In a multiple regression model, how are the values of the error term, ε, assumed to be distributed?

In a multiple regression model, the values of the error term, ε, are assumed to be normally distributed. This assumption is fundamental to the validity of many statistical tests and inference techniques used in regression analysis. The normality of the error terms allows for the derivation of properties regarding the estimators of the model, such as their means and variances.

When the errors are normally distributed, it means that they cluster around the mean of zero, distributing symmetrically in a bell shape. This assumption is crucial because it supports the use of techniques like hypothesis testing and constructing confidence intervals. Violations of this assumption might lead to unreliable estimates and conclusions, making it an essential consideration in regression analysis.

Understanding this helps in recognizing that while other distributions could theoretically be used, the normal distribution's properties make it particularly suitable for the random errors in regression models. This is why normal distribution is the correct assumption for the error term, ε, in multiple regression.