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Function Fit to 3D data set

• To: mathgroup at smc.vnet.net
• Subject: [mg57748] Function Fit to 3D data set
• From: Adrienne R <roehrich at unlserve.unl.edu>
• Date: Tue, 7 Jun 2005 02:03:52 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

I have been trying to do several analyses with an [x,y,z] data set, where z is dependent on x and y.  First, I tried a 3D plot.  However, the only way I was able to get Mathematica to plot my data was to assume a grid form for x and y, and use ListPlot3D.  First question: can Mathematica make a 3D plot from stated x,y,z points?

Secondly, I am trying to fit a function to the data.  I have determined a function to which to fit parameters.  However, Mathematica does not seem to want to accept y as a variable.  Here is a simple suggestion of what I was trying.  Note, my function is much more complicated.  Please also ignore if the given does not work as stated, as I'm making it up.

points = {{1, 1, 1}, {1, 2, 4}, {1, 4, 16}}
f1 = FindFit[points, a + b*x^0 * y^1 + c*x^0 *y^2 +k*x^2 *y^0 + l*x^2 * y^1, {a, b, c, k, l}, x, y]

The error I receive is \!\(\*
  RowBox[{\(FindFit::"nonopt
  "\), \(\(:\)\(\ \)\), "\<\"Options expected (
    instead of \\!\\(y\\)) beyond 
      position \\!\\(4\\) in \\!\\(\[LeftSkeleton] 1 \[RightSkeleton]\\). An \
option must be a rule or a list of rules. \\!\\(\\*ButtonBox[\\\"Moreâ?¦\\\", \
ButtonStyle->\\\"RefGuideLinkText\\\", ButtonFrame->None, \
ButtonData:>\\\"General::nonopt\\\"]\\)\"\>"}]\)

Second question: Can Mathematica take a set of x,y,z data where z is dependent on x and y and fit a function to it?

Secondary question for both: How?  

Thanks for the help!

• Follow-Ups:
  • Re: Function Fit to 3D data set
    • From: Chris Chiasson <chris.chiasson@gmail.com>