SMath vs Mathcad

#1 Posted: 8/6/2024 11:32:14 AM

Valery Ochkov

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I can solve this problem in Mathcad - see pls the picture.
But cannot in SMath - see the SMath-file :-(
Help please

6-1-Mister-Class-a-b-c.sm (15 KiB) downloaded 25 time(s).

#2 Posted: 8/6/2024 1:22:51 PM

Alvaro Diaz Falconi

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Hi. Try this function, from Viacheslav ALGLIB plugin.

Best regards.
Alvaro.

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Valery Ochkov 8/6/2024 2:30:00 PM

#3 Posted: 8/6/2024 2:34:07 PM

Valery Ochkov

55 likes in 633 posts.

Group: User

Thanks and sorry!
I do not see in your solution derivatives!
???

#4 Posted: 8/6/2024 6:36:47 PM

Martin Kraska

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Here is a version with Maxima Fit(). Note that Fit() uses a least squares procedure, whereas Mathcad obviously directly minimizes the average linear distance between data points and model.
Ordinary linear regression with slope and intersect is a least squares fit for the vertical distance.

6-1-Mister-Class-a-b-c_kr.sm (35 KiB) downloaded 31 time(s).

2024-08-06 13_32_52-SMath Solver - [6-1-Mister-Class-a-b-c_kr.sm_].png

Martin Kraska Pre-configured portable distribution of SMath Studio: https://en.smath.info/wiki/SMath%20with%20Plugins.ashx

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Valery Ochkov 8/6/2024 6:53:00 PM

#5 Posted: 8/6/2024 7:22:00 PM

Valery Ochkov

55 likes in 633 posts.

Group: User

Is there in SMath or Maxima the median-median regression

#6 Posted: 8/6/2024 10:02:42 PM

Valery Ochkov

55 likes in 633 posts.

Group: User

See
https://www.researchgate.net/publication/322318078_Alternative_Methods_for_Constructing_of_Linear_Regressions

#7 Posted: 8/7/2024 12:29:39 AM

Martin Kraska

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Interesting paper. Yet the authors keep one question out of scope: In case of orthogonal distance minimizing (be it linear or quadratic), rescaling of the data matter. (other than with ordinary linear regression). This means that you get different results if you provide your data not in cm but in mm.
Perhaps the data should be scaled such that the uncertainty (measurement error) is of similar numeric value for x and y.

Martin Kraska Pre-configured portable distribution of SMath Studio: https://en.smath.info/wiki/SMath%20with%20Plugins.ashx

#8 Posted: 8/7/2024 2:01:47 AM

Valery Ochkov

55 likes in 633 posts.

Group: User

See please three plots

#9 Posted: 8/7/2024 2:12:28 AM

Valery Ochkov

55 likes in 633 posts.

Group: User

See please more

#10 Posted: 8/7/2024 3:24:46 PM

Martin Kraska

1222 likes in 2150 posts.

Group: Moderator

Wrote
See please three plots

The perpendicular distance is only geometrically perpendicular in the graph if the axes tick ratio is 1 (as I tried to set in my earlier post) unless you introduce an anisotropic metric for the distance (or standardize the quantities).

Martin Kraska Pre-configured portable distribution of SMath Studio: https://en.smath.info/wiki/SMath%20with%20Plugins.ashx

#11 Posted: 8/7/2024 7:51:31 PM

Alvaro Diaz Falconi

992 likes in 1674 posts.

Group: User

Hi. Chosen different guess values, we can reproduce the maxima result. Also, notice that meanwhile the Maxima MSE function decreases, the "classical" one increases. I'm not sure how to call Maxima MSE for implicit functions.

mse.sm (25 KiB) downloaded 27 time(s).

Best regards
Alvaro

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