# Math Help - Trouble with a proof...help?

1. ## Trouble with a proof...help?

I must prove that the sum of xiyi is equal to the sum of yiXi

I am given that xi=(Xi-X average) and yi=(Yi-Y average)

This is a question having to do with the Classic Linear Regression Model. The assumptions of the CLRM should hold, that is.

Note that the second part of the equation has a big Xi

Any help with proving this would be awesome.

Thanks.

2. again I have to guess that you want to drop the average in ssxy in simple linear regression.

$\sum_{i=1}^n (x_i-\bar x) (y_i-\bar y) =\sum_{i=1}^n x_i(y_i-\bar y) -\bar x\sum_{i=1}^n (y_i-\bar y)=\sum_{i=1}^n x_i(y_i-\bar y)$

since $\sum_{i=1}^n (y_i-\bar y)=0$.

You can write SSxy three different ways...

$\sum_{i=1}^n (x_i-\bar x) (y_i-\bar y) =\sum_{i=1}^n x_i(y_i-\bar y) =\sum_{i=1}^n y_i(x_i-\bar x)$.

The last is best for obtaining means and variances, since x is usually fixed and y is random.