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Dec 04, 2018
07:08 AM

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Dec 04, 2018
07:08 AM

Regression from tabledata

Hello,

I want to find the function from 2 variables according to table data I have:

c | t=16 | t=25 | t=50 | t=75 |

0 | 4925 | 4511 | 4277 | 3845 |

20 | 4148 | 3975 | 3888 | 3564 |

40 | 3759 | 3672 | 3560 | 3327 |

60 | 3802 | 3586 | 3327 | 3111 |

80 | 3880 | 3664 | 3370 | 3025 |

100 | 4018 | 3698 | 3435 | 3089 |

120 | 4113 | 3802 | 3543 | 3240 |

140 | 4269 | 3932 | 3694 | 3435 |

160 | 4537 | 4104 | 3888 | 3629 |

I read a lot of info at this forum. I found good posts from @ValeryOchkov about the interpolation algo from 2 variables. I did it, but don't know how to get the function.

I attached a file with my experiments. @ValeryOchkov maybe you can help me?

I am a newbie in Mathcad Prime, so please help me how to find the analytical function F(x,y) according to that data.

Thank you in advance!

Solved! Go to Solution.

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Dec 05, 2018
04:27 AM

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Dec 05, 2018
04:27 AM

See please the Mathcad 15 sheet in attach. You can convert it into Mathcad Prime. Or I can do it myself if you can't!

See please the picture! You can choose more optimal function for your data - not the 2-d order plane!

11 REPLIES 11

Dec 04, 2018
08:03 AM

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Dec 04, 2018
08:03 AM

Thanks for the interest on my works!

May by this article help you?

It is not an interpolation but an approximation!

Dec 04, 2018
08:31 AM

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Dec 04, 2018
08:31 AM

… and one more - not linfit but regress

Dec 04, 2018
08:46 AM

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Dec 04, 2018
08:46 AM

Thank you for reply! I saw yesterday similar topic , but didn't understand how to use it in my case.

Also, in your tutorial I can't understand the "magic" of "Conversion from a Plane (fig. 2, __fig. 3__ and fig. 4) to a volume (fig. 1) gives the following regression formula[3]. With this formula, we calculate the minimum price of the car (% of the price of a new car[4]😞".

Can you give me more detailed instruction? I am very sorry, because just yesterday installed a lot of Math programs and started many forum topics, but it seems only here are real professionals.

P.S. Also yesterday I was trying to find somewhere your work Interp_f_x_y.mcd but server is unresponsive.

Dec 04, 2018
08:48 AM

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Dec 04, 2018
08:48 AM

At current moment I have the following:

Dec 04, 2018
10:13 AM

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Dec 04, 2018
10:13 AM

Search help for multivariable regression. The function "regress" will do a polynomial fit regression. Anything but polynomials will require more thought and effort.

Dec 05, 2018
01:07 AM

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Dec 05, 2018
01:07 AM

The regress function need a square matrix of the date! You can delete some rows! Or add some rows!

Dec 04, 2018
12:04 PM

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Dec 04, 2018
12:04 PM

Thank you all for attention and good hints! It helped me a lot!

Finally, I found some solution in this topic . Maybe a little bit later I'll try to find another, more sophisticated solution, but now it's work fine.

Here it is some info for future visitors:

For this you are best to get the equation of the surface.

This is an entirely different approach to the problem I have used professionally to determine the underlying mathematics on a surface in heating and cooling mills in plants.

It involves determining the equation that matches the surface in one direction say the X direction. Same equation but different coefficients at each Y position. Usually can be done with three coefficients in the equation.

Next you find an equations for the variation of these coefficients in terms of the Y direction. Again only three coeffficients are necessary for each coefficient.

Dec 05, 2018
01:05 AM

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Dec 05, 2018
01:05 AM

I will try to solve your problem today with my students in class (IT-lessons)!

Dec 05, 2018
04:27 AM

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Dec 05, 2018
04:27 AM

See please the Mathcad 15 sheet in attach. You can convert it into Mathcad Prime. Or I can do it myself if you can't!

See please the picture! You can choose more optimal function for your data - not the 2-d order plane!

Dec 05, 2018
05:43 AM

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Dec 05, 2018
05:43 AM

… but the 2-d surface is good - the max delta is 6.5%!

Dec 05, 2018
03:28 PM

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Dec 05, 2018
03:28 PM

Thank you for a lot! I installed Mathcad 15.0 and your solution works fine.

I also tried other solutions (attached) with other functions.

Variant 1:

variant 2:

As I understand in a task like this we can automate the calculation of the solution, but always need to think by a head and analyse the dependencies.