\left|s_0\right|=| \stackrel{n-1}{\sum _{k=2}}y₀(k)+ \frac{1}{2}y₀(n)|

\left|s_i\right|=| \stackrel{n-1}{\sum _{k=2}}x_i0(k)+ \frac{1}{2}x_i0(n)|

\left|s_i-s_0\right|=| \stackrel{n-1}{\sum _{k=2}}(x_i0(k)-y₀(k))+ \frac{1}{2}(x_i0(n)-y₀(n))|

ε_i= \frac{1+\left|s_0\right|+\left|s_i\right|}{1+\left|s_0\right|+\left|s_i\right|+|s_i-s_0|}

ε'_i= \frac{1+\left|s\text{'}{}_0\right|+\left|s\text{'}{}_i\right|}{1+\left|s\text{'}{}_0\right|+\left|s\text{'}{}_i\right|+|s\text{'}{}_i-s\text{'}{}_0|}

Y=β₀+β₁X₁+β₂X₂+β₃X₃+β₄X₄+ε

\left\{\begin{array}{l}Y=X\beta +\epsilon \\ \epsilon ~(0,{\sigma }^2{E}_{\mathrm{n}})\end{array}\right.

X= \left[\begin{array}{lllll}1& x_{11}& x_{12}& x_{13}& x_{14}\\ 1& x_{21}& x_{22}& x_{23}& x_{24}\\ \dots & \dots & \dots & \dots & \dots \\ 1& x_{m1}& x_{m2}& x_{m2}& x_{m2}\end{array}\right],Y= \left[\begin{array}{l}{y}_1\\ y_2\\ \dots \\ y_m\end{array}\right]。

β= {\left[{\beta }_0{\beta }_1{\beta }_2{\beta }_3{\beta }_4\right]}^{\mathrm{\tau }},ε= \left[{\epsilon }_1{\epsilon }_2\dots {\epsilon }_m\right]

\dot{Y}= {\dot{\beta }}_0+ {\dot{\beta }}_1X₁+ {\dot{\beta }}_2X₂+ {\dot{\beta }}_3X₃+ {\dot{\beta }}_4X₄

Q=∑(Y_i- {\dot{Y}}_i)²=min

\left\{\begin{array}{l}\frac{\partial Q}{\partial {\dot{\beta }}_0}=\sum (Y_i-{\dot{\beta }}_0-{\dot{\beta }}_1{X}_1-\dots -{\dot{\beta }}_4{X}_4)(-1)=0\\ \frac{\partial Q}{\partial {\dot{\beta }}_1}=\sum (Y_i-{\dot{\beta }}_0-{\dot{\beta }}_1{X}_1-\dots -{\dot{\beta }}_4{X}_4)(-X_1)=0\\ \dots \dots \\ \frac{\partial Q}{\partial {\dot{\beta }}_4}=\sum (Y_i-{\dot{\beta }}_0-{\dot{\beta }}_1{X}_1-\dots -{\dot{\beta }}_4{X}_4)(-X_4)=0\end{array}\right.