I would like to know if there is a way to compute/approximate this formula: $$\sum_{i=0}^n (x_i-y_i)^2$$
when we only know:
$$\sum_{i=0}^n x_i$$ and $$\sum_{i=0}^n y_i$$
Thanks for any help!
Basically there isn't. You could have the sum of $x$ and $y$ very large, but the sum of differences squared be very small or the other way around. Even with $n=2$, think about $x_1=y_1=10000, x_2=y_2=20000$. Your first sum is zero. Alternately, think about $x_1=-y_1=1000, x_2=-y_2=-1000$ The first sum is $8,000,000$ and the last two are zero.