Parameter Calculation by Least Squares Minimization
The method of least squares consists of minimizing 
with respect to β. Setting θ = Xβ, we minimize: 
with respect to β. Setting θ = Xβ, we minimize: subject to:
Let 
be the least squares estimate of β. The fitted regression 
is denoted by:
be the least squares estimate of β. The fitted regression is denoted by:The elements of 
are called the residuals. The value of:
are called the residuals. The value of:
is called the residual sum of squares. The matrix: 
which is the regression matrix without the first column of 1s, is called the predictor data matrix.
