Least Squares Method

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

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

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

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

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