How can I prove that SST=SSTr+SSE (anova) when

I have that

$SST =sum_i sum_j (x_{ij}-bar x_{..} )^2$

$SSTr =sum_i sum_j (bar x_{i.}-bar x_{..} )^2 $

$ SSE= sum_i sum_j (x_{ij}-bar x_{i.} )^2$

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#### Best Answer

Hint:

$SST =sum_i sum_j (x_{ij}-bar x_{..} )^2 = sum_i sum_j (x_{ij}-bar x_{..} + bar x_{i.} – bar x_{i.})^2$ and expand the summand.