Force constant slope in linear regression
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Hello,
I am trying to perform a linear regression with a fixed slope term (i.e., only fitting the intercept). Is there a way to do this using the 'fitlm' function?
I came across this post asking a similar question: https://www.mathworks.com/matlabcentral/answers/67434-how-can-i-do-a-linear-fit-with-forced-slope. However, the solution in this post isn't ideal for my application. I'd like to stay within the fitlm framework so that I can use it's functionality (e.g., the 'predict' function and confidence interval calculation), and also because I'd like to give the user the flexibility to fit the slope or constrain it.
Thank you,
Abed
1 Comment
dpb
on 30 Mar 2021
I don't see any way to do so, directly, no.
AFAICT, none of the ways to specify the model allow you to enter a constant for a given term, nor can you build a LinearModel object other than through fitlm for an OLS fit; you can't try subterfuge of fitting the ordinary model and then replacing the coefficients, either; they're read-only.
The only way I see would be by the other subterfuge of creating a set of data that will produce the desired coefficents and fitting that. That would be relatively easy to have code to do since the intercept is easy-enough to calculate, one can generate a set of points that fit the proposed line and fit those. However, of course, the statistics other than the coefficients themselves will be bogus because the fit will be exact.
So the net result for which reason you propose wanting to do so will not produce the desired results; you'd still have to compute those intervals, etc., directly.
Of course, when one sets the value of the slope, none of the assumptions for those statistics are valid any longer, anyways...
Accepted Answer
Matt J
on 30 Mar 2021
Edited: Matt J
on 30 Mar 2021
Since you know the slope, m, it should be the same as fitting a constant term to y-m*x.
mdl = fitlm(x,y-m*x,'constant')
7 Comments
Matt J
on 5 Apr 2021
I don't think so. Additing or removing the known slope term doesn't change how much stochastic uncertainty you have.
More Answers (1)
Bruno Luong
on 5 Apr 2021
% find intercept such that
% y ~= givenslope*x + intercept
% in the least squares sense
intercept = mean(y - givenslope*x)
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