computing error on least square fitting

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Sumera Yamin 2020-8-13

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编辑： Sumera Yamin 2020-8-16

Hi, i slove a system of equations (Ax-b) using least square method. i get an output with x like [2.5; -11.1; 0.8; 0.5]. the status flag is zero with system converging at iteration 2 and relative residual of 0.019. I want to calculate the error on my fit i--e with which certainity my solution is accurate. Can i claim that the residual which is norm of (Ax-b)/b means that my fit has an error of 1.9%?if not how can i calculate error on my fit?

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Alan Stevens 2020-8-15

0.019 is 1.9% not 19%.

Sumera Yamin 2020-8-15

oh yes obviously, thx for correction

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Answer 1

Bruno Luong 2020-8-15

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Can i claim that the residual which is norm of (Ax-b)/b

No make it

norm(A*x-b) / norm(b)

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Bruno Luong 2020-8-15

If you want an unnambiguous mathematical statement, just state exactly what mean:

norm(A*x-b) / norm(b) is approximatively 0.019

At your place I would say in the speaking language

The fit has a relative l2-norm residual of 1.9%.

The fit error usually designates the difference between the true and the estimated fit (parameters). So to me you shouldn't use the word "error."

Sumera Yamin 2020-8-15

Sorry i am not getting hang of it. " The fit has a relative l2-norm residual of 1.9%." how would i interpret this statement in terms of accuracy of my solution.

"The fit error usually designates the difference between the true and the estimated fit (parameters)" how can i calculate fit error?

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