Extending that Line into the Future

St. Louis CMGFebruary 12, 2008

Wayne Bell – UniGroup, Inc.

Methods of ForecastingExcel Trendlines – Manual ExtensionsPercentage Rate of GrowthRegressionMoving Averages

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Excel TrendlinesLinear vs. Exponential

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Percentage Rate of GrowthUsed if you have a known value and are given a rate of

growth

Normally, you are given an annual rate-of-growth.

Three methods:

Linear Growth – Straight Line

Monthly Compound Growth

Annual Compound Growth

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Linear Growth – Straight LineCalculate the amount of growth.

Current value is 100Growth Rate is 50%Amount is 50 per year

Divide by 12 for monthly increaseAdd this increase to the prior monthXn+1=Xn*(1+(%/(12+%*n)))

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Linear Growth – Straight Line

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Monthly Compound GrowthAnnual percentage divided by 12Increase the current monthly value by this amountXn+1=Xn*(1+(%/12))

The amount at the end of a year will be more than expectedIn this case, the base is 100Increase is 50% per yearActual increase is 163.2 or 63.2%

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Monthly Compound Growth

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Annual Compound GrowthProduces an exponential growthThe beginning months of the year have a lower

growth than the end months of the yearAt the end of the year, the value is exactly the

percentage growth expectedXn+1=Xn*((1+%)^(1/12))

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Annual Compound Growth

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RegressionLinear Regression – produces a straight line that

best fits a single set of dataLinear Trend Line

Exponential Regression – produces an exponential curve that best fits a single set of dataExponential Trend Line

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RegressionExcel’s Data Analysis Toolkit has a Regression Tool

Can be used to judge the correlation of one or more dependent variables to a dependent variable.

Can provide the intercept and slope coefficients to “draw the line” for current and future data points.

The Regression Tool is for Linear Regression onlyExponential Regression can be performed with a

minor change to the dataSimply take the log (Excel Function ‘LN’) of the

dependent variable.

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Regression – Sample OutputSUMMARY OUTPUT

Regression Statistics

Multiple R 0.974268299

R Square 0.949198718 >0.8Adjusted R Square 0.947559967

Standard Error 0.132146441

Observations 33

ANOVA

  df SS MS F Significance F

Regression 1 10.11474893 10.11474893 579.2208241 1.27185E-21 <0.01

Residual 31 0.541343135 0.017462682

Total 32 10.65609207      

  Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept -71.36457274 3.1164205 -22.89953257 5.48666E-21 -77.72055423 -65.00859125 -77.72055423 -65.00859125

Date 0.001908643 7.93054E-05 24.06700696 1.27185E-21 0.001746898 0.002070387 0.001746898 0.002070387

<0.01 Both Positive or Both Negative

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Regression – Sample OutputItems in Red are quick checks on the validity of the

RegressionItems in Green are ‘Rule of Thumb’ valuesIn the case of this Sample, you can calculate the

expected value for any Date: New_Value = Intercept_Coefficient + Date_Coefficient *

Date

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TREND / GROWTH ExampleData is composed of two types of data

Independent – What is known, such as DateDependent – What is unknown – In this case, the

Value is dependent on the Date=TREND(Dependent Variable Range, Independent

Variable Range, New Independent Variable)=TREND($B$2:$B$34,$A$2:$A$34,A2)

B Column is the known Dependent variablesA Column is the known Independent variables

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TREND / GROWTH Example

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Moving AveragesThe Moving Average projects values in the forecast

period, based on the average value of the variable over a specific number of preceding periods.

A Moving Average provides trend information that a simple average of all historical data would mask.

The number of periods in the Moving Average affects the outcome:Small number of periodsLarge number of periods

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Moving AverageSimple average of previous values (Sample of 5)

=AVERAGE(A2:A6)=AVERAGE(A3:A7)

- OR -

Moving Average in Analysis Toolpak

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Moving Average

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Weighted Moving AverageAssumes that the most current value is a better

predictor than an older value.Build a table of WeightsIncorporate these Weights into the Moving AverageTable:

Weights % Month-1 50.0 38% Month-2 35.0 27% Month-3 25.0 19% Month-4 15.0 12% Month-5 5.0 4%

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Weighted Moving Average

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SummaryKnown Starting Point – Known Rate of Increase –

Long Term ForecastLinear TrendingCompound Trending

Data History – Grow at same Rate – Long Term ForecastLinear RegressionExponential Regression

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SummaryOld Data not as important as Current Values – Short

Term ForecastMoving AverageWeighted Moving Average

Can combine methods.Use Moving Average to determine ‘Next’ valueUse Regression or Trending for Long Term Forecast

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SummaryKnow Your DataChart your current dataForecast your current data and overlay the charts

Forecast 2005 and 2006 into 2007.Compare the forecast to the actual 2007.

Choose the forecast method that best fits your data!

The link for this presentation is: http://regions.cmg.org/regions/stlcmg/files/Download/Beyond%20the%20Trend%20Line.ppt

The link for the datasheet is: http://regions.cmg.org/regions/stlcmg/files/Download/Beyond%20the%20Trend%20Line.xls

For more information please contact me at: Wayne_Bell@UniGroupInc.com

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