Normality Test

Learn how to run normality tests for errors.

The Gauss-Markov theorem doesn’t require that the error term is normally distributed. However, inferences based on zz- or tt-statistics do need the error term to be normally distributed. In addition, when the error term isn’t normally distributed, it can be skewed or heavy tailed, affecting the efficiency of estimation. The quantile comparison plot from the car package is an effective way to check whether the residuals from the regression are approximately normally distributed or not.

Quantile comparison plot using qqplot()

The qqPlot() function plot compares the empirical quantiles of studentized residuals from model1 against the theoretical or expected quantiles of a benchmark tt or normal distribution, with a confidence envelopeConfidence envelopes provide a description of the sampling variation of item response curves in the space of the fitted functions.. The closer the residuals follow the quartile line, the closer the studentized residuals meet the theoretical distribution. The option simulate=TRUE means that the confidence envelope is based on parametric bootstrap.

Note: In case we want to compare the quantiles of studentized residuals against a theoretical normal distribution, we can simply replace t in the R code with norm instead. The option simulate=TRUE means the confidence envelope is based on parametric bootstrap.

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