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Causal Forecasting by Gordon Lloyd

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What will be covered? What is forecasting? What is forecasting? Methods of forecasting Methods of forecasting What is Causal Forecasting? What is Causal Forecasting? When is Causal Forecasting Used? When is Causal Forecasting Used? Methods of Causal Forecasting Methods of Causal Forecasting Example of Causal Forecasting Example of Causal Forecasting

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What is Forecasting? Forecasting is a process of estimating the unknown Forecasting is a process of estimating the unknown

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Business Applications Basis for most planning decisions Basis for most planning decisions –Scheduling –Inventory –Production –Facility Layout –Workforce –Distribution –Purchasing –Sales

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Methods of Forecasting Time Series Methods Time Series Methods Causal Forecasting Methods Causal Forecasting Methods Qualitative 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. 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 Know or believe something caused demand to act a certain way Demand or sales patterns that vary drastically with planned or unplanned events Demand or sales patterns that vary drastically with planned or unplanned events

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Types of Causal Forecasting Regression Regression Econometric models Econometric models Input-Output Models: Input-Output Models:

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Regression Analysis Modeling Pros Pros –Increased accuracies –Reliability –Look at multiple factors of demand Cons Cons –Difficult to interpret –Complicated math

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Linear Regression Line 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 ∑x² - nX² a = intercept b = slope of the line X = ∑x = mean of x n the x data n the x data Y = ∑y = mean of y n the y data 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 Measures the strength of the relationship between the dependent and independent variable

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Correlation Coefficient Formula r = ______n∑xy - ∑x∑y______ √[n∑x² - (∑x)²][n∑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 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 Measures the percentage of variation in the dependent (y) variable that is attributed to the independent (x) variable r = r² r = r²

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

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Example of Linear Regression # of Yards of # of Yards of Week Housing starts Concrete Ordered xy xy x²y² 111225 2475 12150625 111225 2475 12150625 215250 3750 22562500 215250 3750 22562500 322336 7392 484112896 322336 7392 484112896 419310 5890 36196100 419310 5890 36196100 517325 5525 289105625 517325 5525 289105625 626463 12038 676214369 626463 12038 676214369 718249 4482 32462001 718249 4482 32462001 818267 4806 32471289 818267 4806 32471289 929379 10991 841143641 929379 10991 841143641 1016 300 4800 25690000 1016 300 4800 25690000 Total 191 310462149 39011009046

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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 ∑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______ √[n∑x² - (∑x)²][n∑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______ √[n∑x² - (∑x)²][n∑y² - (∑y)²] r = 10(62149) – (191)(3104) √[10(3901)-(3901)²][10(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 # of Housing# of Yards WeekStartsof Concrete Ordered xy 111225 215250 322336 419310 517325 626463 718249 818267 929379 1016300

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Excel Regression Example SUMMARY OUTPUT Regression Statistics Multiple R0.8433 R Square0.7111 Adjusted R Square0.6750 Standard Error40.5622 Observations10 ANOVA dfSSMSFSignificance F Regression132402.0532402.051219.69380.0022 Residual813162.351645.2936 Total945564.40 CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0% Intercept94.205250.37731.87000.0984-21.9652210.3757-21.9652210.3757 X Variable 111.31912.55064.43780.00225.437317.20095.437317.2009

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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 = 94.2052 + 11.3191(25) y = 377

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Excel Correlation and Coefficient of Determination Multiple R0.8433 R Square0.7111 Regression Statistics

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Compare Excel to Manual Regression Manual Results Manual Results r =.8344 r² =.7111 Excel Results Excel Results r =.8344 r² =.7111

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Conclusion Causal forecasting is accurate and efficient Causal forecasting is accurate and efficient When strong correlation exists the model is very effective When strong correlation exists the model is very effective No forecasting method is 100% 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 http://morris.wharton.upenn.edu/forecast www.uoguelph.ca/~dsparlin/forecast.htm, www.uoguelph.ca/~dsparlin/forecast.htm Forecasting Forecasting

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