The purpose of Regression analysis is to develop a cause and effect "Model" in the form of an equation. To keep things simple, let's talk about Simple Linear Regression, in which the equation is y = bx + aThe Regression analysis comes up with the values for b and a. Residuals represent the Error in the Regression Model. They represent the Variation in the y variable which is not explainedby the Regression Model. So, Residuals must be Random. If not -- if Residuals form a pattern -- that is evidence that one or more additional factors (x's) influence y.A Scatterplot of Residuals against y-values should illustrate Randomness: Being Random means that the Residuals
- are Normally distributed
- have constant Variance
- show no patterns when graphed
- have no unexplained Outliers
Here are some patterns which indicate the Regression Model is incomplete.
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## AuthorAndrew A. (Andy) Jawlik is the author of the book, Statistics from A to Z -- Confusing Concepts Clarified, published by Wiley. ## Archives
December 2020
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