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Tri-quadratic LINEST...possible?

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    Tri-quadratic LINEST...possible?

    I am trying to curve fit (line regression) a curve that is a function of three variables. I have successfully plotted other curves with bi-quadratic methods using LINEST, but I cannot figure out how to do this with a function that contains three variables.

    For two variables I have 6 columns; Outdoor Air Temp, Wetbulb Temp, and Superheat given in the form of:
    OAT, OAT^2, WB, WB^2, OD*WB, SH.
    I use LINEST(SH1:SH13,OAT:1:OD*WB:13,,TRUE) and I come out with a VERY accurate representation of the curve.

    How can I use this function for three-variables..is it possible?

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    Re: Tri-quadratic LINEST...possible?

    I know a lot of us try really hard to use as few cells as possible. When I do regressions using LINEST(), rather than create the "known_x" matrix directly in the LINEST() function like you have been doing, I prefer to use a block of helper cells to create the known_x matrix. For a regression like this, I would have

    regression column
    1 -- 2 -- 3 -- 4 -- 5 -- 6
    =OAT -- =OAT^2 -- =WB -- =WB^2 -- =OD*WB -- =SH
    copied down.

    Then, my known_x argument is simply a reference to this block of cells.

    If you really need to have this in a single cell without the block of helper cells, someone else will have to help you put that together.
    Quote Originally Posted by shg
    Mathematics is the native language of the natural world. Just trying to become literate.

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    Re: Tri-quadratic LINEST...possible?

    I can see what youre saying but I dont need to modify something thats already working 100%. Im actually trying to set up a tri-quadratic (function of three variables) into LINEST, and I dont know how to set it up. I simply gave the bi-quadratic as an example of what I have been able to do thus far-

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    Re: Tri-quadratic LINEST...possible?

    Which is a good part of why I like to use a helper range for this.

    With a helper range, adding terms to make this a tri quadratic (whatever that looks like exactly y=ax^6+bx^3+c maybe?) is simply a matter of editing/adding columns to the helper range. When you try to do it in a single cell, you have to figure out how to formulate the function to add those columns inside of a single cell. I'm sure this can be done in a single cell. I just never bothered to develop the skill of building complex single cell formulas like this.

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    Re: Tri-quadratic LINEST...possible?

    What's the form of the resulting formula?

    y = a*? + b*? + c*? + ...?
    Entia non sunt multiplicanda sine necessitate

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    Re: Tri-quadratic LINEST...possible?

    Im not sure, I think it would be something like:

    ax1^2+bx1x2+cx1x3+dx2^2+dx2x1+ex2x3+fx3^2+gx3x1+hx3x2+i....?

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    Re: Tri-quadratic LINEST...possible?

    Once you decide,

    =linest(y1:y100, choose({1,2,3,4,...}, x1:100, z1:z100, x1:100*z1:z100, x1:100*w1:w100, ...), , TRUE)

    ... for y = ax + bz + cxz + dxw + ...
    Last edited by shg; 06-19-2014 at 06:42 PM.

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