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Confidence band around linear least-squares line

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z8080 on 4 Apr 2018
Commented: z8080 on 5 Apr 2018
I am using lsline in Matlab 2016b to add a linear least-squares line to a scatter plot. I would like to add a 95% confidence band around that fit line, such that it looks like this (plot is made with the python function seaborn):
However, lsline returns no fit parameters from which to construct the 95% confidence band, and the only Matlab function I could find that does return these, is nlpredci, but that function is used for something else (nonlinear regression prediction)


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Accepted Answer

Star Strider
Star Strider on 4 Apr 2018
One option is the Statistics and Machine Learning Toolbox fitlm (link) function. Then use the predict function (linked at the end of that page).
Another option is to sue polyfit and polyval with the File Exchange polypredci function, or the Statistics and Machine Learning Toolbox polyconf (link) function.


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z8080 on 5 Apr 2018
Many thanks once again, this is indeed what I wanted.
I had made a mistake earlier, what I meant to say was that I found it surprising that the confidence band is of constant width. Especially around that outlier at x=24, I'd have expected the confidence band to be much wider than towards the centre of the distribution.
But it could well be this just shows my inexperience with confidence bands and curve fits...
Star Strider
Star Strider on 5 Apr 2018
As always my pleasure.
The width isn’t constant. It may look that way if you use only the original ‘x’ values. However if you use my code (with the ‘xv’ vector) you can easily see that it is not constant, and diverges appropriately from the mean values to the extremes.
It’s not your inexperience. When I plot a nonlinear regression, confidence intervals, or anything else that needs nigher-than normal resolution to depict correctly, I use something like ‘xv’ instead of only using the original *‘x’*values, unless they are sufficiently high resolution. The image you posted appears to have used the same sort of approach.

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