Residual Plot

To construct a residual plot, we use the same x-axis as the scatterplot, but we use a vertical axis of residual values. For an individual sample point, the residual is the value of the y coordinate minus the predicted value of y that is obtained by substituting the x value into the regression equation. The residual is the vertical “error” or difference between the y coordinate that is observed and the y coordinate predicted from the regression equation.

When analyzing a residual plot, look for a pattern in the way the points are configured, and use these criteria:
(1) The residual plot should not have an obvious pattern other than a straight-line pattern (confirming that a scatterplot of the sample data is a straight-line pattern and not some other pattern that is not a straight line);
(2) the residual plot should not become thicker (or thinner) when viewed from left to right (confirming the requirement that for the different fixed values of x, the distributions of the corresponding y-values all have the same standard deviation).