Causal Forecasting by Gordon Lloyd

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

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

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

Methods of Forecasting Time Series Methods Time Series Methods Causal Forecasting Methods Causal Forecasting Methods Qualitative Methods Qualitative Methods

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.

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

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

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

Linear Regression Line Formula y = a + bx y = the dependent variable a = the intercept b = the slope of the line x = the independent variable

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

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

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

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

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

Example of Linear Regression # of Yards of # of Yards of Week Housing starts Concrete Ordered xy xy x²y² Total

Example of Linear Regression X = 191/10 = Y = 3104/10 = b = ∑xy – nxy = (62149) – (10)(19.10)(310.40) ∑x² -nx² (3901) – (10)(19.10)² ∑x² -nx² (3901) – (10)(19.10)² b = a = Y - bX = – (19.10) a =

Example of Linear Regression Regression Equation y = a + bx y = (x) Concrete ordered for 25 new housing starts y = (25) y = 377 yards

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

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( )- ( )²] r =.8433

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

Excel Regression Example # of Housing# of Yards WeekStartsof Concrete Ordered xy

Excel Regression Example SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations10 ANOVA dfSSMSFSignificance F Regression Residual Total CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0% Intercept X Variable

Excel Regression Example

Compare Excel to Manual Regression Manual Results a = b = y = (25) y = 377 Excel Results a = b = y = (25) y = (25) y = 377

Excel Correlation and Coefficient of Determination Multiple R R Square Regression Statistics

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

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

Reading List  Lapide, Larry, New Developments in Business Forecasting, Journal of Business Forecasting Methods & Systems, Summer 99, Vol. 18, Issue 2  Principles of Forecasting, A Handbook for Researchers and Practitioners, Edited by J. Scott Armstrong, University of Pennsylvania  Forecasting Forecasting