In simple regression, the observed Type I error rates are all between 0.0380 and 0.0529, very close to the target significance level of 0.05. If you meet this guideline, the test results are usually reliable for any of the nonnormal distributions.
The study found that a sample size of at least 15 was important for both simple and multiple regression. If the test performs well, the Type I error rates should be very close to the target significance level. The study determined whether the tests incorrectly rejected the null hypothesis more often or less often than expected for the different nonnormal distributions. There were 10,000 tests for each condition. The residual distributions included skewed, heavy-tailed, and light-tailed distributions that depart substantially from the normal distribution.
If you have nonnormal residuals, can you trust the results of the regression analysis?Īnswering this question highlights some of the research that Rob Kelly, a senior statistician here at Minitab, was tasked with in order to guide the development of our statistical software.