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Causal Forecasting

Causal Forecasting. by Gordon Lloyd. 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. What is Forecasting?.

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Causal Forecasting

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  1. Causal Forecasting by Gordon Lloyd

  2. 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

  3. What is Forecasting? • Forecasting is a process of estimating the unknown

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

  5. Methods of Forecasting • Time Series Methods • Causal Forecasting Methods • Qualitative Methods

  6. What is Causal Forecasting? • Causal forecasting methods are based on the relationship between the variable to be forecasted and an independent variable. 

  7. 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

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

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

  10. Linear RegressionLine Formula y = a + bx y = the dependent variable a = the intercept b = the slope of the line x = the independent variable

  11. 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 Linear Regression Formulas

  12. Correlation • Measures the strength of the relationship between the dependent and independent variable

  13. 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

  14. 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

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

  16. 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

  17. 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

  18. 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

  19. 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

  20. 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

  21. Coefficient of Determination r = .8433 r² = (.8433)² r² = .7111

  22. # of Housing # of Yards Week Starts of Concrete Ordered x y 1 11 225 2 15 250 3 22 336 4 19 310 5 17 325 6 26 463 7 18 249 8 18 267 9 29 379 10 16 300 Excel Regression Example

  23. SUMMARY OUTPUT Regression Statistics Multiple R 0.8433 R Square 0.7111 Adjusted R Square 0.6750 Standard Error 40.5622 Observations 10 ANOVA df SS MS F Significance F Regression 1 32402.05 32402.0512 19.6938 0.0022 Residual 8 13162.35 1645.2936 Total 9 45564.40 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 94.2052 50.3773 1.8700 0.0984 -21.9652 210.3757 -21.9652 210.3757 X Variable 1 11.3191 2.5506 4.4378 0.0022 5.4373 17.2009 5.4373 17.2009 Excel Regression Example

  24. SUMMARY OUTPUT Regression Statistics Multiple R 0.8433 R Square 0.7111 Adjusted R Square 0.6750 Standard Error 40.5622 Observations 10 ANOVA df Regression 1 Residual 8 Total 9 Coefficients Intercept 94.2052 X Variable 1 11.3191 Excel Regression Example

  25. 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 Compare Excel to Manual Regression

  26. Regression Statistics Multiple R 0.8433 R Square 0.7111 Excel Correlation and Coefficient of Determination

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

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

  29. 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

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