3. (3 points) Let $y_{1}, \ldots, y_{n}$ be numbers, and $\bar(y)=\frac{1}{n} \sum_{i=1}^{n} y_{i}$. Show that $\sum_{i=1}^{n}\left(y_{i}-\bar{y} ight)^{2}=\sum_{i=1}^{n} y_{i}^{2}-n \bar{y}^{2} .$ SP.PB. 189