Residuals

Abstract

Most commonly used statistical procedures, for analysis and interpretation of statistical data, rest on assumptions about the behaviour of the data. Quite often these assumptions can be adequately justified, and the procedures accepted as fair and reasonable. But that is not always so, and it behoves the analyst to check consistency of the data with the assumptions. Failure to do this may lead to a grossly misleading analysis and the drawing of wrong conclusions. Just how consistency can be checked depends on the complexity of the data. Often a step is calculation of residuals, which are measures of deviation between the observed values of a variable and the fitted (or estimated or predicted) values for that variable, calculated in accordance with the assumptions. The residuals, when found, are sometimes combined into a summary measure of goodness of fit, or sometimes they are displayed graphically, in various possible ways.