A residual is the vertical distance between a data point and the line of fit. When a line of fit has been drawn on a scatter plot, not all of the data points lie exactly on the line — some of them are above the line and some below. Therefore, each data point has one residual, which can be positive, negative, or zero.

A residual can also be defined as the observed y-value of a data point minus its predicted y-value, found using the line of fit.

Generally, the smaller the absolute values of the residuals, the more reliable the line of fit is. A scatter plot of the residuals can be used to determine how well a model fits data set. The independent variable and the residuals are graphed as ordered pairs (x,residual). The appropriate models can be determined by looking at the scatter plot of residuals.

• If the points in the plot are randomly placed about the x-axis, then a linear model describes the data set well.
• If some kind of pattern appears in the scatter plot, a non-linear model is more appropriate for the data.