Understanding Causal Forecasting Methods: A Practical Guide

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