# Thread: Deriving the Least Squares Estimates

1. Once again thanks for the help guys, its made this whole concept a lot easier to understand. I think I have definitely improved especially dealing with sigmas.

Originally Posted by Villa Incognito
didnt even think to do that.

The part I am struggling with right now is:

I was wondering though, if perhaps you could go over how to do this question again for me. In particular how to use the second equation as part of the proof. It's something I cannot grasp right now.

Thanks.

2. I was asked to expand SSxy

which can be written as $\sum_{k=1}^n (x_k-\bar x) (y_k-\bar y)$

$=\sum_{k=1}^n (x_k-\bar x) y_k- \sum_{k=1}^n (x_k-\bar x) \bar y$

$=\sum_{k=1}^n (x_k-\bar x) y_k- \bar y\sum_{k=1}^n (x_k-\bar x)$

$=\sum_{k=1}^n (x_k-\bar x) y_k$

since

$\sum_{k=1}^n (x_k-\bar x)=0$

by expanding that as well.
You can drop either sample mean in SSxy, but not both.

3. next time, just post your question
Lots of people could have solved this
You shouldn't make a request through messages.

4. ## Re: Deriving the Least Squares Estimates

I had to study the same question in my university and as a homework question we had to derive the least square estimator in matrix notation. The full step by step derivation for the estimator for beta is provided here.

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