Goal of small residuals
As in simple linear models, the residuals in a multiple regression model are the errors that would have been made if the model had been used to predict the response values for the individuals in the data set. Small residuals are therefore desirable and the model's coefficients can be chosen to minimise the sum of squared residuals — the method of least squares.
In practice, statistical software should always be used
to obtain least squares parameter estimates.
Illustration