Causal Forecasting

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Causal Forecasting

• by Gordon Lloyd

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What will be covered?

• What is forecasting?
• Methods of forecasting
• What is Causal Forecasting?
• When is Causal Forecasting Used?
• Methods of Causal Forecasting
• Example of Causal Forecasting

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What is Forecasting?

• Forecasting is a process of estimating the
  unknown

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Business Applications

• Basis for most planning decisions
• Scheduling
• Inventory
• Production
• Facility Layout
• Workforce
• Distribution
• Purchasing
• Sales

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Methods of Forecasting

• Time Series Methods
• Causal Forecasting Methods
• Qualitative Methods

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What is Causal Forecasting?

• Causal forecasting methods are based on the
  relationship between the variable to be
  forecasted and an independent variable. 

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When Is Causal Forecasting Used?

• Know or believe something caused demand to act a
  certain way
• Demand or sales patterns that vary drastically
  with planned or unplanned events

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Types of Causal Forecasting

• Regression
• Econometric models
• Input-Output Models

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Regression Analysis Modeling

• Pros
• Increased accuracies
• Reliability
• Look at multiple factors of demand
• Cons
• Difficult to interpret
• Complicated math

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Linear RegressionLine Formula

• y a bx
• y the dependent variable
• a the intercept
• b the slope of the line
• x the independent variable

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Linear Regression Formulas

• a Y bX
• b ?xy nXY
• ?x² - nX²

• a intercept
• b slope of the line
• X ?x mean of x
• n the x data
• Y ?y mean of y
• n the y data
• n number of periods

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Correlation

• Measures the strength of the relationship between
  the dependent and independent variable

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Correlation Coefficient Formula

• r ______n?xy - ?x?y______
  
• vn?x² - (?x)²n?y² - (?y)²
• ______________________________________
• r correlation coefficient
• n number of periods
• x the independent variable
• y the dependent variable

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Coefficient of Determination

• Another measure of the relationship between the
  dependant and independent variable
• Measures the percentage of variation in the
  dependent (y) variable that is attributed to the
  independent (x) variable
• r r²

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Example

• Concrete Company
• Forecasting Concrete Usage
• How many yards will poured during the week
• Forecasting Inventory
• Cement
• Aggregate
• Additives
• Forecasting Work Schedule

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Example of Linear Regression

• of Yards of
• Week Housing starts Concrete
  Ordered
• x y xy x² y²
• 1 11 225 2475 121 50625
• 2 15 250 3750 225 62500
• 3 22 336 7392 484 112896
• 4 19 310 5890 361 96100
• 5 17 325 5525 289 105625
• 6 26 463 12038 676 214369
• 7 18 249 4482 324 62001
• 8 18 267 4806 324 71289
• 9 29 379 10991 841 143641
• 10 16 300 4800 256 90000
• Total 191 3104 62149
  3901 1009046

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Example of Linear Regression

• X 191/10 19.10
• Y 3104/10 310.40
• b ?xy nxy (62149) (10)(19.10)(310.40)
• ?x² -nx² (3901) (10)(19.10)²
• b 11.3191
• a Y - bX 310.40 11.3191(19.10)
• a 94.2052

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Example of Linear Regression

• Regression Equation
• y a bx
• y 94.2052 11.3191(x)
• Concrete ordered for 25 new housing starts
• y 94.2052 11.3191(25)
• y 377 yards

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Correlation Coefficient Formula

• r ______n?xy - ?x?y______
  
• vn?x² - (?x)²n?y² - (?y)²
• ______________________________________
• r correlation coefficient
• n number of periods
• x the independent variable
• y the dependent variable

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Correlation Coefficient

• r ______n?xy - ?x?y______
  
• vn?x² - (?x)²n?y² - (?y)²
• r 10(62149) (191)(3104)
• v10(3901)-(3901)²10(1009046)-(1009046)²
• r .8433

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Coefficient of Determination

• r .8433
• r² (.8433)²
• r² .7111

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Excel Regression Example
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Excel Regression Example
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Excel Regression Example
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Compare Excel to Manual Regression

• Manual Results
• a 94.2052
• b 11.3191
• y 94.2052 11.3191(25)
• y 377

• Excel Results
• a 94.2052
• b 11.3191
• y 94.2052 11.3191(25)
• y 377

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Excel Correlation and Coefficient of Determination
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Compare Excel to Manual Regression

• Manual Results
• r .8344
• r² .7111

• Excel Results
• r .8344
• r² .7111

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Conclusion

• Causal forecasting is accurate and efficient
• When strong correlation exists the model is very
  effective
• No forecasting method is 100 effective

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Reading List

• Lapide, Larry, New Developments in Business
  Forecasting, Journal of Business Forecasting
  Methods Systems, Summer 99, Vol. 18, Issue 2
• http//morris.wharton.upenn.edu/forecast,
  Principles of Forecasting, A Handbook for
  Researchers and Practitioners, Edited by J. Scott
  Armstrong, University of Pennsylvania
• www.uoguelph.ca/dsparlin/forecast.htm,
• Forecasting