The least squares problem
Summary
- Definition of residual sum of squares:
\[S\left( b \right)=\sum_{i=1}^{n}{ e_i^2 }\]
- Alternative formulas for residual sum of squares:
\[S\left( b \right)=\sum_{i=1}^{n}{ {\left( y_i-x'_ib \right)}^2 }\]
- Or
\[S\left( b \right)=e'e\]
- Or
\[S\left( b \right)={\left( y-Xb \right)}'\left( y-Xb \right)\]
- The least squares problem:
\[\min_{b} S(b)\]