CFA Level I · CFA Level I Exam · Applications of Simple Linear Regression in Finance
An analyst plots the residuals of a simple linear regression against the independent variable and observes that the spread of the residuals widens steadily as the independent variable increases. Which assumption of the linear regression model is most likely violated?
The homoskedasticity assumption is most likely violated. A residual spread that widens as the independent variable rises shows that the error variance is not constant across observations, which is the definition of heteroskedasticity. It does not indicate nonlinearity or non-normality of the errors.
- AHomoskedasticity of the error termCorrect
- BNormality of the error term
- CLinearity of the relationship between the variables
Explanation
A residual spread that changes with the independent variable means the error variance is not constant, which is heteroskedasticity. This violates homoskedasticity. A curved pattern would suggest nonlinearity, and a non-bell-shaped histogram or Q-Q plot would suggest non-normality.
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