Society of Actuaries (SOA) PA Practice Exam

Which of the following is a key assumption of OLS Regression?

1. The response variable follows a uniform distribution.

2. The conditional distribution of the response variable is normal.

3. The response variable is always positive.

4. The response variable must be discrete.

The correct answer is: The conditional distribution of the response variable is normal.

In ordinary least squares (OLS) regression, one of the primary assumptions is that the conditional distribution of the response variable, given the explanatory variables, is normally distributed. This assumption is crucial because OLS regression relies on the normality of the errors (the differences between observed and predicted values) to ensure that the estimates of the coefficients are unbiased, efficient, and have the minimum variance among all linear estimators. Normality of the conditional distribution is important for valid hypothesis testing and for constructing confidence intervals for the regression coefficients. If this assumption holds, it means that for any given set of independent variables, the distribution of the predicted values will be normally distributed around the true regression line, which is foundational for making statistical inferences about the model parameters. Other options do not accurately represent key assumptions underlying OLS regression. For instance, there is no requirement for the response variable to follow a uniform distribution, nor is there a restriction that it must always be positive or discrete. The response variable can be continuous and can take any real value, without necessarily being constrained to specific types of distributions.