Generate Quadratic Equation from Data Set

E

emoat

New Member
Joined
Apr 3, 2006
Messages
7
Hi all,
This may be asking too much of Excel or VBA.
I'm trying to generate the quadratic equation (ax^2 + bx + c) for a set of data using only VBA. I don't have the equation constants (a, b, and c), only the x and y coordinates.
As a simple example (x,y): (0, 586) (1, 20450) (2, 46222) and (5, 119450).
I can plot these in a scatter plot, select Add Trendline, then choose Polynomial (2nd order = Quadratic) and check "Display Equation on Chart". Here I get y = 442.04x^2 + 21715x - 69.293.
This works fine for one set of data. What I'd like to do is be able to generate the equation for any given set of data using VBA only (not generating a chart).
I have a brute force method already whereby VBA generates the chart/equation as described previously, copies the equation from the chart, then deletes the chart and stores the copied a, b, and c values. This takes a long time when dealing with 800+ different sets of data. Seems like something more elegant should be possible. Excel must have something internal to the program to determine the quadratic function given a set of data or it wouldn't be possible in the chart. I'm just hoping there is a more elegant way of getting at the calculation.
Hopefully I've explained properly what I'm looking for and thanks in advance if anyone has suggestions!!
 

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Hi again

As I told in the other thread you can calculate the coefficients of the equation using Linest() and then use then to automate the calculations.

Using your values, this is an example.

First, calculate the coefficients.

In F3:

=INDEX(LINEST($C$3:$C$6,$B$3:$B$6^{1,2}),COLUMNS($F:F))

Copy accross till H3

Then, the equation, in D3:

=$F$3*B3^2+$G$3*B3+$H$3

Copy down to D6.


<table border="1" cellpadding="1" style="background:#FFF; border-collapse:collapse;border-width:2px;border-color:#CCCCCC;font-family:Arial,Arial; font-size:10pt" ><tr><th style="border-width:1px;border-color:#888888;background:#9CF " > </th><th style="border-width:1px;border-color:#888888;background:#9CF; text-align:center" width=30 >A</th><th style="border-width:1px;border-color:#888888;background:#9CF; text-align:center" width=30 >B</th><th style="border-width:1px;border-color:#888888;background:#9CF; text-align:center" >C</th><th style="border-width:1px;border-color:#888888;background:#9CF; text-align:center" >D</th><th style="border-width:1px;border-color:#888888;background:#9CF; text-align:center" width=30 >E</th><th style="border-width:1px;border-color:#888888;background:#9CF; text-align:center" >F</th><th style="border-width:1px;border-color:#888888;background:#9CF; text-align:center" >G</th><th style="border-width:1px;border-color:#888888;background:#9CF; text-align:center" >H</th><th style="border-width:1px;border-color:#888888;background:#9CF; text-align:center" width=30 >I</th></tr><tr><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;background:#9CF; text-align:center; " ><b>1</b></td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td></tr><tr><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;background:#9CF; text-align:center; " ><b>2</b></td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:center;border-width: 1px;border-color:#888888; ">X</td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:center;border-width: 1px;border-color:#888888; ">Y</td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:center;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td></tr><tr><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;background:#9CF; text-align:center; " ><b>3</b></td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">0</td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> 586 </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">-69</td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">442.044</td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">21,715.481</td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">-69.293</td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td></tr><tr><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;background:#9CF; text-align:center; " ><b>4</b></td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">1</td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> 20,450 </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">22,088</td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td></tr><tr><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;background:#9CF; text-align:center; " ><b>5</b></td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">2</td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> 46,222 </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">45,130</td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td></tr><tr><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;background:#9CF; text-align:center; " ><b>6</b></td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">5</td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> 119,450 </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; ">119,559</td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td></tr><tr><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;background:#9CF; text-align:center; " ><b>7</b></td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td><td style="border-width:1px;border-color:#000000; padding-left:0.5em; padding-top:0.4em; padding-right:0.5em; padding-bottom:0.25em;text-align:right;border-width: 1px;border-color:#888888; "> </td></tr><tr><td colspan=10 style="background:#9CF; padding-left:1em" > [Book1]Sheet4</td></tr></table>
 
Upvote 0
Remark: you don't have to calculate the coefficients is separate cells, if you have only one cell where you want to use the formula you can get the equation directly. If you have, however, several cells where you want to use the formula then the previous solution is more efficient.

For ex., given an X value in F2, in F3:

=SUMPRODUCT(LINEST($C$3:$C$6,$B$3:$B$6^{1,2}),IF({1,1,0},F2^{2,1},1))


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BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px" width=30>B</TH><TH style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: center; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; BACKGROUND: #9cf; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px">C</TH><TH style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: center; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; BACKGROUND: #9cf; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px" width=30>D</TH><TH style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: center; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; BACKGROUND: #9cf; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px">E</TH><TH style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: center; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; BACKGROUND: #9cf; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px">F</TH><TH style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: center; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; BACKGROUND: #9cf; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px" width=30>G</TH></TR><TR><TD style="BORDER-BOTTOM-COLOR: #000000; TEXT-ALIGN: center; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #000000; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BACKGROUND: #9cf; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #000000; BORDER-LEFT-COLOR: #000000; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">1</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD></TR><TR><TD style="BORDER-BOTTOM-COLOR: #000000; TEXT-ALIGN: center; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #000000; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BACKGROUND: #9cf; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #000000; BORDER-LEFT-COLOR: #000000; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">2</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: center; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">X</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: center; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">Y</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: center; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: center; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">X</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: center; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">1.5</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: center; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD></TR><TR><TD style="BORDER-BOTTOM-COLOR: #000000; TEXT-ALIGN: center; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #000000; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BACKGROUND: #9cf; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #000000; BORDER-LEFT-COLOR: #000000; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">3</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">0</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">586 </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: center; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">Y est. </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">33,499 </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD></TR><TR><TD style="BORDER-BOTTOM-COLOR: #000000; TEXT-ALIGN: center; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #000000; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BACKGROUND: #9cf; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #000000; BORDER-LEFT-COLOR: #000000; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">4</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">1</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">20,450 </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD></TR><TR><TD style="BORDER-BOTTOM-COLOR: #000000; TEXT-ALIGN: center; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #000000; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BACKGROUND: #9cf; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #000000; BORDER-LEFT-COLOR: #000000; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">5</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">2</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">46,222 </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD></TR><TR><TD style="BORDER-BOTTOM-COLOR: #000000; TEXT-ALIGN: center; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #000000; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BACKGROUND: #9cf; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #000000; BORDER-LEFT-COLOR: #000000; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">6</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">5</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">119,450 </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD></TR><TR><TD style="BORDER-BOTTOM-COLOR: #000000; TEXT-ALIGN: center; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #000000; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BACKGROUND: #9cf; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #000000; BORDER-LEFT-COLOR: #000000; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">7</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD></TR><TR><TD style="PADDING-LEFT: 1em; BACKGROUND: #9cf" colSpan=8>[Book1]Sheet4</TD></TR></TBODY></TABLE>
 
Upvote 0
That was EXACTLY what I was looking for. I do apologize if this had been asked previously, but I had no luck finding it prior to this (after looking on and off over the past several years).
If I can impose on your knowledge once more, I have never come across the use of "^" in my past Excel dealings and am having trouble finding reference material descrbing the usage here (most things talk about its use for exponents). In your equation "=INDEX(LINEST($C$3:$C$6,$B$3:$B$6^{1,2}),COLUMNS($F:F))", what is the "^{1,2}" term doing?

Thanks a lot for your quick and helpful response.
 
Upvote 0
emoat said:
...I have never come across the use of "^" in my past Excel dealings and am having trouble finding reference material descrbing the usage here (most things talk about its use for exponents). In your equation "=INDEX(LINEST($C$3:$C$6,$B$3:$B$6^{1,2}),COLUMNS($F:F))", what is the "^{1,2}" term doing?
Click to expand...

I'm glad it helped.

Since you want the coefficients for X and X^2, you should feed the corresponding values in the input to Linest().

So, the simple approach would be to have an auxilliary column where you calculate the X^2 input and then use it directly in the Linest(), without the ^{1,2}.

In the example, in G3:

=INDEX(LINEST($D$3:$D$6,$B$3:$C$6),COLUMNS($F:F))

Copy accross


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PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD></TR><TR><TD style="BORDER-BOTTOM-COLOR: #000000; TEXT-ALIGN: center; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #000000; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BACKGROUND: #9cf; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #000000; BORDER-LEFT-COLOR: #000000; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">3</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: center; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">0</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: center; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">0</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">586</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">-69</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">442.044</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">21,715.481</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">-69.293</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD></TR><TR><TD style="BORDER-BOTTOM-COLOR: #000000; TEXT-ALIGN: center; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #000000; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BACKGROUND: #9cf; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #000000; BORDER-LEFT-COLOR: #000000; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">4</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: center; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">1</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: center; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">1</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">20,450</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">22,088</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD></TR><TR><TD style="BORDER-BOTTOM-COLOR: #000000; TEXT-ALIGN: center; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #000000; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BACKGROUND: #9cf; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #000000; BORDER-LEFT-COLOR: #000000; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">5</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: center; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">2</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: center; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">4</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">46,222</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">45,130</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD></TR><TR><TD style="BORDER-BOTTOM-COLOR: #000000; TEXT-ALIGN: center; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #000000; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BACKGROUND: #9cf; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #000000; BORDER-LEFT-COLOR: #000000; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">6</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: center; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">5</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: center; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">25</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">119,450</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">119,559</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD></TR><TR><TD style="BORDER-BOTTOM-COLOR: #000000; TEXT-ALIGN: center; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #000000; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BACKGROUND: #9cf; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #000000; BORDER-LEFT-COLOR: #000000; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">7</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; 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TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD></TR><TR><TD style="PADDING-LEFT: 1em; BACKGROUND: #9cf" colSpan=11>[Book1]Sheet1</TD></TR></TBODY></TABLE>


This would be the direct approach, but the truth is that you'd like not to have to create the auxilliary column.

That's why you use $B$3:$B$6^{1,2}. The result of this is an array with 4x2 columns. The first column is $B$3:$B$6^1, which is $B$3:$B$6, and the second column is $B$3:$B$6^2.

This way you are feeding X and X^2 input values, but without having to create the auxilliary column.

Another thing: you mentioned in the other thread that you also needed the R^2 value. Check the help for Linest(). If you set the fourth parameter of Linest() to True, then you also get the statistics of the regression. R^2 is the value in the third row, column 1.

In G5:

=INDEX(LINEST($C$3:$C$6,$B$3:$B$6^{1,2},TRUE,TRUE),3,1)


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TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">0</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">586</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">442.044</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">21,715.481</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">-69.293</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD></TR><TR><TD style="BORDER-BOTTOM-COLOR: #000000; TEXT-ALIGN: center; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #000000; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BACKGROUND: #9cf; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #000000; BORDER-LEFT-COLOR: #000000; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">4</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">1</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">20,450</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD></TR><TR><TD style="BORDER-BOTTOM-COLOR: #000000; TEXT-ALIGN: center; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #000000; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BACKGROUND: #9cf; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #000000; BORDER-LEFT-COLOR: #000000; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">5</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">2</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">46,222</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: left; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">R^2</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">0.99946747</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD></TR><TR><TD style="BORDER-BOTTOM-COLOR: #000000; TEXT-ALIGN: center; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #000000; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BACKGROUND: #9cf; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #000000; BORDER-LEFT-COLOR: #000000; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">6</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">5</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">119,450</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD></TR><TR><TD style="BORDER-BOTTOM-COLOR: #000000; TEXT-ALIGN: center; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #000000; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BACKGROUND: #9cf; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #000000; BORDER-LEFT-COLOR: #000000; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em">7</TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD><TD style="BORDER-BOTTOM-COLOR: #888888; TEXT-ALIGN: right; PADDING-BOTTOM: 0.25em; BORDER-RIGHT-WIDTH: 1px; BORDER-TOP-COLOR: #888888; PADDING-LEFT: 0.5em; PADDING-RIGHT: 0.5em; BORDER-TOP-WIDTH: 1px; BORDER-BOTTOM-WIDTH: 1px; BORDER-RIGHT-COLOR: #888888; BORDER-LEFT-COLOR: #888888; BORDER-LEFT-WIDTH: 1px; PADDING-TOP: 0.4em"> </TD></TR><TR><TD style="PADDING-LEFT: 1em; BACKGROUND: #9cf" colSpan=10>[Book1]Sheet2</TD></TR></TBODY></TABLE>
 
Upvote 0
Well, it's a few months since this problem was solved and now I've hit another road block. The solutions that were provided on this forum were FANTASTIC! The quadratic solutions from the LINEST equation work beautifully.
The whole point of my project is to reproduce the calculations performed by ChemStation (the software that operates the GC/MS in the lab where I work) during calibration. I have a working spreadsheet for the method I initially set out to create, but have recently tried to adapt this to another method. The new wrinkle is to "weight" the curve fit. After a lot of web searching and playing with Excel I managed to get the linear calibration to work with an "Inverse of Concentration" weighting... both 1/x and 1/x^2.
I have very little idea of how to apply a weighting factor to a quadratic fit. Additionally I don't know how to calculate an R^2 value for the quadratic or linear fit when the weighting factor is applied to the curve. I am fairly handy with Excel, but I guess my knowledge of statistics is the thing that is lacking now.
If anyone has an idea of how to approach this I would be extremely grateful. Also if I haven't explained something clearly (definitely a possibility) I can try and explain in more detail/provide data/etc.
Thanks in advance!
 
Upvote 0
Re: Generate Quadratic Equation from *ROW* Data Set

Hi All,

This post has been dormant for awhile, but maybe one of you is monitoring...

I'm looking to do this exact thing - generate quadratic coefficients without having to graph and "add trendline" to each one. However, my data is row data, and the INDEX(LINEST.....) formula here doesn't seem to be working. I've tried using transpose on the Y-value and X-value inputs, but regardless I just get the #VALUE! response from excel.

Any idea how to get this to work on row data? I have 1 row of X's, and dozens of rows of Y's. It would be preferable not to have to re-orient all the data to columns.

Thank you!
 
Upvote 0
So you want to regress

x = a*y1 + b*y1^2 + c*y2 + d*y2^2 + e*y3 + f*y3^2 + ... + some constant

?
 
Upvote 0
Not so complex as that ;)

What I have is one row of "X-values", and dozens of rows of "Y-values" and for each row of Yn-values, I want the quadratic coefficients for the equation relating Yn to X (=dozens of quadratic equations).

I think I'm onto something using ^{1;2} instead of ^{1,2} as the example above showed. It's still not looking quite right though - I'm comparing to a previously solved data/coefficient combination.

Perhaps version of excel makes a difference? (I'm using Mac 2011, data I'm comparing to used some previous Windows Excel version).

Thanks!
 
Upvote 0
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