Causal Forecasting :Causal Forecasting by Gordon Lloyd


What will be covered? :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? :What is Forecasting? Forecasting is a process of estimating the unknown


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


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


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


When Is Causal Forecasting Used? :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


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


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


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


Linear Regression Formulas :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


Correlation :Correlation Measures the strength of the relationship between the dependent and independent variable


Correlation Coefficient Formula :Correlation Coefficient Formula r = ______n?xy - ?x?y______ v[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 :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


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


Example of Linear Regression :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


Example of Linear Regression :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


Example of Linear Regression :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


Correlation Coefficient Formula :Correlation Coefficient Formula r = ______n?xy - ?x?y______ v[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 :Correlation Coefficient r = ______n?xy - ?x?y______ v[n?x² - (?x)²][n?y² - (?y)²] r = 10(62149) – (191)(3104) v[10(3901)-(3901)²][10(1009046)-(1009046)²] r = .8433


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


Excel Regression Example :Excel Regression Example


Excel Regression Example :Excel Regression Example


Excel Regression Example :Excel Regression Example


Compare Excel to Manual Regression :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


Excel Correlation and Coefficient of Determination :Excel Correlation and Coefficient of Determination


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


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


Reading List :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