causal forecasting by gordon lloyd. what will be covered? what is forecasting? what is forecasting?...
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Causal ForecastingCausal Forecasting
by Gordon Lloydby Gordon Lloyd
What will be covered?What will be covered?
What is forecasting?What is forecasting? Methods of forecastingMethods of forecasting What is Causal Forecasting?What is Causal Forecasting? When is Causal Forecasting Used?When is Causal Forecasting Used? Methods of Causal ForecastingMethods of Causal Forecasting Example of Causal ForecastingExample of Causal Forecasting
What is Forecasting?What is Forecasting?
Forecasting is a process of Forecasting is a process of estimating the unknownestimating the unknown
Business Applications Business Applications
Basis for most Basis for most planning decisionsplanning decisions– SchedulingScheduling– Inventory Inventory – ProductionProduction– Facility LayoutFacility Layout– WorkforceWorkforce– DistributionDistribution– PurchasingPurchasing– SalesSales
Methods of Methods of ForecastingForecasting
Time Series MethodsTime Series Methods
Causal Forecasting MethodsCausal Forecasting Methods
Qualitative MethodsQualitative Methods
What is Causal Forecasting?What is Causal Forecasting?
Causal forecasting methodsCausal forecasting methods are based on the are based on the relationship between the variable to be relationship between the variable to be forecasted and an independent variable. forecasted and an independent variable.
When Is Causal Forecasting When Is Causal Forecasting Used?Used?
Know or believe something Know or believe something caused demand to act a certain caused demand to act a certain wayway
Demand or sales patterns that Demand or sales patterns that vary drastically with planned or vary drastically with planned or unplanned eventsunplanned events
Types of Causal ForecastingTypes of Causal Forecasting
RegressionRegression Econometric modelsEconometric models Input-Output Models:Input-Output Models:
Regression Analysis ModelingRegression Analysis Modeling
Pros Pros – Increased accuraciesIncreased accuracies– ReliabilityReliability– Look at multiple factors of demandLook at multiple factors of demand
ConsCons– Difficult to interpretDifficult to interpret– Complicated math Complicated math
Linear RegressionLinear RegressionLine FormulaLine Formula
y = a + bxy = a + bx
y = the dependent variabley = the dependent variable
a = the intercepta = the intercept
b = the slope of the lineb = the slope of the line
x = the independent variablex = the independent variable
Linear Regression Linear Regression FormulasFormulas
a = Y – bXa = Y – bX b = b = ∑xy – nXY∑xy – nXY ∑ ∑x² - nX²x² - nX²
a = intercepta = intercept
b = slope of the lineb = slope of the line
X = X = ∑x∑x = mean of x = mean of x
n the x datan the x data
Y = Y = ∑y∑y = mean of y = mean of y
n the y datan the y data
n = number of periodsn = number of periods
Correlation Correlation
Measures the strength of the Measures the strength of the relationship between the relationship between the dependent and independent dependent and independent variablevariable
Correlation Coefficient Correlation Coefficient FormulaFormula
r = r = ______n∑xy - ∑x∑y______ ______n∑xy - ∑x∑y______
√√[n∑x² - (∑x)²][n∑y² - (∑y)²][n∑x² - (∑x)²][n∑y² - (∑y)²]
____________________________________________________________________________
r = correlation coefficientr = correlation coefficient
n = number of periodsn = number of periods
x = the independent variablex = the independent variable
y = the dependent variabley = the dependent variable
Coefficient of Coefficient of DeterminationDetermination
Another measure of the Another measure of the relationship between the relationship between the dependant and independent dependant and independent variablevariable
Measures the percentage of Measures the percentage of variation in the dependent (y) variation in the dependent (y) variable that is attributed to the variable that is attributed to the independent (x) variableindependent (x) variable
r = r²r = r²
ExampleExample
Concrete CompanyConcrete Company Forecasting Concrete UsageForecasting Concrete Usage
– How many yards will poured during the How many yards will poured during the weekweek
Forecasting InventoryForecasting Inventory– CementCement– AggregateAggregate– Additives Additives
Forecasting Work ScheduleForecasting Work Schedule
Example of Linear Example of Linear RegressionRegression
# of # of Yards of Yards of WeekWeek Housing starts Housing starts Concrete Ordered Concrete Ordered
xx yy xy xy x² x² y²y² 11 1111 225225 2475 2475 121 121 5062550625 22 1515 250250 3750 3750 225 225 6250062500 33 2222 336336 7392 7392 484 484 112896112896 44 1919 310310 5890 5890 361 361 9610096100 55 1717 325325 5525 5525 289 289 105625105625 66 2626 463463 12038 12038 676 676
214369214369 77 1818 249 249 4482 4482 324 324 6200162001 88 1818 267267 4806 4806 324 324 7128971289 99 2929 379 379 10991 10991 841 841
143641143641 1010 16 16 300300 4800 4800 256 256 9000090000TotalTotal 191 191 3104 3104 62149 390162149 3901 10090461009046
Example of Linear Example of Linear RegressionRegressionX = 191/10 = 19.10X = 191/10 = 19.10
Y = 3104/10 = 310.40Y = 3104/10 = 310.40
b = b = ∑xy – nxy∑xy – nxy = = (62149) – (10)(19.10)(310.40)(62149) – (10)(19.10)(310.40)
∑ ∑x² -nx² (3901) – (10)(19.10)²x² -nx² (3901) – (10)(19.10)²
b = 11.3191b = 11.3191
a = Y - bX = 310.40 – 11.3191(19.10)a = Y - bX = 310.40 – 11.3191(19.10)
a = 94.2052a = 94.2052
Example of Linear Example of Linear RegressionRegression
Regression EquationRegression Equation
y = a + bxy = a + bx
y = 94.2052 + 11.3191(x)y = 94.2052 + 11.3191(x)
Concrete ordered for 25 new housing Concrete ordered for 25 new housing startsstarts
y = 94.2052 + 11.3191(25)y = 94.2052 + 11.3191(25)
y = 377 yardsy = 377 yards
Correlation Coefficient Correlation Coefficient FormulaFormula
r = r = ______n∑xy - ∑x∑y______ ______n∑xy - ∑x∑y______
√√[n∑x² - (∑x)²][n∑y² - (∑y)²][n∑x² - (∑x)²][n∑y² - (∑y)²]
____________________________________________________________________________
r = correlation coefficientr = correlation coefficient
n = number of periodsn = number of periods
x = the independent variablex = the independent variable
y = the dependent variabley = the dependent variable
Correlation CoefficientCorrelation Coefficient
r = r = ______n∑xy - ∑x∑y______ ______n∑xy - ∑x∑y______
√√[n∑x² - (∑x)²][n∑y² - (∑y)²][n∑x² - (∑x)²][n∑y² - (∑y)²]
r = r = 10(62149) – (191)(3104)10(62149) – (191)(3104)
√√[10(3901)-(3901)²][10(1009046)-[10(3901)-(3901)²][10(1009046)-(1009046)²](1009046)²]
r = .8433r = .8433
Coefficient of Coefficient of DeterminationDetermination
r = .8433r = .8433
r² = (.8433)²r² = (.8433)²
r² = .7111r² = .7111
Excel Regression Excel Regression ExampleExample
# of Housing # of YardsWeek Starts of Concrete
Orderedx y
1 11 2252 15 2503 22 3364 19 3105 17 3256 26 4637 18 2498 18 2679 29 379
10 16 300
Excel Regression Excel Regression ExampleExample
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 Excel Regression ExampleExample
SUMMARY OUTPUT
Regression StatisticsMultiple R 0.8433R Square 0.7111
Adjusted R Square 0.6750Standard Error 40.5622
Observations 10
ANOVA
dfRegression 1
Residual 8Total 9
CoefficientsIntercept 94.2052
X Variable 1 11.3191
Compare Excel to Compare Excel to Manual RegressionManual Regression
Manual Results Manual Results
a = 94.2052a = 94.2052
b = 11.3191b = 11.3191y = 94.2052 + y = 94.2052 +
11.3191(25)11.3191(25)
y = 377y = 377
Excel ResultsExcel Results
a = 94.2052a = 94.2052
b = 11.3191b = 11.3191
y = 94.2052 + y = 94.2052 + 11.3191(25)11.3191(25)
y = 377y = 377
Excel Correlation and Excel Correlation and Coefficient of Coefficient of DeterminationDetermination
Multiple R 0.8433R Square 0.7111
Regression Statistics
Compare Excel to Compare Excel to Manual RegressionManual Regression
Manual ResultsManual Results
r = .8344r = .8344
r² = .7111r² = .7111
Excel ResultsExcel Results
r = .8344r = .8344
r² = .7111 r² = .7111
ConclusionConclusion
Causal forecasting is accurate Causal forecasting is accurate and efficientand efficient
When strong correlation exists When strong correlation exists the model is very effectivethe model is very effective
No forecasting method is 100% No forecasting method is 100% effectiveeffective
Reading ListReading List
Lapide, Larry, Lapide, Larry, New Developments in Business New Developments in Business Forecasting,Forecasting, Journal of Business Forecasting Journal of Business Forecasting Methods & Systems, Summer 99, Vol. 18, Methods & Systems, Summer 99, Vol. 18, Issue 2Issue 2
http://morris.wharton.upenn.edu/forecasthttp://morris.wharton.upenn.edu/forecast, , Principles of Forecasting, A Handbook for Principles of Forecasting, A Handbook for Researchers and Practitioners, Researchers and Practitioners, Edited by J. Edited by J. Scott Armstrong, University of Pennsylvania Scott Armstrong, University of Pennsylvania
www.uoguelph.ca/~dsparlin/forecast.htmwww.uoguelph.ca/~dsparlin/forecast.htm,, ForecastingForecasting