This is not normal! (Re‐) Evaluating the lower nn guidelines for regression analysis

The rule of thumb that a sample size of is sufficient for valid regression analysis is often cited but rarely scrutinized. This paper evaluates the minimum number of observations required by examining how distributional characteristics like skewness and kurtosis affect the convergence of estimated t ‐statistics to the t ‐distribution in linear models. Through simulations involving over 22 billion regressions, sample sizes from 4 to 10,000 are tested across various combinations of distributions. Results show that it is sufficient that either the dependent or independent variable follow a symmetric distribution for the t ‐statistics to converge at much smaller sample sizes than , unless the other variable is extremely skewed. However, when both variables are highly skewed, much larger sample sizes are required. These findings suggest the rule is overly conservative in some cases and insufficient in others, offering revised guidelines for determining minimum sample sizes.