See please the end of the attached file.
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Wrote

See please the end of the attached file.

Triplet roots ... FindRoot not doctored.

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The first error can be handled by wrapping the function in eval(). For the second one this does not help.

I take the opportunity to advertise the Maxima Fit() function.

It is explained in https://doi.org/10.25933/opus4-2949 chapter 6 (English) and in https://doi.org/10.25933/opus4-2948, chapter 9 (German).

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And the Lord God created the function eval and the lord said this is good!
And the Lord God created the Maxima and the lord said this is sehr kompliziert!

Hm, where exactly do you see the most severe сложности in the use of the Maxima plugin? Perhaps everything that needs a handbook is too complicated nowadays
I really like the curve fitting interface with the Fit() function, which might even be comprehensible from the подсказка in the dynamic help.

Hi. Polynomial fitting, returning the same values that Excel returns. From this post.

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Best regards.
Alvaro.

Sorry!
But the question was Why not How

Wrote

Sorry!
But the question was Why not How

Hi Valery. Martin showed why. But for the quadratic case Máxima's Fit function does not return the same result as Excel, which could be said to have been taken as standard, since they are also the same as those usually obtained with the 'all powerful' (talking about of gods) a\b of Matlab. I made the post to show how those mythical values can also be obtained in SMath.

Because SMath' solver isn't very powerful you can get those same values with your method using another, like the following one



About the error vectorizing, you can see why taking a look of this



Best regards.
Alvaro.

Wrote

Wrote

Sorry!
But the question was Why not How

Hi Valery. Martin showed why. But for the quadratic case Máxima's Fit function does not return the same result as Excel, which could be said to have been taken as standard, since they are also the same as those usually obtained with the 'all powerful' (talking about of gods) a\b of Matlab. I made the post to show how those mythical values can also be obtained in SMath.

Because SMath' solver isn't very powerful you can get those same values with your method using another, like the following one



About the error vectorizing, you can see why taking a look of this



Best regards.
Alvaro.

Send please sm-file!

Wrote

Send please sm-file!

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Best regards.
Alvaro.

There is not much sense in fitting functions with many degrees of freedom to data containing not much information. Any function which goes through the centroid of the data points will come up with a similar MSE.

Is the second result really the best just because of it's lowest MSE?

Valery, as it looks all doctored.
Thanks Alvaro for the robust Broyden.
Curious, Solver 30405 Slope/Intercept back on foot.

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And what about 3D fitting in SMath?

See please my old problem in Mathcad
http://twt.mpei.ac.ru/ochkov/car/c_e.html

Online calculation
http://twt.mpei.ac.ru/MCS/Worksheets/old-car.xmcd

The second and third fit aren't really robust (quite some dependence on initial guesses)



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Wunderbar!
Send me please the M matrix as sm-file!

Wrote

And what about 3D fitting in SMath?

See please my old problem in Mathcad
http://twt.mpei.ac.ru/ochkov/car/c_e.html

Online calculation
http://twt.mpei.ac.ru/MCS/Worksheets/old-car.xmcd

Another way, from the same previous post .

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Best regards.
Alvaro.

Thanks!

But the last plot must be so

Wrote

Wunderbar!
Send me please the M matrix as sm-file!

The data is from your website. I copy-pasted the table to a new text file and imported it. Just use the files provided in my post.

As to the last plot: I guess the mileage limits of the individual lines are taken from the minimum and maximum slope observed in the age-mileage plot (fig.2 in your reference)?

Do you see any particular problem or do you just want the work getting done?

do you just want the work getting done?
Yes ;-)

Global fit Cholesky
Frequently, you can manage the Phi vector for a best regional fit.

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