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# How to automate the LINEST function in vba to find the best fit for a second order or higher polynomial?

I have hundreds of data sets showing change (y) over time (t) at different locations.  I am attempting to plot the (y,t) data for each location and fit a second order polynomial line of regression to each of the data sets.  I would like to automate the LINEST function in VBA to accomplish this by finding the constants C1, C2, and b; i.e. y = C1*t^2 + C2*t + b.  I would also like the statistical data that LINEST provides.

Thanks, BL
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brandonlampe
1 Solution

Commented:
Are you familiar with matrices?

Compose the Vandermonde matrix for the t_i data, that is:

[ 1  t_1  t_1^2 ]
[ 1  t_2  t_2^2 ]
X = [   .       .        .  ]
[   .          .     .  ]
[ 1  t_n  t_n^2 ]

Then compute:

(X^t X)^-1 X

and multiply this (from the left of course) by:

[ y_1 ]
Y = [   .    ]
[ y_n ]

then the answer will be a vector consisting of the coefficients:

[  b  ]
[ C2 ]
[ C1 ]

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Commented:
The trendline formulas are here if it helps: http://spreadsheetpage.com/index.php/tip/chart_trendline_formulas/

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Author Commented:
I guess I was looking for a little more help with writing the VBA code.
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Commented:
brandonlampe -- I hope you still need help on this because I know the answer.

You have to install the Analysis Toolpak - VBA add-in, which I assume you know how to do since you're a VBA programmer.

Make sure you choose both the Analysis Toolpak AND the Analysis Toolpak - VBA

The resource for the Analysis Toolpak - VBA is something like

C:\Program Files\Microsoft Office\Office12\LIBRARY\ANALYSIS\ATPVBAEN.XLAM

Then, when you're in the VBA editor in Excel, you can call the data analysis functions. The native LINEST is actually surpassed by the Regress function which gives all the output you want.

One the Analysis Toolpak add-ins are installed correctly, go to your VBA editor and add a Reference to ATPVBAEN.XLS

Here's a little snippet:

Sub test()
Dim Res As Variant
Res = [atpvbaen.xls].Regress( ARGS = X AND Y RANGE,  DESIRED OUTPUT STATISTICS )
Debug.Print Res
End Sub

What you want to do is totally possible.

Good luck, hope this helps!

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Commented:
Question PAQ'd, 250 points not refunded, and stored in the solution database.
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