When fitting a linear model to data, it can be useful to look at the residuals. Residuals are the difference between the -value of a point in a scatter plot and the value predicted by the linear model for the same -value.

For example, in the scatter plot showing the length of the fish and the age of the fish, the residual for the fish that is 2 years old and 100 mm long is 8.06 mm, because the point is at and the linear function has the value 91.94 mm () when is 2. The residual of 8.06 mm means that the actual fish is about 8 millimeters longer than the linear model estimates for a fish of that same age.

A scatterplot. Horizontal, from 0 to 5, by 0 point 5’s, labeled age of fish, years. Vertical, from 50 to 175, by 5’s, labeled length of fish, millimeters. 12 dots, trend linearly upward and right, dot 1at 1 comma 61 and dot 12 at 4 comma 164 with line of best fit.

When the point on the scatter plot is above the line, it has a positive residual. When the point on the scatter plot is below the line, the residual is a negative value. A line that has smaller residuals is more likely to produce estimates that are close to the actual value.