Confidence intervals of linear multiple regression
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Considering following linear multiple regression model:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/570219/image.png)
where observations
, coefficents
and
is a white Gaussian noise term.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/570224/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/570229/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/570234/image.png)
By the definition of the confidence interval:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/570239/image.png)
where
is the critical value, and standard error
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/570244/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/570249/image.png)
I understand that
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/570254/image.png)
My question is that why in post:https://stats.stackexchange.com/questions/16493/difference-between-confidence-intervals-and-prediction-intervals
and
they use sqaure root of Variance
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/570269/image.png)
rather than the standard error?? Where is the
?
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/570264/image.png)
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