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jroth5-Regular Member
5-Regular Member
October 19, 2017
Solved

Multivariable Regression, Curve Fitting & Surface Plots

  • October 19, 2017
  • 7 replies
  • 12961 views

Hello,

 

I'm looking to reduce a dataset of 25 points to a surface curve fit.  An older program (and required to be used) generated the points in question.  Rather than spending many more hours on input the values, I was hoping to get a curve fit to the equations.  Two variables of distance (x) and elevation (y) provide and output of heatflux (Q).  I'm looking to essentially extrapolate the data into a large portion of points that will undergo more transformations pending the target geometry.

 

However, I'm unsure how to appropriately reduce the data.  There isn't any issue with generating a x^3 curve for more than 3 points of data (as I've done before), but I'm seeming to be inputing something incorrect into MathCAD for trying to reduce the data to an appropriate approximation.

 

In addition, if somebody knows a way to accomplish this task in excel, that would also be benificial (though I question if excel has that power built into it).

 

 

Best answer by terryhendicott

Hi,

 

You mention 'extrapolation'.  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.

 

See mathcad sheet for how it is done.

 

 

Capture.JPG

7 replies

J
jroth5-Regular MemberAuthor
5-Regular Member
October 19, 2017

P.S., if anybody knows how to get multiple files uploaded that would also be great.  I keep getting a file 'type' being incorrect.  (Guess it doesn't like mcdx and xmcd files?) 

V
24-Ruby IV
ValeryOchkov24-Ruby IV
24-Ruby IV
October 19, 2017

May be this will be any help forvyou

1-1[1].png

    V
    24-Ruby IV
    ValeryOchkov24-Ruby IV
    24-Ruby IV
    October 20, 2017

    Prime with Excel

    1-2a.png

    See too 

    The chapter 1 from the book @Thermalengineering studies with Marhcad, Excel and Internet

     

      F
      Fred_Kohlhepp23-Emerald I
      23-Emerald I
      October 19, 2017

      In Prime 3.0

      V
      ViktorKorobov1-Visitor
      1-Visitor
      October 20, 2017

      Multidimensional fitting in Mathcad 15:

      multidfit.png 

        T
        21-Topaz II
        terryhendicott21-Topaz II
        21-Topaz II
        October 20, 2017

        Hi,

        to be complete need to answer if Excel can do it.

        It can do linear interpolation in two directions.

         

        http://www.engineerexcel.com/bilinear-interpolation-excel/

         

        Cheers

        Terry

        T
        21-Topaz II
        terryhendicott21-Topaz IIAnswer
        21-Topaz II
        October 20, 2017

        Hi,

         

        You mention 'extrapolation'.  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.

         

        See mathcad sheet for how it is done.

         

         

        Capture.JPG

          J
          jroth5-Regular MemberAuthor
          5-Regular Member
          October 23, 2017

          Thank you very much to everybody for the answers.  It makes sense and I'll be able to expand on the MathCAD documents and implement in excel (as needed) for value outputs.

           

          I did alter the numbers I used to a format of:  Q = (a + b*x + c*x^2) + (d + e*x + f*x^2)*y + (g + h*x + i*x^2)*y^2  

          The equation fits the original data with less than a 0.05% error, which is pretty good.

          T
          21-Topaz II
          terryhendicott21-Topaz II
          21-Topaz II
          October 22, 2017

          Hi,

          one more approach.  In the original Excel sheet written at the bottom is a function for Y in terms of

          seven coefficients c,a1,a2,a3,b1,b2,b3. in terms of x1 and  x2.

          Y = c + a1*x1 + a2*x1^2 + a3^x1^3 + b1*x2 + b2*x2^2 + b3*x2^3.

          It is possible to create seven equation to determine the seven coefficients.

          The resulting surface is not as close as the previous post where the form of the equation is guessed as a fit to the data.

           

           

          Regards

          Terry

          T
          21-Topaz II
          terryhendicott21-Topaz II
          21-Topaz II
          October 22, 2017

          Hi,

          Obtain a good fitting equation in both directions for the surface given to 0.02% or closer is enclosed.

           

          Capture.JPG

          T
          21-Topaz II
          terryhendicott21-Topaz II
          21-Topaz II
          October 22, 2017

          Hi,

           

          Here is the calculation of the surface in Excel using the formula found in MathCad

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