Definition

Let $RS S_{p}$ be a RSS of pooled (combined) regression’s, $RS S_{i}$ ‘s be RSS of regression in each group or time period, $k$ be the number of parameters estimated in each model, $n_{i}$ be the number of data of group $i$ , and $H_{0} : β_{11} = β_{21}, β_{12} = β_{22}, \dots, β_{1 k} = β_{2 k}$ , then the test Statistic is $F = \frac{(( RS S _{p} ) - ( RS S _{1} + RS S _{2} )) / k}{( RS S _{1} + RS S _{2} ) / ( n _{1} + n _{2} - 2 k )} \sim F (k, n_{1} + n_{2} - 2 k)$

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