# Least Squares Method

The function ${\displaystyle t(y_{1}...y_{n})}$

1. must belong to the set of all possible values for E(y)
2. must minimize ${\displaystyle \sum _{i=1}^{n}(y_{i}-t(y_{1}...y_{n}))^{2}}$

${\displaystyle t=t(y_{1}...y_{n})}$ is the LS Estimate.

${\displaystyle \sum _{i=1}^{n}(y_{i}-t)^{2}=\sum _{i-1}^{n}(y_{i}-{\bar {y}})^{2}+n({\bar {y}}-t)^{2}}$

${\displaystyle t}$ must equal ${\displaystyle {\bar {y}}}$ to minimize!