How to open square brackets of the sum?

Question

For example Σ(y[i]-mean(y[i]))^2 = ? Please describe the way how it opens.

What do you mean by open? – BigbearZzz Oct 31 '15 at 13:49 — BigbearZzz, Oct 31 '15 at 13:49

score 0 · Accepted Answer · answered Oct 31 '15 at 13:53

0

Hint

Denote $\bar y=\frac{\sum_{i=1}^ny_i}{n}.$ Then

$$\sum_{i=1}^n (y_i-\bar{y})^2=\sum_{i=1}^n(y_i^2-2\bar{y}y_i+\bar y^2)=\sum_{i=1}^ny_i^2-2\bar{y}\sum_{i=1}^ny_i+\sum_{i=1}^n\bar y^2.$$

What is the relation between $\sum_{i=1}^ny_i$ and $\bar y?$ How can you simplify the whole expression?

answered Oct 31 '15 at 13:53

mfl

Thank you. So it equals Σy[i]^2-mean(y)*Σy[i],right? – ZsideZ Oct 31 '15 at 14:03
Yes. You can also write it as $\sum_{i=1}^n y_i^2-n\bar{y}^2.$ – mfl Oct 31 '15 at 14:39

1 Answers1