How can I accurately set up a tri-quadratic equation for curve fitting in Excel?

  • Context: Undergrad 
  • Thread starter Thread starter mattskie
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SUMMARY

The discussion focuses on setting up a tri-quadratic equation for curve fitting in Excel using linear regression techniques. The user successfully implemented a bi-quadratic equation and attempted a tri-quadratic equation of the form x^2 + xy + xz + y^2 + yz + z^2 + b, calculated via the LINEST function. Initial accuracy was observed with the tri-quadratic model, but performance deteriorated with additional data points. The user seeks guidance on achieving a more accurate fitting curve, questioning the correct formulation of the equation.

PREREQUISITES
  • Familiarity with Excel's LINEST function for regression analysis
  • Understanding of polynomial equations, specifically tri-quadratic forms
  • Basic knowledge of curve fitting techniques
  • Experience with data analysis in Excel
NEXT STEPS
  • Research advanced polynomial regression techniques in Excel
  • Learn about the use of the Solver add-in for optimization in curve fitting
  • Explore the implementation of multi-variable regression models
  • Investigate alternative curve fitting software or libraries, such as Python's SciPy
USEFUL FOR

Data analysts, statisticians, and researchers involved in curve fitting and regression analysis using Excel, particularly those working with multi-variable datasets.

mattskie
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Hey,

So I am trying to do a tri-quadratic curve fit (linear regression) in excel. I have successfully completed a bi-quadratic, and it is of the form:
x+x^2+y+y^2+x*y+b (b is calculated by LINEST in excel)

My attempt at a tri-linear was:
x^2+x*y+x*z+y^2+y*z+z^2+b (b is calculated by LINEST in excel)

This equation was fairly accurate for my first few data points in the 4-curve family of curves I am attempting to curve fit, but after that the accuracy plummets.

I am assuming I am on the right track with this, as I attained some initial accuracy, but this equation isn't 100% because I can see it failing. Any/all help appreciated.

Note: I attempted to use the equation on http://www.rmi.ge/~kade/LecturesT.Kadeishvili/MathEconomics/Term3/Week3QuadraticLEC.pdf
but it gave an extremely erroneous solution.
 
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Shouldn't the fitting curve be:
ax^2 + by^2 + cz^2 + etc.?
 

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