Table 1 Anova Table

Regression

df_R = 1

${\text{SS}}_{\text{R}}={\displaystyle \sum _{\text{i}=\text{1}}^{\text{I}}{\text{J}}_{\text{i}}{\left({\widehat{\text{y}}}_{\text{i}}-\overline{\overline{\text{y}}}\right)}^2}$

${\text{MS}}_{\text{R}}=\frac{{\text{SS}}_{\text{R}}}{{\text{df}}_{\text{R}}}$

$\frac{{\text{MS}}_{\text{R}}}{{\text{s}}_{\text{p}}^{\text{2}}}$

Error

${\text{df}}_{\text{E}}=\left(\text{I}-\text{2}\right)+{\displaystyle \sum _{\text{i}=\text{1}}^{\text{I}}\left({\text{J}}_{\text{i}}-\text{1}\right)}$

${\text{SS}}_{\text{E}}={\displaystyle \sum _{\text{i}=\text{1}}^{\text{I}}{\displaystyle \sum _{\text{j}=1}^{{\text{J}}_{\text{i}}}{\left({\text{y}}_{\text{ij}}-{\widehat{\text{y}}}_{\text{i}}\right)}^2}}$

${\text{MS}}_{\text{E}}=\frac{{\text{SS}}_{\text{E}}}{{\text{df}}_{\text{E}}}$

   Lack of fit

df_L = (I – 2)

${\text{SS}}_{\text{L}}={\displaystyle \sum _{\text{i}=\text{1}}^{\text{I}}{\text{J}}_{\text{i}}}{\left({\widehat{\text{y}}}_{\text{i}}-{\overline{\text{y}}}_{\text{i}}\right)}^{\text{2}}$

${\text{MS}}_{\text{L}}=\frac{{\text{SS}}_{\text{L}}}{{\text{df}}_{\text{L}}}$

$\frac{{\text{MS}}_{\text{L}}}{{\text{s}}_{\text{p}}^{\text{2}}}$

   Pure error

${\text{df}}_{\text{P}}={\displaystyle \sum _{\text{i}=\text{1}}^{\text{I}}\left({\text{J}}_{\text{i}}-\text{1}\right)}$

${\text{SS}}_{\text{P}}={\displaystyle \sum _{\text{i}=\text{1}}^{\text{I}}{\displaystyle \sum _{\text{j}=\text{1}}^{{\text{J}}_{\text{i}}}{\left({\text{y}}_{\text{ij}}-{\overline{\text{y}}}_{\text{i}}\right)}^{\text{2}}}}$

${\text{s}}_{\text{p}}^{\text{2}}=\frac{{\text{SS}}_{\text{p}}}{{\text{df}}_{\text{p}}}$

Total corrected

${\text{df}}_{\text{T}}=\left({\displaystyle \sum _{\text{i}=\text{1}}^{\text{I}}{\text{J}}_{\text{i}}}\right)-1$

${\text{SS}}_{\text{T}}={\displaystyle \sum _{\text{i}=\text{1}}^{\text{I}}{\displaystyle \sum _{\text{j}=\text{1}}^{{\text{J}}_{\text{i}}}{\left({\text{y}}_{\text{ij}}-\overline{\overline{y}}\right)}^{\text{2}}}}$