Graphical Normality Tests on Residuals in Linear Regression

Abstract

Non-normal features of the population distribution such as skewness, kurtosis, long or short tails can be easily identified from the normal probability plot. The non-graphical hypotheses tests of normality do not have this diagnostic feature. For the statistical literature, 1 simultaneous probability intervals for augmenting a normal probability plot for a simple random sample are available where  is a significance level. The main objective of this research is on construction of simultaneous probability intervals on normal probability plots for residuals from linear regression providing objective judgements whether on residuals fall close to a straight line. We then compare the powers of these graphical tests and some non-graphical tests for residuals in order to assess the power performances of the graphical tests
and to identify the ones that have better power. Finally, the example is provided to illustrate the effectiveness of the tests.