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##### Subject 7. Functional Forms for Simple Linear Regression

In the field of investments, the estimated parameters and other relationships have a tendency to change through time. Thus, the relationships between variables found during one period may not persist through a future period. For example, the betas estimated for stocks tend to vary and drift over time. Also, the correlations between currencies fluctuate over time.

If the relationship between the independent variable and the dependent variable is not linear, we can often transform one of both of these variables to convert this relation to a linear form, which then allows the use of simple linear regression.

The log-lin model: logarithmic dependent variable - linear independent variable. The model is typically used when the variables may have an exponential growth relationship. For example, if you put some cash in a saving account, you expect to see the effect of compounding interest with an exponential growth of your money! The original model in these types of scenarios isn�t linear in parameters, but a log transformation generates the desired linearity.

The lin-log model: linear dependent variable - logarithmic independent variable. This model is typically used when the impact of the independent variable on the dependent variable decreases as the value of the independent variable increases.

The log-log model: logarithmic dependent variable - logarithmic independent variable.

The key to selecting the correct form is to examine the goodness of fit measures:

• the coefficient of determination (R2)
• the F-statistic
• the standard error of the estimate (se)
• patterns in the residuals

Learning Outcome Statements

h. describe different functional forms of simple linear regressions.

CFA® 2022 Level I Curriculum, , Volume 1, Reading 7 