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$$(A^TA)^{-1}A^T(y + noise) = \hat x$$ where $noise$ is vector of the same size as $y$ with all elements equal to unknown constant. That is all. You can get your estimated solution as a function of noise mean position in explicit form.


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I ran your code and got the below plot as well as an almost zero vector of: [-1.19209290e-07, -2.42083020e-09, -8.94069672e-08, 2.23517418e-07, -6.33299351e-08] This means numpy successfully curve-fit a line to your data. An order of 6 works a lot better, though: [-2.79396772e-09 -2.04281037e-14 -1.27897692e-13 4.33431069e-12 -2.27373675e-11] numpy ...


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