Are You Trendy? (Part 2)

Posted on January 26th, 2011 in Charts and Graphs , Excel Howtos , Huis , Learn Excel , Posts by Hui - 38 comments

Forecasting using Excel Functions

“Todays forecast will be Hot and Humid with a Chance of Snow?”

(Even the experts with big computers get it wrong)

In the previous post we looked at Manual Forecasting techniques and how Excel can be used to assist. In this post we will look at how we can use Excel built in functions to aid us in forecasting.

This post is going to delve slowly at first and then deeper into some of Excels Statistical Functions. Readers are encouraged to follow along at your own pace and use the examples in the Examples Workbook attached.

All charts, tables and diagrams in this post with the associated Excel formulas are included in the Example workbook.

In this post I will be using the following nomenclature

^ means raise to the power eg: 10^2 = Power(10,2) = 100

.  means multiply eg 10.2.M.X = 10.2 * m * x

Why do we need to use Excel Functions?

In the first post we looked at some simple data with only a few points and a trend that was very fairly obvious or was it.

A number of other linear trends could have equally been used and all look about right.

However in real life data is rarely this simple.

Fortunately Excel has a Number of Functions and Tools that allow us to look for trends and use the data natively for forecasting purposes.

There are a number of standard types of trends which can be classified as:

Linear – Approximating a straight line

Polynomial – Approximating a Polynomial function to a power

Power – Approximating a power function

Logarithmic – Approximating a Logarithmic line

Exponential – Approximating an Exponential line

Excel supports the use of these trend types in a number of ways.

Excel Functions and Tools

Excel has a number of Worksheet functions specifically designed to assist us with analysing various trends.

They are categorised by type below

Excel Functions for Linear Trends

  • Slope
  • Intercept
  • Linest
  • Trend
  • Forecast

Excel Functions for Exponential Trends

  • Logest
  • Growth

Other Excel Tools

  • Excel Chart + Trendline


USING EXCELS WORKSHEET FUNCTIONS


Linear Estimates

In the first Post we looked at using a linear equation in the form Y=mX + c to express our estimated line of best fit which we manual estimated was linear.

Excel has 2 functions which we can use to calculate the actual slope (m) and intercept (c) for the above equation.

Slope

The Slope function returns the slope or gradient of the linear regression line through data points in Known_Y’s and Known_X’s.

eg: =SLOPE(Known Y values, Known X values)

Intercept

The Intercept function calculates the point at which a linear regression line will intersect the Y-axis by using existing X-values and Y-values.

eg: = INTERCEPT (Known Y values, Known X values)

Use

To use the above 2 equations we simply enter 2 equations in cells

m = SLOPE(C47:C51, B47:B51)                     = 1.298

c = INTERCEPT(C47:C51, B47:B51)            = 0.140

We can now use our revised linear equation to plot a line of best fit

Y = m.X + c

Y = 1.298.X + 0.140

So for

X = 5, Y= 6.63 &

X = 30, Y = 39.07

Which we can plot as a new series on our chart


Linest

The Linest function can be used to calculate the Slope and Intercept parameters for a linear function

Linest is an array formula which must be entered as an array formula to return all the values that it can return.

Eg:   = LINEST(Known Y Values, Known X Values,Const , Stats)

=LINEST(C47:C51,B47:B51,TRUE,FALSE) will return the Slope (m) component of the equation

Const = True b parameter is calculated

False b is set to 0 (zero)

Stats =  True Return additional regression statistics

False Return the m co-efficient and const b

To return both components you must enter the same formula in adjacent cells in the same row

and the equation must be entered as an array formula

Eg: = LINEST(C47:C51, B47:B51, TRUE, FALSE) Ctrl Shift Enter

Slope (m) Intercept (c)
Linest 1.298 0.140

Alternatively the values can be retrieved from the Linest array function using the Index function

Gradient m =INDEX(LINEST(C47:C51, B47:B51, TRUE, FALSE),1)

Intercept c =INDEX(LINEST(C47:C51, B47:B51, TRUE, FALSE),2)

The use of the Index function negates the requirement to use an Array Entered formula.

Stats

Linest can also return a number of statistics when Stats parameter is set to True

Eg: =LINEST(C47:C51, B47:B51, TRUE,TRUE) Ctrl Shift Enter

This must be entered as an array formula of 2 columns by 5 rows

The formula can also be entered as a normal equation also using the Index function to extract the array values

Eg:          = INDEX( LINEST($C$47:$C$51, $B$47:$B$51, TRUE, TRUE), Row ,Column)

If you want to know the r2 value (discussed later) it is in the 3rd row, 1st column.

Eg:          = INDEX( LINEST($C$47:$C$51, $B$47:$B$51, TRUE, TRUE), 3 , 1)

The above table shows the statistic and the value for our example above using both array entered and Index formulas

The r2 parameter highlighted will be discussed later.

Trend

The Trend function is used to calculate a straight line best fit line based on a number of known X & Y values.

Values of Y can be calculated for values of X inside or outside the know range of X values and so Trend can be used to interpolate or extrapolate data.

eg:          = INTERCEPT (known Y values, known X values, New X Value, Const)

Const    = True; Calculate the Intercept value

= False; Set the Intercept value c = 0

If for example you are using this to model your power cost.

If you have a fixed monthly cost plus a cost per kW, you would set Const to True

If you have no fixed monthly cost and are only charged per kW set Const to false

eg:          =TREND($C$101:$C$105,$B$101:$B$105,B106,TRUE)

Forecast

The Forecast function is used to calculate a straight line best fit line based on a number of known X & Y values.

Values of Y can be calculated for values of X inside or outside the know range of X values and so Trend can be used to interpolate or extrapolate data.

eg:      = FORECAST (New X Value, Known Y values, Known X values)

= FORECAST(B129, $C$124:$C$128, $B$124:$B$128)


Non-Linear Estimates

So far our examination of trends has revolved around the use of linear estimates and the Excel functions that support that.

But as we saw above there are lots of cases where non-linear estimates are required.

This section will deal with the following estimate types.

  • Polynomial – Approximating a Polynomial function, a.x^n + b.x^(n-1) + c.x^(n-2) + … + m = 0
  • Power – Approximating a Power function, y = a.x^b
  • Logarithmic – Approximating a Logarithmic line, y = b.ln(x) + a
  • Exponential – Approximating an Exponential line, y = b.m^x

Luckily Excel has a number of function and some tools to assist us here as well.

Exponential Functions

Exponential functions are based around the formula y = b.m^x

Excel has one function specific to growth estimates and that is the Logest function.

As with Linest, Logest is an array function.

eg:     =LOGEST(Known Y’s, Known X’s, Const, Stats)

=LOGEST(C6:C13, B6:B13, true, false)  Ctrl Shift Enter

Const = True or omitted b parameter is calculated

False b is set to 1

Stats =  True Return additional regression statistics in an array

False Return the m co-efficient and const b

Alternatively the values can be retrieved from the Logest array function using the Index function

B = INDEX( LOGEST( C6:C13, B6:B13, True, False), 1)

X = INDEX( LOGEST(C6:C13, B6:B13, True, False), 2)

The use of the Index function negates the requirement to use an Array Entered formula.1

However Logest, is a tricky function as it actually just passes values to the Linest function!

So we can actually use the Linest function for doing nearly all of our Exponential, Logarithmic and Power function trends.

But you ask “Doesn’t Linest give us the parameters for a straight line?”

Absolutely.

To use Linest to analyse an Exponential function we need to unwrap it so to speak and that is done by taking the Log of the Y values prior to putting them into the Linest equation, like this:

Form:    = LINEST( LN(Known Y Values), Known X Values)

eg:          = LINEST( LN(C32:C39), B32:B39) Which is an array formula

or            = INDEX( LINEST( LN(C32:C39), B32:B39), 1) as a normal formula

Now the tricky part is that the m component or array parameter 2 must now be converted back to an exponential so we can use exp(m component) or  =EXP( INDEX( LINEST( LN(C32:C39), B32:B39),2))

This is difficult to explain but is shown in a worked example on the Exponential Functions section of the Non-linear Functions page of the example workbook attached.

Growth

The Growth function can be used to calculate an exponential curve that best fits your data based on a number of known X & Y values.

Form:    = LINEST(Known Y Values, Known X Values, New X Values)

eg:          = GROWTH($C$32:$C$39, $B$32:$B$39, B40) as a normal formula

This is also shown in a worked example on the Exponential Functions section of the Non-linear Functions page of the example workbook attached.

Logarithmic Functions

Logarithmic functions are based around the formula y = b.LN(x)+a

Excel doesn’t have a specific function dealing with Logarithmic functions, however we can use the Linest function as previously described by first converting the data from a Logarithmic to Straight line and this is done by talking the LN of the X values.

Form:    = LINEST( Known Y Values, LN(Known X Values))

eg:          = LINEST( LN(C32:C39), B32:B39) as an array formula

or            = INDEX( LINEST( LN(C32:C39), B32:B39), 1) as a normal formula

This is shown in a worked example on the Logarithmic Functions section of the Non-linear Functions page of the example workbook attached.

Power Functions

Power functions are based around the formula y = a.x^b

Excel doesn’t have a specific function dealing with Power functions, however we can again use the Linest function as previously described by first converting the data from a Power function to Straight line and this is done by talking the LN of the X and Y values.

Form:    =LINEST( LN(Known Y Values), LN(Known X Values))

eg:          =LINEST( LN(C58:C65), LN(B58:B65)) as an array formula

or            =INDEX( LINEST( LN(C58:C65), LN(B58:B65)), 1) as a normal formula

The above equations return Parameter 1 as b and Parameter 2 as LN(a)

LN(a) must be converted back to Parameter a by taking the Exp(a)

This is shown in a worked example on the Power Functions section of the Non-linear Functions page of the example workbook attached.

Polynomial Functions

Polynomial functions are based around the formula y = a.x^n + b.x^(n-1) + c.x^(n-2) + … + m

Which typically looks like  y = a.x^5 + b.x^4 + c.x^3 + d.x^2 + e.x +m

And if any of the parameters a to m are zero that part of the function will be zero and not shown.

Excel does have a specific function dealing with Polynomial functions, and you guessed it, it is the Linest function. The Linest function must be told that it is dealing with a polynomial function and this is done by adding another parameter to it’s input. The extra parameter is added by raising the know X values to the power of an array of number 1..n, where n is the power of the polynomial you want to use.

Form:  = LINEST( Known Y Values, Known X Values^{1,2,3,..n})

eg:     for a polynomial of power 3

= LINEST(C84:C94, B84:B94^{1,2,3}) as an array formula

or      =INDEX( LINEST(C84:C94, B84:B94^{1,2,3}), 1) as a normal formula

The above equations return Parameter 1 as a, Parameter 2 as b, Parameter 3 as c if a power 3 polynomial is used.

This is shown in a worked example on the Power Functions section of the Non-linear Functions page of the example workbook attached.


Multiple Variable Linear Regressions

The Linest function is able to be used to determine the regressions of multiple input variables (X1, X2, … Xn)  that may contribute to a single output variable (Y).

This is best demonstrated with a simple example:

Hui’s Fruit Shop

Say we have a Fruit Shop and we only sell Apples & Oranges and we know how many Staff and what our Overhead Costs were and how much Profit we have made each year for the past decade.

This could be tabulated below:

We can use Linest to work out a regression for this model. That is what is the relationship between the output and all the inputs.

The format of this will be

Form:    = LINEST(Known Y values, Known X Values, TRUE, TRUE) as an Array Formula

eg:          = LINEST(E122:E132, A122:D132, TRUE, TRUE)

Note that the Known X Values of this example is a 4 column wide area representing the 4 variables.

This must be array entered in an area Xn + 1 columns wide and 5 rows deep, in our case a 5 column x 5 row area.

Note that the equation for then profit is made up of the array values from the first row of the answer array in reverse order

Y = 18.84.X1 + 27.98.X2 + 3851.79.X3 -0.26.X4 -15406.84

And that the parameters are in highest X4 to lowest X1 order followed by b at the end

You can also see the other parameters of the array of which the most important is the r2 factor which in this example is 0.90 indicating that there is a good fit between the Inputs and the Profit. Hence we could be relatively comfortable using our profit equation for the estimate of future profits.

Measuring the accuracy of the Estimation.

In the linear Linest section at the start and in the previous example we briefly mentioned a measure called the r2 parameter and said that because it had a value of 0.90 we would be comfortable using our estimation parameters to estimate future profits.

r2 is a measure of the error between the data points and the estimated values.

Its values vary between 0 = no relationship and 1 = a perfect relationship.

For example here are 3 charts based on the equation of Y = 3 X + 5

The equations of the lines of best fit and the r2 values are shown on each chart.

You can see that the data of Chart Y1 has a very close fit to the equation both visually and through a very high r2 value of 0.9962, where as at Y3 there is a very loose relationship between the data and the estimate which is shown visually as well as a low r2 value of 0.2552.

The derivation and use of this is beyond this post and I would refer you to the Excel Help of the Linest function, where it is discussed or Wikipedia.

How Does All This Work ?

The Excel Linest, Logest and Growth Functions all use a technique called “Least Squares Approximation”.

This is an iterative process which minimises the sum of the square of the distance from the estimated line to the actual data for all known data points. Once this is minimised the parameters which define the estimated line are returned to the user.

The scope of how Least Squares works is beyond the scope of this post, but if you are interested have a read at Wikipedia.

There are a number of other estimation techniques available which excel doesn’t support.

One should never assume that “just because Excel gave me the answer – it is correct” and this applies to the use of statistics more than any other area in maths or Excel usage.

Limitations:

The above techniques need to be used with a degree of caution.

Often a trend will exactly mathematically fit the data but in reality you wouldn’t use the equations.

In the picture below (courtesy of Wikipedia) 10 data points are exactly matched by a Polynomial function , whereas the linear estimate misses every point.

Which estimate would you choose to use?  The linear function I hope.

This is discussed in more detail at Wikipedia.

Disclaimer

It should be noted that just because Excel returns an estimated line of best fit to your data, it doesn’t mean that your data actually follows that trend, it just may be coincidental and that user discretion is advised in all cases, refer Limitations above.

There are a number of other estimation techniques available and users interested should discuss these if required with a person expert in their data distribution.

Excel Functions Referred to in this Post

Exp – Return the exponential value of the input

Forecast – Forecast intermediate or future values based on known X and Y values

Growth – Derive an exponential estimate for a known set of X & Y values

Index – Lookup a value at row/column intercept from a table or array of data

Intercept – Return the intercept of a linear estimate

Linest – Derive a linear estimate for a known set of X & Y values

LN – Return the Natural Log value of the input

Logest – Derive an exponential estimate for a known set of X & Y values

Power – Returns the value of a number raised to a power

Slope – Return the slope of a linear estimate

Trend – Forecast intermediate or future values based on known X and Y values

Further Readings

Excel has a number of extra Statistical functions hidden in the Data Analysis addin.

I have not discussed or used these tools here as not all users will have access to them and the post is getting longish already.

Functions you may want to have a look at include:

Correl & Pearson: Both functions allow the calculation of correlation coefficients between variables.

Exponential Smoothing: The Exponential Smoothing analysis tool predicts a value that is based on the forecast for the prior period, adjusted for the error in that prior forecast

Fourier Analysis: The Fourier Analysis tool solves problems in linear systems and analyzes periodic data by using the Fast Fourier Transform (FFT) method to transform data, great for analysing periodic and frequency based data.

I would direct readers who are interested in using these techniques to look at the following sources

Microsoft Excel Help – Statistical Functions

Wikipedia

Physics Labs Tutorials

Newton Excel Bach, not (just) an Excel Blog

 

Further Readings

Are You Trendy (Part 1)

Are You Trendy (Part 3)

 

What’s Next ?

In the next post we will looks at some Tools that Excel has to assist us in quickly determining which estimate method we can use.

I will also give you a neat little UDF to assist in your interpolations/extrapolations of your data which was used to make the animated GIF at the top of the first post.

ps: Happy Australia Day Everyone :) !

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38 Responses to “Are You Trendy? (Part 2)”

  1. […] This post was mentioned on Twitter by Chandoo.org and Stray__Cat, Excel Insider. Excel Insider said: Are You Trendy? (Part 2): Forecasting using Excel Functions “Todays forecast will be Hot and Humid with a Chance… http://bit.ly/dX8kBX […]

  2. Cyril Z. says:

    Nice second part but I’ve notice some kind of cut/paste between TREND and FORECAST which disturb my understanding of the differences between them.

    Can you explain a bit more how they differ ?

  3. Hui... says:

    @Cyril
    They give the same results but ask for input in a slightly different way.
    Forecast is useful for a single point
    Trend is an array function and can do 1 point as a normal function or a number of points as an array function

  4. bill says:

    again, a wonderful post. quick questions: are you suggesting that r2 be the only evaluative statistic on model form and goodness of fit? what statistic could/should be used to compare “goodness of fit” across all linear and non-linear regression model forms? how can it be derived from the Excel formulas?

  5. John M. says:

    I’ve used about 27 difference variations of the linear model transforming X and/or Y with square root, squared, natural log, and reciprocal. This includes the linear model and two models for when both X and Y have values between 0 and 1. These two models are the logistic and log probit models.

  6. Prem Sivakanthan says:

    Hi Hui, great post…very timely as I was just scratching my head yesterday trying to work out the growth function. I have a question: one of the data models I was working on was corrupted (not by excel, but by its lesser equivilent, a human being) so I need to estimate a set of data points for December 2010. The data in question was definiately not linear, and has no clear trend, upward or downward. I’m thinking some type of average would be the best way to go (I have a couple of years worth of data), what would be your thoughts?

    Prem
    from EHA

  7. C.S. Ganti says:

    Excellent tutorial. I must say that not many are aware of these features in EXCEL — how they added from pure Pivot Tables to all the way in Data Analysis and array functions all types – Stats, Math, Date and many more. Thank you, I am intimately familiar what you presented here and have used at one time or another…

    Thanks, may be MS will give you some credit for advancing their tools beyond their own publicity.

    Keep it coming

  8. Fred says:

    Wonderful Post. Man, I’m going to bookmark it for later reference.

    @bill. r2 is very good only if the outcome has certain randomness (think stock price). But like Hui has shown in the last chart. An polynomial chart hitting almost all the dots like that may have r2 = .99 or so, given the known x and y. but the straight line which miss all the points may have a r2 = .96 or .95 So in that case I “eye-ball” them and make a human judgement as to which to use. Right, Hui?

  9. […] For more details on the individual Tren Types refer to Are You Trendy (Part 2). […]

  10. Pablo Molina says:

    Chandoo: Googled 2 days for information related to logarithmic trends, including Microsoft sites and Excel forums.

    None of them had a comprehensible, complete, graphical, professional explanation that match your level.

    Congratulations!

  11. […] be a part of your forecasting system. Now, let's have an overview of the FORECAST function in Excel.Let's begin by saying that FORECAST function in Microsoft Excel is not a complete inventory forecast…el. WordPress › […]

  12. […] A useful post I found about Logest. The handiest tip I found is to use the “Index” function when using LOGEST, which makes it not necessary to enter it as an array formula. […]

  13. Lewis says:

    Excellent. Thank you…

  14. T Lyle says:

    Thanks so much for this great resource. I do have a question though. In theory, I would think that Slope and Trend are both trying to get to the same thing, right? Aren’t they both based on finding the line of best fit? If so, I would think that the following might be true (although it isn’t):

    Let’s assume a time series (monthly data) of rates and I am trying to predict the next value in that series (think extending a forward curve). I would think that if I took the Slope of the series and added it to the last number in the series, I should get a reasonable ‘forecast’ for the next month. However, this doesn’t always match the number that TREND or FORECAST predict. I think if you have a perfect R^2 then perhaps it matches. Not sure. But in most real situations it doesn’t match.

    Is this because [SLOPE + Last Data Point] doesn’t take into account the volatility or ‘tightness’ of the line of best fit, and TREND / FORECAST do? Very interested in any suggestions.

    • Hui... says:

      @Tracy
      Your totally correct about the r2 value and its impact on adding the slope to the last value for linear functions
      If r2=1.0 then the last value will be on the average slope line and adding the slope will give you the next Y value for the next X Value

      There is a small but important caveat here.

      Dates, especially Monthly data is not linear on the X Axis, because some months have 28, 29, 30 or 31 days
      so you do need to be careful when assuming this applies to Date based data.
      It sort of depends is the data based on say an accumulation of data from the month in which case the no of days is important or is the Month just a name for the X Axis and the data is independent of the days per month.

      • T Lyle says:

        Thank you for your quick response. I understand about the daily/monthly issue. In my case, I am looking at a monthly rate so the amount of days in a month doesn’t matter, but the point is well taken.

        So just to confirm, Trend & Forecast use the variance in the R^2 to inject additional volatility (based on passed behavior) back into the future forecast which moves it off of (but within the overall regression and continuing to maintain the line of best fit) the perfect slope line? If so, I think I am on the same page.

        And a Logarithmic forecast would basically be the inverse of a Growth forecast, right? Based on the shape of the curve?

        Thanks a ton!

  15. manjunathan says:

    dear sir …. how to calculate a,b, and c from Y=ax+by+c using excel 2007.
    i know Y ,x,and y values but i need a,b ,c sd, R values
     

  16. Pandu Rakimanputra says:

    BIG THanks pal..
     
    It’s very useful for me… Keep posting

  17. SATYA SWARUP says:

    I need to use Winter-Holt’s model of forecasting in Excel. If there is any user defined function, it would be of great help to me.

  18. David says:

    Hi Hui, great work, this was very helpful!

    However, the link for downloading the Trend2.xls file seems to be broken. I was able to download the Trend1 and Trend 3 files successfully though. Can you repost it or email it to me?

    Thank you!

  19. Tim says:

    Chandoo – This is awesome; great example workbook too! I never leave your site without knowing a little bit more about excel and what it can do. Thanks a ton.

    Tim

  20. Mike says:

    Chandoo,

    Looking at your formulas for the Logarithmic function on the example workbook and trying to recreate for a project I’m working on. I’m curious, for your a and b you have the exact same formula, but with two different results (cells B19 and C19). Can explain how these two are working?

    Thanks!

    -Mike

  21. Mubin says:

    Hello!

    I am doing commodity price forecasting, and I have data of daily prices from April 2012- April 2014.

    The problem i’m having is (1) There are some daily data values missing, and (2) after I have dealt with the missing values (using smoothing), i have a problem calculating the seasonal indices because there are different numbers of working days in each month. some months have 23 days, some 21, some 20. because of the differing number of days, I cannot successfully calculate the seasonal effect. how do i tackle this problem?

    P.S. I’m fairly new to excel, so please be gentle :)

    • Hui... says:

      @Mubin
      Can you post your data?

      I’d suggest asking the question in the Chandoo.org Forums
      http://chandoo.org/forum/

      • Mubin says:

        Ill post on the forum too, thanks a lot

        Week-DayNo.-Day- Date Wheat Prices/100kg (PKR)
        1 1 Monday 02-Apr-12 2625.00
        2 Tuesday 03-Apr-12 2625.00
        3 Wednesday04-Apr-12 2625.00
        4 Thursday 05-Apr-12 2625.00
        5 Friday 06-Apr-12 2625.00
        2 6 Monday 09-Apr-12 2625.00
        7 Tuesday 10-Apr-12 2625.00
        8 Wednesday 11-Apr-12 2625.00
        9 Thursday 12-Apr-12 2625.00
        10 Friday 13-Apr-12 2625.00
        3 11 Monday 16-Apr-12 2625.00
        12 Tuesday 17-Apr-12 2625.00
        13 Wednesday 18-Apr-12 2625.00
        14 Thursday 19-Apr-12 2625.00
        15 Friday 20-Apr-12 2625.00
        4 16 Monday 23-Apr-12 2625.00
        17 Tuesday 24-Apr-12 2625.00
        18 Wednesday 25-Apr-12 2625.00
        19 Thursday 26-Apr-12 2625.00
        20 Friday 27-Apr-12 2625.00
        5 21 Monday 30-Apr-12 2625.00
        22 Tuesday 01-May-12 2625.00
        23 Wednesday 02-May-12 2625.00
        24 Thursday 03-May-12 2625.00
        25 Friday 04-May-12 2600.00
        6 26 Monday 07-May-12 2600.00
        27 Tuesday 08-May-12 2600.00
        28 Wednesday 09-May-12 2588.00
        29 Thursday 10-May-12 2588.00
        30 Friday 11-May-12 2588.00
        7 31 Monday 14-May-12 2575.00
        32 Tuesday 15-May-12 2588.00
        33 Wednesday 16-May-12 2588.00
        34 Thursday 17-May-12 2588.00
        35 Friday 18-May-12 2600.00
        8 36 Monday 21-May-12 2613.00
        37 Tuesday 22-May-12 2613.00
        38 Wednesday 23-May-12 2613.00
        39 Thursday 24-May-12 2569.00
        40 Friday 25-May-12 2568.00
        9 41 Monday 28-May-12 2588.00
        42 Tuesday 29-May-12 2598.00
        43 Wednesday 30-May-12 2588.00
        44 Thursday 31-May-12 2588.00
        45 Friday 01-Jun-12 2588.00
        10 46 Monday 04-Jun-12 2588.00
        47 Tuesday 05-Jun-12 2588.00
        48 Wednesday 06-Jun-12 2588.00
        49 Thursday 07-Jun-12 2588.00
        50 Friday 08-Jun-12 2588.00
        11 51 Monday 11-Jun-12 2588.00
        52 Tuesday 12-Jun-12 2588.00
        53 Wednesday 13-Jun-12 2588.00
        54 Thursday 14-Jun-12 2588.00
        55 Friday 15-Jun-12 2588.00
        12 56 Monday 18-Jun-12 2588.00
        57 Tuesday 19-Jun-12 2588.00
        58 Wednesday 20-Jun-12 2588.00
        59 Thursday 21-Jun-12 2588.00
        60 Friday 22-Jun-12 2588.00
        13 61 Monday 25-Jun-12 2588.00
        62 Tuesday 26-Jun-12 2588.00
        63 Wednesday 27-Jun-12 2588.00
        64 Thursday 28-Jun-12 2588.00
        65 Friday 29-Jun-12 2588.00
        14 66 Monday 02-Jul-12 2588.00
        67 Tuesday 03-Jul-12 2588.00
        68 Wednesday 04-Jul-12 2588.00
        69 Thursday 05-Jul-12 2588.00
        70 Friday 06-Jul-12 2588.00
        15 71 Monday 09-Jul-12 2588.00
        72 Tuesday 10-Jul-12 2588.00
        73 Wednesday 11-Jul-12 2588.00
        74 Thursday 12-Jul-12 2588.00
        75 Friday 13-Jul-12 2588.00
        16 76 Monday 16-Jul-12 2588.00
        77 Tuesday 17-Jul-12 2588.00
        78 Wednesday 18-Jul-12 2588.00
        79 Thursday 19-Jul-12 2588.00
        80 Friday 20-Jul-12 2588.00
        17 81 Monday 23-Jul-12 2588.00
        82 Tuesday 24-Jul-12 2588.00
        83 Wednesday 25-Jul-12 2588.00
        84 Thursday 26-Jul-12 2588.00
        85 Friday 27-Jul-12 2588.00
        18 86 Monday 30-Jul-12 2588.00
        87 Tuesday 31-Jul-12 2588.00
        88 Wednesday 01-Aug-12 2588.00
        89 Thursday 02-Aug-12 2588.00
        90 Friday 03-Aug-12 2588.00
        19 91 Monday 06-Aug-12 2588.00
        92 Tuesday 07-Aug-12 2588.00
        93 Wednesday 08-Aug-12 2588.00
        94 Thursday 09-Aug-12 2588.00
        95 Friday 10-Aug-12 2588.00
        20 96 Monday 13-Aug-12 2600.00
        97 Tuesday 14-Aug-12 2600.00
        98 Wednesday 15-Aug-12 2600.00
        99 Thursday 16-Aug-12 2600.00
        100 Friday 17-Aug-12 2600.00
        21 101 Monday 20-Aug-12 2600.00
        102 Tuesday 21-Aug-12 2600.00
        103 Wednesday 22-Aug-12 2600.00
        104 Thursday 23-Aug-12 2600.00
        105 Friday 24-Aug-12 2600.00
        22 106 Monday 27-Aug-12 2600.00
        107 Tuesday 28-Aug-12 2600.00
        108 Wednesday 29-Aug-12 2600.00
        109 Thursday 30-Aug-12 2600.00
        110 Friday 31-Aug-12 2600.00
        23 111 Monday 03-Sep-12 2600.00
        112 Tuesday 04-Sep-12 2600.00
        113 Wednesday 05-Sep-12 2600.00
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        24 116 Monday 10-Sep-12 2575.00
        117 Tuesday 11-Sep-12 2575.00
        118 Wednesday 12-Sep-12 2575.00
        119 Thursday 13-Sep-12 2575.00
        120 Friday 14-Sep-12 2575.00
        25 121 Monday 17-Sep-12 2575.00
        122 Tuesday 18-Sep-12 2575.00
        123 Wednesday 19-Sep-12 2575.00
        124 Thursday 20-Sep-12 2575.00
        125 Friday 21-Sep-12 2575.00
        26 126 Monday 24-Sep-12 2575.00
        127 Tuesday 25-Sep-12 2575.00
        128 Wednesday 26-Sep-12 2575.00
        129 Thursday 27-Sep-12 2575.00
        130 Friday 28-Sep-12 2575.00
        27 131 Monday 01-Oct-12 2575.00
        132 Tuesday 02-Oct-12 2575.00
        133 Wednesday 03-Oct-12 2575.00
        134 Thursday 04-Oct-12 2575.00
        135 Friday 05-Oct-12 2575.00
        28 136 Monday 08-Oct-12 2575.00
        137 Tuesday 09-Oct-12 2575.00
        138 Wednesday 10-Oct-12 2575.00
        139 Thursday 11-Oct-12 2575.00
        140 Friday 12-Oct-12 2575.00
        29 141 Monday 15-Oct-12 2575.00
        142 Tuesday 16-Oct-12 2575.00
        143 Wednesday 17-Oct-12 2575.00
        144 Thursday 18-Oct-12 2575.00
        145 Friday 19-Oct-12 2575.00
        30 146 Monday 22-Oct-12 2838.00
        147 Tuesday 23-Oct-12 2838.00
        148 Wednesday 24-Oct-12 2838.00
        149 Thursday 25-Oct-12 2838.00
        150 Friday 26-Oct-12 2838.00
        31 151 Monday 29-Oct-12 2838.00
        152 Tuesday 30-Oct-12 2838.00
        153 Wednesday 31-Oct-12 2838.00
        154 Thursday 01-Nov-12 2838.00
        155 Friday 02-Nov-12 2838.00
        32 156 Monday 05-Nov-12 2838.00
        157 Tuesday 06-Nov-12 2875.00
        158 Wednesday 07-Nov-12 2875.00
        159 Thursday 08-Nov-12 2875.00
        160 Friday 09-Nov-12 2875.00
        33 161 Monday 12-Nov-12 2875.00
        162 Tuesday 13-Nov-12 2875.00
        163 Wednesday 14-Nov-12 2875.00
        164 Thursday 15-Nov-12 2875.00
        165 Friday 16-Nov-12 2875.00
        34 166 Monday 19-Nov-12 2875.00
        167 Tuesday 20-Nov-12 2875.00
        168 Wednesday 21-Nov-12 2875.00
        169 Thursday 22-Nov-12 2875.00
        170 Friday 23-Nov-12 3025.00
        35 171 Monday 26-Nov-12 3025.00
        172 Tuesday 27-Nov-12 3025.00
        173 Wednesday 28-Nov-12 3025.00
        174 Thursday 29-Nov-12 3025.00
        175 Friday 30-Nov-12 3025.00
        36 176 Monday 03-Dec-12 3025.00
        177 Tuesday 04-Dec-12 3025.00
        178 Wednesday 05-Dec-12 3025.00
        179 Thursday 06-Dec-12 3025.00
        180 Friday 07-Dec-12 3025.00
        37 181 Monday 10-Dec-12 3025.00
        182 Tuesday 11-Dec-12 3025.00
        183 Wednesday 12-Dec-12 3025.00
        184 Thursday 13-Dec-12 3025.00
        185 Friday 14-Dec-12 3025.00
        38 186 Monday 17-Dec-12 3025.00
        187 Tuesday 18-Dec-12 3025.00
        188 Wednesday 19-Dec-12 3025.00
        189 Thursday 20-Dec-12 3025.00
        190 Friday 21-Dec-12 3025.00
        39 191 Monday 24-Dec-12 3075.00
        192 Tuesday 25-Dec-12 3075.00
        193 Wednesday 26-Dec-12 3075.00
        194 Thursday 27-Dec-12 3075.00
        195 Friday 28-Dec-12 3075.00
        40 196 Monday 31-Dec-12 3075.00
        197 Tuesday 01-Jan-13 3075.00
        198 Wednesday 02-Jan-13 3075.00
        199 Thursday 03-Jan-13 3075.00
        200 Friday 04-Jan-13 3075.00
        41 201 Monday 07-Jan-13 3075.00
        202 Tuesday 08-Jan-13 3075.00
        203 Wednesday 09-Jan-13 3075.00
        204 Thursday 10-Jan-13 3075.00
        205 Friday 11-Jan-13 3075.00
        42 206 Monday 14-Jan-13 3075.00
        207 Tuesday 15-Jan-13 3075.00
        208 Wednesday 16-Jan-13 3075.00
        209 Thursday 17-Jan-13 3075.00
        210 Friday 18-Jan-13 3075.00
        43 211 Monday 21-Jan-13 3075.00
        212 Tuesday 22-Jan-13 3075.00
        213 Wednesday 23-Jan-13 3075.00
        214 Thursday 24-Jan-13 3075.00
        215 Friday 25-Jan-13 3075.00
        44 216 Monday 28-Jan-13 3075.00
        217 Tuesday 29-Jan-13 3075.00
        218 Wednesday 30-Jan-13 2995.20
        219 Thursday 31-Jan-13 2997.68
        220 Friday 01-Feb-13 3000.17
        45 221 Monday 04-Feb-13 3002.65
        222 Tuesday 05-Feb-13 3005.14
        223 Wednesday 06-Feb-13 3007.62
        224 Thursday 07-Feb-13 3010.11
        225 Friday 08-Feb-13 3012.59
        46 226 Monday 11-Feb-13 3015.08
        227 Tuesday 12-Feb-13 3017.56
        228 Wednesday 13-Feb-13 3020.05
        229 Thursday 14-Feb-13 3022.53
        230 Friday 15-Feb-13 3025.02
        47 231 Monday 18-Feb-13 3027.51
        232 Tuesday 19-Feb-13 3029.99
        233 Wednesday 20-Feb-13 3032.48
        234 Thursday 21-Feb-13 3034.96
        235 Friday 22-Feb-13 3037.45
        48 236 Monday 25-Feb-13 3039.93
        237 Tuesday 26-Feb-13 3042.42
        238 Wednesday 27-Feb-13 3044.90
        239 Thursday 28-Feb-13 3047.39
        240 Friday 01-Mar-13 3049.87
        49 241 Monday 04-Mar-13 3052.36
        242 Tuesday 05-Mar-13 3054.84
        243 Wednesday 06-Mar-13 3057.33
        244 Thursday 07-Mar-13 3059.81
        245 Friday 08-Mar-13 3062.30
        50 246 Monday 11-Mar-13 3064.79
        247 Tuesday 12-Mar-13 3067.27
        248 Wednesday 13-Mar-13 3069.76
        249 Thursday 14-Mar-13 3072.24
        250 Friday 15-Mar-13 3074.73
        51 251 Monday 18-Mar-13 3077.21
        252 Tuesday 19-Mar-13 3079.70
        253 Wednesday 20-Mar-13 3082.18
        254 Thursday 21-Mar-13 3084.67
        255 Friday 22-Mar-13 3087.15
        52 256 Monday 25-Mar-13 3089.64
        257 Tuesday 26-Mar-13 3092.12
        258 Wednesday 27-Mar-13 3094.61
        259 Thursday 28-Mar-13 3097.09
        260 Friday 29-Mar-13 3099.58
        53 261 Monday 01-Apr-13 3102.07
        262 Tuesday 02-Apr-13 3104.55
        263 Wednesday 03-Apr-13 3107.04
        264 Thursday 04-Apr-13 3109.52
        265 Friday 05-Apr-13 3112.01
        54 266 Monday 08-Apr-13 3114.49
        267 Tuesday 09-Apr-13 3116.98
        268 Wednesday 10-Apr-13 3119.46
        269 Thursday 11-Apr-13 3121.95
        270 Friday 12-Apr-13 3124.43
        55 271 Monday 15-Apr-13 3126.92
        272 Tuesday 16-Apr-13 3129.40
        273 Wednesday 17-Apr-13 3131.89
        274 Thursday 18-Apr-13 3134.37
        275 Friday 19-Apr-13 3136.86
        56 276 Monday 22-Apr-13 3139.35
        277 Tuesday 23-Apr-13 3141.83
        278 Wednesday 24-Apr-13 3144.32
        279 Thursday 25-Apr-13 3146.80
        280 Friday 26-Apr-13 2938.00
        57 281 Monday 29-Apr-13 2938.00
        282 Tuesday 30-Apr-13 2938.00
        283 Wednesday 01-May-13 2938.00
        284 Thursday 02-May-13 2938.00
        285 Friday 03-May-13 2938.00
        58 286 Monday 06-May-13 2938.00
        287 Tuesday 07-May-13 2844.00
        288 Wednesday 08-May-13 2844.00
        289 Thursday 09-May-13 2844.00
        290 Friday 10-May-13 2844.00
        59 291 Monday 13-May-13 2844.00
        292 Tuesday 14-May-13 2844.00
        293 Wednesday 15-May-13 2844.00
        294 Thursday 16-May-13 2844.00
        295 Friday 17-May-13 2844.00
        60 296 Monday 20-May-13 2844.00
        297 Tuesday 21-May-13 2844.00
        298 Wednesday 22-May-13 2844.00
        299 Thursday 23-May-13 2844.00
        300 Friday 24-May-13 2844.00
        61 301 Monday 27-May-13 2844.00
        302 Tuesday 28-May-13 2988.00
        303 Wednesday 29-May-13 3031.00
        304 Thursday 30-May-13 3031.00
        305 Friday 31-May-13 3031.00
        62 306 Monday 03-Jun-13 3031.00
        307 Tuesday 04-Jun-13 2975.00
        308 Wednesday 05-Jun-13 2975.00
        309 Thursday 06-Jun-13 2975.00
        310 Friday 07-Jun-13 2975.00
        63 311 Monday 10-Jun-13 2975.00
        312 Tuesday 11-Jun-13 2975.00
        313 Wednesday 12-Jun-13 3013.00
        314 Thursday 13-Jun-13 3013.00
        315 Friday 14-Jun-13 3157.00
        64 316 Monday 17-Jun-13 3157.00
        317 Tuesday 18-Jun-13 3157.00
        318 Wednesday 19-Jun-13 3157.00
        319 Thursday 20-Jun-13 3157.00
        320 Friday 21-Jun-13 3157.00
        65 321 Monday 24-Jun-13 3157.00
        322 Tuesday 25-Jun-13 3157.00
        323 Wednesday 26-Jun-13 3275.00
        324 Thursday 27-Jun-13 3288.00
        325 Friday 28-Jun-13 3338.00
        66 326 Monday 01-Jul-13 3338.00
        327 Tuesday 02-Jul-13 3338.00
        328 Wednesday 03-Jul-13 3338.00
        329 Thursday 04-Jul-13 3338.00
        330 Friday 05-Jul-13 3338.00
        67 331 Monday 08-Jul-13 3338.00
        332 Tuesday 09-Jul-13 3338.00
        333 Wednesday 10-Jul-13 3338.00
        334 Thursday 11-Jul-13 3338.00
        335 Friday 12-Jul-13 3338.00
        68 336 Monday 15-Jul-13 3363.00
        337 Tuesday 16-Jul-13 3363.00
        338 Wednesday 17-Jul-13 3363.00
        339 Thursday 18-Jul-13 3363.00
        340 Friday 19-Jul-13 3363.00
        69 341 Monday 22-Jul-13 3363.00
        342 Tuesday 23-Jul-13 3363.00
        343 Wednesday 24-Jul-13 3363.00
        344 Thursday 25-Jul-13 3363.00
        345 Friday 26-Jul-13 3363.00
        70 346 Monday 29-Jul-13 3363.00
        347 Tuesday 30-Jul-13 3363.00
        348 Wednesday 31-Jul-13 3363.00
        349 Thursday 01-Aug-13 3363.00
        350 Friday 02-Aug-13 3363.00
        71 351 Monday 05-Aug-13 3363.00
        352 Tuesday 06-Aug-13 3363.00
        353 Wednesday 07-Aug-13 3363.00
        354 Thursday 08-Aug-13 3363.00
        355 Friday 09-Aug-13 3363.00
        72 356 Monday 12-Aug-13 3363.00
        357 Tuesday 13-Aug-13 3363.00
        358 Wednesday 14-Aug-13 3363.00
        359 Thursday 15-Aug-13 3363.00
        360 Friday 16-Aug-13 3588.00
        73 361 Monday 19-Aug-13 3588.00
        362 Tuesday 20-Aug-13 3588.00
        363 Wednesday 21-Aug-13 3588.00
        364 Thursday 22-Aug-13 3588.00
        365 Friday 23-Aug-13 3588.00
        74 366 Monday 26-Aug-13 3488.00
        367 Tuesday 27-Aug-13 3488.00
        368 Wednesday 28-Aug-13 3488.00
        369 Thursday 29-Aug-13 3488.00
        370 Friday 30-Aug-13 3488.00
        75 371 Monday 02-Sep-13 3635.00
        372 Tuesday 03-Sep-13 3635.00
        373 Wednesday 04-Sep-13 3635.00
        374 Thursday 05-Sep-13 3635.00
        375 Friday 06-Sep-13 3635.00
        76 376 Monday 09-Sep-13 3635.00
        377 Tuesday 10-Sep-13 3650.00
        378 Wednesday 11-Sep-13 3638.00
        379 Thursday 12-Sep-13 3635.00
        380 Friday 13-Sep-13 3635.00
        77 381 Monday 16-Sep-13 3650.00
        382 Tuesday 17-Sep-13 3635.00
        383 Wednesday 18-Sep-13 3635.00
        384 Thursday 19-Sep-13 3635.00
        385 Friday 20-Sep-13 3635.00
        78 386 Monday 23-Sep-13 3686.00
        387 Tuesday 24-Sep-13 3635.00
        388 Wednesday 25-Sep-13 3594.00
        389 Thursday 26-Sep-13 3944.00
        390 Friday 27-Sep-13 3635.00
        79 391 Monday 30-Sep-13 3594.00
        392 Tuesday 01-Oct-13 3638.00
        393 Wednesday 02-Oct-13 3656.00
        394 Thursday 03-Oct-13 3656.00
        395 Friday 04-Oct-13 3656.00
        80 396 Monday 07-Oct-13 3656.00
        397 Tuesday 08-Oct-13 3656.00
        398 Wednesday 09-Oct-13 3656.00
        399 Thursday 10-Oct-13 3656.00
        400 Friday 11-Oct-13 3656.00
        81 401 Monday 14-Oct-13 3656.00
        402 Tuesday 15-Oct-13 3675.00
        403 Wednesday 16-Oct-13 3675.00
        404 Thursday 17-Oct-13 3675.00
        405 Friday 18-Oct-13 3675.00
        82 406 Monday 21-Oct-13 3675.00
        407 Tuesday 22-Oct-13 3675.00
        408 Wednesday 23-Oct-13 3675.00
        409 Thursday 24-Oct-13 3675.00
        410 Friday 25-Oct-13 3675.00
        83 411 Monday 28-Oct-13 3725.00
        412 Tuesday 29-Oct-13 3725.00
        413 Wednesday 30-Oct-13 3725.00
        414 Thursday 31-Oct-13 3725.00
        415 Friday 01-Nov-13 3738.00
        84 416 Monday 04-Nov-13 3763.00
        417 Tuesday 05-Nov-13 3763.00
        418 Wednesday 06-Nov-13 3675.00
        419 Thursday 07-Nov-13 3675.00
        420 Friday 08-Nov-13 3675.00
        85 421 Monday 11-Nov-13 3853.00
        422 Tuesday 12-Nov-13 3550.00
        423 Wednesday 13-Nov-13 3788.00
        424 Thursday 14-Nov-13 3853.00
        425 Friday 15-Nov-13 3853.00
        86 426 Monday 18-Nov-13 3925.00
        427 Tuesday 19-Nov-13 3925.00
        428 Wednesday 20-Nov-13 3925.00
        429 Thursday 21-Nov-13 4025.00
        430 Friday 22-Nov-13 3925.00
        87 431 Monday 25-Nov-13 4013.00
        432 Tuesday 26-Nov-13 4013.00
        433 Wednesday 27-Nov-13 4013.00
        434 Thursday 28-Nov-13 4013.00
        435 Friday 29-Nov-13 4013.00
        88 436 Monday 02-Dec-13 4013.00
        437 Tuesday 03-Dec-13 4013.00
        438 Wednesday 04-Dec-13 3200.00
        439 Thursday 05-Dec-13 3943.00
        440 Friday 06-Dec-13 3943.00
        89 441 Monday 09-Dec-13 3988.00
        442 Tuesday 10-Dec-13 3988.00
        443 Wednesday 11-Dec-13 3988.00
        444 Thursday 12-Dec-13 3988.00
        445 Friday 13-Dec-13 3988.00
        90 446 Monday 16-Dec-13 3988.00
        447 Tuesday 17-Dec-13 3988.00
        448 Wednesday 18-Dec-13 3988.00
        449 Thursday 19-Dec-13 3938.00
        450 Friday 20-Dec-13 3988.00
        91 451 Monday 23-Dec-13 3988.00
        452 Tuesday 24-Dec-13 3943.00
        453 Wednesday 25-Dec-13 3943.00
        454 Thursday 26-Dec-13 3988.00
        455 Friday 27-Dec-13 3988.00
        92 456 Monday 30-Dec-13 3988.00
        457 Tuesday 31-Dec-13 3988.00
        458 Wednesday 01-Jan-14 3988.00
        459 Thursday 02-Jan-14 3988.00
        460 Friday 03-Jan-14 3988.00
        93 461 Monday 06-Jan-14 3988.00
        462 Tuesday 07-Jan-14 3982.00
        463 Wednesday 08-Jan-14 3794.67
        464 Thursday 09-Jan-14 3988.00
        465 Friday 10-Jan-14 3975.00
        94 466 Monday 13-Jan-14 3975.00
        467 Tuesday 14-Jan-14 3807.09
        468 Wednesday 15-Jan-14 3988.00
        469 Thursday 16-Jan-14 3975.00
        470 Friday 17-Jan-14 3975.00
        95 471 Monday 20-Jan-14 3975.00
        472 Tuesday 21-Jan-14 3988.00
        473 Wednesday 22-Jan-14 3988.00
        474 Thursday 23-Jan-14 3988.00
        475 Friday 24-Jan-14 3988.00
        96 476 Monday 27-Jan-14 3988.00
        477 Tuesday 28-Jan-14 3988.00
        478 Wednesday 29-Jan-14 3858.80
        479 Thursday 30-Jan-14 3861.97
        480 Friday 31-Jan-14 3865.13
        97 481 Monday 03-Feb-14 3888.00
        482 Tuesday 04-Feb-14 3888.00
        483 Wednesday 05-Feb-14 3888.00
        484 Thursday 06-Feb-14 3888.00
        485 Friday 07-Feb-14 3888.00
        98 486 Monday 10-Feb-14 3888.00
        487 Tuesday 11-Feb-14 3888.00
        488 Wednesday 12-Feb-14 3888.00
        489 Thursday 13-Feb-14 3888.00
        490 Friday 14-Feb-14 3888.00
        99 491 Monday 17-Feb-14 3900.34
        492 Tuesday 18-Feb-14 3903.50
        493 Wednesday 19-Feb-14 3906.66
        494 Thursday 20-Feb-14 3909.83
        495 Friday 21-Feb-14 3913.00
        100 496 Monday 24-Feb-14 3913.00
        497 Tuesday 25-Feb-14 3913.00
        498 Wednesday 26-Feb-14 3913.00
        499 Thursday 27-Feb-14 3913.00
        500 Friday 28-Feb-14 3913.00
        101 501 Monday 03-Mar-14 3888.00
        502 Tuesday 04-Mar-14 3888.00
        503 Wednesday 05-Mar-14 3888.00
        504 Thursday 06-Mar-14 3888.00
        505 Friday 07-Mar-14 3888.00
        102 506 Monday 10-Mar-14 3888.00
        507 Tuesday 11-Mar-14 3888.00
        508 Wednesday 12-Mar-14 3888.00
        509 Thursday 13-Mar-14 3888.00
        510 Friday 14-Mar-14 3888.00
        103 511 Monday 17-Mar-14 3888.00
        512 Tuesday 18-Mar-14 3888.00
        513 Wednesday 19-Mar-14 3941.00
        514 Thursday 20-Mar-14 3041.00
        515 Friday 21-Mar-14 3962.80
        104 516 Monday 24-Mar-14 3965.93
        517 Tuesday 25-Mar-14 3969.05
        518 Wednesday 26-Mar-14 3972.17
        519 Thursday 27-Mar-14 3975.30
        520 Friday 28-Mar-14 3978.42
        105 521 Monday 31-Mar-14 3981.54

  22. […] If you want to learn about how to do simple forecasting and trend analysis, please see the official forecast function in Excel post on the Microsoft website, and this handy tutorial on trend lines and forecasting in excel. […]

  23. […] If you want to learn about how to do simple forecasting and trend analysis, please see the official forecast function in Excel post on the Microsoft website, and this handy tutorial on trend lines and forecasting in excel. […]

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