Society of Actuaries (SOA) PA Practice Exam

Which of the following is NOT an underlying assumption of an ordinary least squares (OLS) model?

1. Errors are dependent

2. Errors have a constant variance

3. Errors have a mean of zero

4. Errors are normally distributed

The correct answer is: Errors are dependent

In the context of an ordinary least squares (OLS) model, one of the key assumptions is that the errors, or residuals, are independent. This means that the value of one error does not influence another, which is crucial for ensuring that the estimates derived from the model are reliable. When considering the provided options, the assumption that errors are dependent contradicts the foundational requirement of independence in OLS. In an OLS model, maintaining independence among the residuals allows for the application of statistical techniques that rely on this independence for hypothesis testing and inference. The other choices reflect valid assumptions of the OLS model. Errors having a constant variance (known as homoscedasticity) ensures that the spread of the errors remains the same across all levels of the independent variable. Errors having a mean of zero indicates that the model has captured all systematic variation in the dependent variable, meaning any remaining variance is random noise. Lastly, the assumption of errors being normally distributed often aids in the interpretation of results, especially in small sample sizes, as it allows for the application of certain statistical tests and confidence intervals. Therefore, the statement that errors are dependent is not an acceptable assumption within the OLS framework, making it the correct choice in this context.