Ordinary least squares

Ordinary least squares minimizes the unweighted sum of squared residuals between observed and fitted responses.

In simple linear regression with a nonconstant predictor,

For a nonconstant predictor, putThe minimized residual sum of squares isEach centered sum can be recovered in constant time from the five raw sums $\sum x_i$, $\sum y_i$, $\sum x_i^2$, $\sum x_i{y}_i$, and $\sum y_i^2$.