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

An analyst regresses the natural log of a company's annual revenue on a time trend measured in years (a log-lin model) and obtains a slope coefficient of 0.08. The slope coefficient is most appropriately interpreted as:

The slope of 0.08 in a log-lin model is the change in the log of revenue per year, which approximates a relative growth rate of about 8% per year. It is not an absolute change in currency units, and it is not 0.08 percent.

  1. Arevenue grows by an estimated 0.08 currency units each year.
  2. Brevenue grows by an estimated 0.08% each year.
  3. Crevenue grows at an estimated relative rate of about 8% per year.Correct

Explanation

In a log-lin model, ln(Y) = b0 + b1X, so the slope is the change in ln(Y) per unit of X, which approximates a relative (proportional) change in Y. A slope of 0.08 means about 8% growth per year. Reading it as 0.08% confuses a decimal with a percentage, and reading it as currency units ignores the log transformation of Y.

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