A normal distribution for the disturbance term in regression theory

TL;DR

This paper provides an elementary proof that the disturbance term in regression models follows a normal distribution when the sample size is large, supporting the common assumption in regression analysis.

Contribution

It offers a straightforward proof confirming the normality of the disturbance term in large-sample regression, reinforcing theoretical foundations.

Findings

Disturbance term is normally distributed for large n

Supports the use of normality assumption in regression analysis

Provides an elementary proof of the normality result

Abstract

In regression theory, it is stated that the disturbance term follows the normal distribution when the sample size is large. In Professor J.Johnston's words: "In view of the many factors involved, an appeal to the Central Limit Theorem would further suggest a normal distribution for u." This paper includes an elementary proof that the disturbance term follows the normal distribution when n is large.