Regression from tabledata

[zeonet]

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!

[ValeryOchkov]

Thanks for the interest on my works!

May by this article help you?

It is not an interpolation but an approximation!

http://twt.mpei.ac.ru/ochkov/car/c_e.html

[ValeryOchkov]

… and one more - not linfit but regress

[zeonet]

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.

[zeonet]

At current moment I have the following:

[Fred_Kohlhepp]

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

[ValeryOchkov]

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

[zeonet]

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.

[ValeryOchkov]

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

[ValeryOchkov · Accepted solution]

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!

[ValeryOchkov]

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

[zeonet]

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.