Solve for a specific "Y" variable given the "Slope" of the line.

ramjet81

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Jun 2, 2013
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I am using Excel to calculate thresholds for slope. X's are the number of a day. Y's are the price of a stock at the close of the day. Here is my Array:


X's Y's
3 68.82
2 70.12
1 69.40


The 3 day Slope of this array is -0.29 using the SLOPE function.


Now I want to replace 68.82 with a number such that my slope calculates to -0.02. Sure, I could simply manually iterate the 68.82 number to get it to equal -0.02, but I need a solution to mathematically solve the 68.82 number to achieve the -0.02 slope given the rest of the X's and Y's remain unchanged.


Thanks in advance!
 

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p45cal

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Ugh!
Would using Solver in the Analysis part of the Data tab be acceptable?
 

ramjet81

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Jun 2, 2013
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p45cal, do you know if solver can be used for that cell throughout the spreadsheet? What I mean is, I have 1,700 rows of data. I need to calculate this value for each day given the Y value for each of the two proceeding days. Or is Solver intended to only calculate one cell at a time? What I am trying to do is for every day in the spreadsheet take the prior 2 stock close prices to calculate the "threshold" price for any given day.

Thanks In Advance.
 

p45cal

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Nov 10, 2009
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4,763
I suppose a bit of vba could be persuaded to do it for you, but see if the simple formula below, copied down gives you the right answer (69.36 is the same answer that solver gave me):
Excel Workbook
ABCDEF
1X'sY'sSlope >>-0.02
2368.8269.36
3270.12
4169.4
Sheet
 

ramjet81

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p54cal,

Thanks for the formula. Can you explain your approach for coming to the formula in C2? That will help me understand if this is a long term solution or not.

Many Thanks.
 

p45cal

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Well, I looked at the Help in Excel for Slope where there's a formula showing how it determines slope. I re-arranged it after substituting the known slope and had your unknown value for the 3rd Y on its lonesome on one side of the equation and discovered that a lot of things could cancel out and be simplified. It assumes that the x values are equidistant from each other. The gradient of a best straight line through three points (with equidistant x values) is dependent only on the first and third points, the middle point can be any value, the slope remains the same. The slope of the best straight line is the same as the slope of a straight line joining the first and third points. It would not be so simple if there were more than three points to consider.
 
Last edited:

ramjet81

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P54cal, What if the X's are not equidistant? Sounds like I need to take a similar approach as you did and see if I can "boil it down" to a simple formula. Thanks for your help...I will be back if I struggle.
 

shg

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May 7, 2008
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Office Version
  1. 2010
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  1. Windows
The gradient of a best straight line through three points (with equidistant x values) is dependent only on the first and third points
That was a very clever observation. I would have stared at that result and wondered what I'd done wrong.
 

p45cal

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P54cal, What if the X's are not equidistant? Sounds like I need to take a similar approach as you did and see if I can "boil it down" to a simple formula. Thanks for your help...I will be back if I struggle.
Well, it was a condition that they were equidistant, so yes, it'd be significantly more complex if they weren't. If a worksheet formula got too involved, I'd consider going down a user-defined function route, probably one which would require your 1700 rows as an argument(s) and would be array-entered in the cells where you wanted to see the results so as to save on calculation (interim values would only need to be calculated once).

But can the threshold for today that you're calculating based on a single value 2 days ago and an arbitrary slope be useful? it seems to ignore price volatility.


That was a very clever observation. I would have stared at that result and wondered what I'd done wrong.
Thank you!
 
Last edited:

pgc01

MrExcel MVP
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Apr 25, 2006
Messages
19,873
Hi

This is a solution for a more general case:

Given N points, you want to add a new point with a given X value and a target slope. What's the Y value for the new point?
In this example I start with a table in A2:A20, with slope 1.98.

I want to add a new point with X=17 (in A21) and a target slope of 2 for the whole A2:B21 table. The formula calculates the new Y at B21.

I then add yet a new point, with X=19 (in A22) and the same target slope. The formula calculates the new Y at B22.

This could go on. You just specify the X value for a new point and drag down the formula.

To make the formula simpler I defined the named ranges for the X values and the Y values

XVal =Sheet1!$A$2:INDEX(Sheet1!$A:$A,ROW()-1)
YVal =Sheet1!$B$2:INDEX(Sheet1!$B:$B,ROW()-1)

I also defined a named range for the target slope:

bTarget =Sheet1!$F$3


The formula in B21:

=(((ROWS(XVal)+1)*VAR.P(XVal)+(A21-AVERAGE(XVal))^2)*bTarget-(ROWS(XVal)+1)*COVARIANCE.P(XVal,YVal))/(A21-AVERAGE(XVal))+AVERAGE(YVal)

Copy down

Just to confirm the results I calculated the slopes for the tables. In F7:

=SLOPE($B$2:$B20,$A$2:$A20)
Copy down

I seems to work, but I cannot garantee it, as I'm half asleep.

If you want to try it, this is the example I used:


<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" >A</th><th style="border-width:1px;border-color:#888888;background:#9CF; text-align:center" >B</th><th style="border-width:1px;border-color:#888888;background:#9CF; text-align:center" width=30 >C</th><th style="border-width:1px;border-color:#888888;background:#9CF; text-align:center" width=30 >D</th><th style="border-width:1px;border-color:#888888;background:#9CF; text-align:center" >E</th><th style="border-width:1px;border-color:#888888;background:#9CF; text-align:center" width=30 >F</th><th style="border-width:1px;border-color:#888888;background:#9CF; text-align:center" width=30 >G</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></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; ">1.10</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; ">3.70</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:left;border-width: 1px;border-color:#888888; ">Target</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; ">1.58</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; ">5.76</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:left;border-width: 1px;border-color:#888888; ">B Target</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; "> </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; ">1.89</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; ">7.23</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; ">2.80</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; ">8.67</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; ">3.90</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; ">9.00</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:left;border-width: 1px;border-color:#888888; ">Calculated</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; ">4.90</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; ">10.36</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:left;border-width: 1px;border-color:#888888; ">b_N</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; ">1.98</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>8</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; ">5.58</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; ">12.66</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:left;border-width: 1px;border-color:#888888; ">b_N+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; ">2.00</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>9</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; ">6.06</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; ">15.30</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:left;border-width: 1px;border-color:#888888; ">b_N+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; ">2.00</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>10</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; ">7.33</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; ">17.34</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>11</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; ">8.07</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; ">18.94</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>12</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; ">8.52</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; ">20.36</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>13</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; ">9.44</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; ">22.65</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>14</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; ">10.41</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; ">24.01</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>15</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; ">11.51</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; ">26.63</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>16</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; ">12.69</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; ">27.17</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>17</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; ">13.48</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; ">29.36</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>18</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; ">13.88</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; ">30.24</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>19</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; ">14.92</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; ">30.82</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>20</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; ">15.96</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; ">32.87</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>21</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;background:#FFFF00;text-align:right;border-width: 1px;border-color:#888888; ">17.00</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;background:#FFFF00;text-align:right;border-width: 1px;border-color:#888888; ">37.43</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>22</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;background:#FFFF00;text-align:right;border-width: 1px;border-color:#888888; ">19.00</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;background:#FFFF00;text-align:right;border-width: 1px;border-color:#888888; ">40.42</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>23</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></tr><tr><td colspan=8 style="background:#9CF; padding-left:1em" > [Book1]Sheet1</td></tr></table>
 

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