Variation

Source

Degree of

FreedomDf

Sum of Squares

SS

Mean Square

MS

Fisher Ratio

F-value

Error of residuals

n − 2

$SSE={\displaystyle \sum _{i=1}^c{\displaystyle \sum _{j=1}^{ni}{\left(y_{ij}-{\widehat{y}}_{ij}\right)}^2}}$

$MSE=\frac{SSE}{n-2}$

Regression

1

$SSR={\displaystyle \sum _{i=1}^c{\displaystyle \sum _{j=1}^{ni}{\left({\widehat{y}}_{ij}-\overline{y}\right)}^2}}$

$MSR=\frac{SSR}{1}$

$F=\frac{MSR}{MSE}$

Lack of fit

C − 2

$SSL{F}_i={\displaystyle \sum _{i=1}^c{\displaystyle \sum _{j=1}^{ni}{\left({\overline{y}}_{ij}-{\widehat{y}}_{ij}\right)}^2}}$

$MSLF=\frac{SSLF}{c-2}$

$F^{*}=\frac{MSLF}{MSPE}$

Total

n − 1

$SSTD={\displaystyle \sum _{i=1}^c{\displaystyle \sum _{j=1}^{ni}{\left(y_{ij}-{\overline{y}}_{ij}\right)}^2}}$

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