Linear regression with a minimum intercept value

Question

Brian Scannell 2018-2-15

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https://ww2.mathworks.cn/matlabcentral/answers/382939-linear-regression-with-a-minimum-intercept-value

编辑： Brian Scannell 2018-2-15

I am using linear regression to compute the coefficients for both y = B0 + B1*x and y = B0 + B1*x + B3*x^3. I know that the measurement technique has a minimum instrument noise level, Nmin, so I have a minimum value for B0. But the actual noise value for a set of measurements can be higher than Nmin, so B0 is not fixed - just constrained to be >= Nmin.

I can execute the regression with B0 unconstrained and test for B0 < Nmin, but if that is the case, is it then reasonable to assume that the best constrained least squares solution is achieved by fixing B0 as Nmin (i.e. just deduct Nmin from all my x values and repeat the regression with a zero intercept)?

Or is it possible that the same set of data points that give B0 < Nmin when B0 is unconstrained, could result in an intercept higher than the Nmin given the constraint that B0 >= Nmin?

I appreciate that this is more of a maths question than a Matlab question per se, but I'm hoping there might be a Matlab solution I can implement without too high a processing cost as I need to execute millions of these regressions per dataset (hence I am currently using mldivide (B = x\y) rather than regress or fitlm).

Thanks, Brian