# How fitlm computes confidence bounds?

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Christos Tsallis on 5 Feb 2023
Edited: the cyclist on 7 Feb 2023
I have used fitmid=fitlm(x1,y1), fitmax=fitlm(x2,y2), fitmin=fitlm(x3,y3) in order to return a linear regression model for my data. Then, I plot them using "plot" function. I saw that confidence bounds were also included but I would like to ask, how are they computed? Is it 95% confident interval? the cyclist on 5 Feb 2023
Yes, the coefCI property of the model object output from fitlm gives the 95th percentile confidence intervals of the fitted coefficients.
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the cyclist on 7 Feb 2023
Edited: the cyclist on 7 Feb 2023
fitlm estimates a coefficient for each term in the fitting equation. Call one of those coefficients beta. There is a true value of beta (that is unknown), and you have an estimate of it.
Now suppose you performed the whole experiment thousands of times, and calculated thousands of confidence intervals. You would expect that the true value beta to be inside the 95th confidence interval in 95% of those experiments.
Note that this is not quite the same as saying there is a 95% chance that the true value beta lies inside this confidence interval. But that is the nature of frequentist statistics.

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