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

  • Thread starter mattskie
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In summary, the conversation pertains to the difficulty of performing a tri-quadratic curve fit in Excel. The individual has successfully completed a bi-quadratic fit, but their attempt at a tri-linear fit is not accurate for all data points. They are seeking help and wondering if the fitting curve should be in the form of ax^2 + by^2 + cz^2 + etc. rather than the current form they are using.
  • #1
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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  • #2
Shouldn't the fitting curve be:
ax^2 + by^2 + cz^2 + etc.?
 

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

What is a tri-quadratic equation?

A tri-quadratic equation is a type of polynomial equation that involves three variables raised to the second power. It can also be referred to as a cubic equation.

How do you set up a tri-quadratic equation?

To set up a tri-quadratic equation, you must first identify the three variables and then arrange them in the form of ax^2 + bx + c = 0, where a, b, and c are coefficients and x is the variable.

What is the difference between a tri-quadratic equation and a quadratic equation?

The main difference between a tri-quadratic equation and a quadratic equation is the number of variables involved. A quadratic equation has only one variable raised to the second power, while a tri-quadratic equation has three variables raised to the second power.

What are the solutions to a tri-quadratic equation?

The solutions to a tri-quadratic equation can be found by using the quadratic formula or by factoring. In some cases, the solutions may be complex numbers.

What are some real-world applications of tri-quadratic equations?

Tri-quadratic equations have various applications in fields such as physics, engineering, and economics. They can be used to model parabolic motion, solve optimization problems, and predict the behavior of systems with three variables.

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