable
  3. Csum of the residuals, which equals the total variation in the dependent variable

Explanation

OLS minimizes the sum of squared residuals, which are the vertical distances between actual and predicted values of the dependent variable. Absolute horizontal distances are not the OLS criterion. The sum of residuals is always zero in OLS with an intercept, so minimizing it is meaningless.

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