I am working through the proof for partitioning sum of squares.
Could someone please explicitly explain how one goes from line 14 to 15 in the following PDF:
http://capone.mtsu.edu/dwalsh/4380/438PARTN.pdf
That is, how one moves between these lines -
\begin{align} \rm{SSTO} &= \sum_{i=1}^r \sum_{j=1}^{n_i} (Y_{ij}-\overline{Y}_{..})^2 \\ &= \sum_{i=1}^r \sum_{j=1}^{n_i} [(Y_{ij}-\overline{Y}_{i.})+(\overline{Y}_{i.}-\overline{Y}_{..})]^2 \end{align}
I'm actually reading through Casella and Berger's "Statistical Inference" (pg 536), but the same jump occurs in both. Sorry, I was never the best at algebra... would someone please explain this.