CFA Level I · CFA Level I Exam · Applications of Simple Linear Regression in Finance
Residuals from a linear regression of a company's earnings on time show a pattern of increasing, curved deviations, while earnings grow at a roughly constant percentage rate. The most appropriate response is to:
Earnings growing at a constant percentage rate follow an exponential path, which is linear in the log of earnings. Using ln(earnings) as the dependent variable in a log-lin model is therefore the most appropriate fix for the curved residual pattern.
- Aadd more observations to the linear model without changing its form.
- Buse the natural log of earnings as the dependent variable in a log-lin model.Correct
- Cuse the natural log of time as the independent variable in a lin-log model.
Explanation
Constant percentage growth implies exponential growth in earnings, which becomes linear in the log of earnings. A log-lin model, with ln(earnings) as the dependent variable, fits this pattern and typically removes the curved residuals. A lin-log model transforms the independent variable and suits a diminishing effect of X, and merely adding data does not fix a misspecified form.
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