Statistics Tip: Analysis of Residuals is required for a Regression Model

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 + a
 
The 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.