The sum of squares of the deviations can also be used to provide an estimate of how closely the data cluster around the line. The standard error of estimate (S
e) is a measure of the accuracy of predictions. It is calculated according to the following formula, where
S denotes summation, and the
yi and
i are the observed and theoretical y-values of the data points, respectively.
For example, the Standard Error of Estimate Se for line A in the preceding example is the following:
For line B, the S
e is 12.114
For line C, the S
e is 17.656.
The smaller the standard error of estimate in a regression line, the more accurate the prediction.
