# Regression

• Apr 17th 2013, 12:25 AM
Jon123
Regression
Hello everyone!

I have a question.
Let c = b - a and show the regression c on a has slope b hat - 1 where b hat slope from regression b on a.

answer should be b hat = SSab/SSaa - 1 (i think....)

What I want is to show that it is true. Could I please get help in answering this question.
I have attempted below.

c = b hat = SSac/SSaa
= [sum] (ai - c hat)(bi - b hat) / SSaa
= [sum] (ai - c hat)bi / SSaa - [sum] (ai - c hat)b hat / SSaa
= [sum] (ai - c hat)bi / [sum](ai-c hat) - 1

Therefore, b hat = SSab/SSaa - 1

is this correct?

Thanks for those who help me out.

• Apr 17th 2013, 08:52 PM
chiro
Re: Regression
Hey Jon123.

By regression do you mean a simple y vs x regression (one independent, one dependent with one intercept)?
• Apr 18th 2013, 01:07 AM
Jon123
Re: Regression
Hi Chiro!
using simples linear regression model y on x, what I have used was b on a.
the question is quite confusing for me. I don't know how to start except for SSxc/Sxx i think?
• Apr 18th 2013, 01:36 AM
chiro
Re: Regression
You are headed in the right direction: Just use the definition and show that you get what you get.