# Problem with a summation suffix.

Please can someone tell me why we drop the summation of i here?

$S = \sum_{i,j}(y_{ij}-\mu -\alpha_i)^2$

$\frac{dS}{d\alpha_i} = \sum_{j}(y_{ij}-\mu -\alpha_i)$

It's part of a question which is really bugging me?

Thank you for any help I really appreciate it!

Consider one particular term of the sum:

$$S_k = \sum_j (y_{kj}-\mu-\alpha_k)^2$$

Now, you have

$$\frac{\partial S_k}{\partial \alpha_i} = \left\{\begin{matrix}-2\sum_j(y_{ij}-\mu-\alpha_i) &\text{ if } i=k\\0 &\text{ otherwise}\end{matrix}\right.$$ So when you sum over all of the $k$ values, you're left with $$\frac{\partial S}{\partial \alpha_i} = -2\sum_j (y_{ij}-\mu-\alpha_i)$$

• Awesome Glen, thank you. Is there a way a can improve your $\textit{reputation}$ on here? I'm new. – Kane Blackburn Apr 21 '13 at 12:19
• By answering questions, by asking interesting questions, and things like that. More info here. – Glen O Apr 21 '13 at 12:22
• I realise that. I was asking more whether I had to do vote for you in someway so you gain credit for the answer you've just given me. I guess you gain it automatically as soon as I tick your answer as my accepted answer? – Kane Blackburn Apr 21 '13 at 12:27
• Ah, sorry - yes, accepting the answer, which is what the tick does, gives me 15 reputation points. Voting my answer up also gives me 10 reputation points. – Glen O Apr 21 '13 at 12:29
• Okay once I have the 15 reputation required I will vote your answer up so that you get the further points. Thanks again. – Kane Blackburn Apr 21 '13 at 12:31