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Least squares regression sum must be zero
- Thread starter chengeto
- Start date
D
Deleted member 4993
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chengeto said:On an old exam paper they have this proof question. How do l work it out ?
What was the question?
D
Deleted member 4993
Guest
chengeto said:The question says show that the sum of residuals in least squares regression must always be zero ?
Please share with us your work/thoughts, indicating exactly where you are stuck - so that we know where to begin to help you.
Subhotosh Khan said:chengeto said:The question says show that the sum of residuals in least squares regression must always be zero ?
Please share with us your work/thoughts, indicating exactly where you are stuck - so that we know where to begin to help you.
Here is my attempt:
=\(\displaystyle y_{i}=a+bx_{i}+\epsilon\)
=\(\displaystyle \epsilon=y_{i}-a-bx_{i}\)
=\(\displaystyle \epsilon^2_{1}+\epsilon^2_{2}+\dots+\epsilon^2_{n}\)
=\(\displaystyle (y_{1}-a-bx_{1})^2+ (y_{2}-a-bx_{2})^2+\dots(y_{n}-a-bx_{n})^2\)
It is here that l get stuck. I don't know what to do ?