# Summation Simplification for Neumerator of Beta Estimator

1. May 24, 2013

### LBJking123

I need simplify this equation:

Ʃwixiyi - (ƩxiwiƩyiwi)/Ʃwi

Into an equation of the form: Ʃ(something - something)yi

I am pretty sure the first something is xiwi, but I have no idea what the second something would be.....

Any help would be greatly appreciated. Thanks!

2. May 24, 2013

### DrDu

Come on, that's easy:
$\sum_i w_i(x_i-\sum_j x_j w_j/\sum_k w_k) y_i$
Note that I chose a separate index for each summation for clarity.
The term in brakets is x minus <x>, i.e. the mean of x.

3. May 24, 2013

### LBJking123

Ohhhhh I kept thinking it was going to be

Ʃ(xiwi-(xiwi2)/Ʃwi)yi

I makes more sense when you choose a separate index for each summation.

Thanks for the help DrDu!