As we have covered, in regression analysis a key assumption is that the residuals (the differences between observed and predicted values) follow a normal distribution.

This assumption is particularly important for statistical inference, as it ensures that confidence intervals and hypothesis tests are valid. When residuals are normally distributed, regression coefficients and their associated p-values can be interpreted correctly.

Deviations from normality may indicate that the model is missing important variables, nonlinear relationships, or heteroscedasticity (unequal variance).

Checking Normality of Residuals

There are several methods to check the normality of residuals. Visual methods include histograms, Q-Q plots (quantile-quantile plots), and density plots:

Statistical tests such as the Shapiro-Wilk test and the Kolmogorov-Smirnov test can provide formal assessments:

Note that statistical tests can be sensitive to sample size. Small datasets may fail to detect non-normality, while large datasets may flag minor deviations that are not practically significant. Therefore, a combination of visual inspection and statistical testing is generally recommended.

Next reading:

Homoscedasticity