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.