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Causal Forecasting Causal Forecasting by Gordon Lloyd by Gordon Lloyd

Causal Forecasting by Gordon Lloyd. What will be covered? What is forecasting? What is forecasting? Methods of forecasting Methods of forecasting What

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Page 1: Causal Forecasting by Gordon Lloyd. What will be covered? What is forecasting? What is forecasting? Methods of forecasting Methods of forecasting What

Causal ForecastingCausal Forecasting

by Gordon Lloydby Gordon Lloyd

Page 2: Causal Forecasting by Gordon Lloyd. What will be covered? What is forecasting? What is forecasting? Methods of forecasting Methods of forecasting What

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

Page 3: Causal Forecasting by Gordon Lloyd. What will be covered? What is forecasting? What is forecasting? Methods of forecasting Methods of forecasting What

What is Forecasting?What is Forecasting?

Forecasting is a process of Forecasting is a process of estimating the unknownestimating the unknown

Page 4: Causal Forecasting by Gordon Lloyd. What will be covered? What is forecasting? What is forecasting? Methods of forecasting Methods of forecasting What

Business Applications Business Applications

Basis for most Basis for most planning decisionsplanning decisions– SchedulingScheduling– Inventory Inventory – ProductionProduction– Facility LayoutFacility Layout– WorkforceWorkforce– DistributionDistribution– PurchasingPurchasing– SalesSales

Page 5: Causal Forecasting by Gordon Lloyd. What will be covered? What is forecasting? What is forecasting? Methods of forecasting Methods of forecasting What

Methods of Methods of ForecastingForecasting

Time Series MethodsTime Series Methods

Causal Forecasting MethodsCausal Forecasting Methods

Qualitative MethodsQualitative Methods

Page 6: Causal Forecasting by Gordon Lloyd. What will be covered? What is forecasting? What is forecasting? Methods of forecasting Methods of forecasting What

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. 

Page 7: Causal Forecasting by Gordon Lloyd. What will be covered? What is forecasting? What is forecasting? Methods of forecasting Methods of forecasting What

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

Page 8: Causal Forecasting by Gordon Lloyd. What will be covered? What is forecasting? What is forecasting? Methods of forecasting Methods of forecasting What

Types of Causal ForecastingTypes of Causal Forecasting

RegressionRegression Econometric modelsEconometric models Input-Output Models:Input-Output Models:

Page 9: Causal Forecasting by Gordon Lloyd. What will be covered? What is forecasting? What is forecasting? Methods of forecasting Methods of forecasting What

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

Page 10: Causal Forecasting by Gordon Lloyd. What will be covered? What is forecasting? What is forecasting? Methods of forecasting Methods of forecasting What

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

Page 11: Causal Forecasting by Gordon Lloyd. What will be covered? What is forecasting? What is forecasting? Methods of forecasting Methods of forecasting What

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

Page 12: Causal Forecasting by Gordon Lloyd. What will be covered? What is forecasting? What is forecasting? Methods of forecasting Methods of forecasting What

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

Page 13: Causal Forecasting by Gordon Lloyd. What will be covered? What is forecasting? What is forecasting? Methods of forecasting Methods of forecasting What

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

Page 14: Causal Forecasting by Gordon Lloyd. What will be covered? What is forecasting? What is forecasting? Methods of forecasting Methods of forecasting What

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

Page 15: Causal Forecasting by Gordon Lloyd. What will be covered? What is forecasting? What is forecasting? Methods of forecasting Methods of forecasting What

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

Page 16: Causal Forecasting by Gordon Lloyd. What will be covered? What is forecasting? What is forecasting? Methods of forecasting Methods of forecasting What

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

Page 17: Causal Forecasting by Gordon Lloyd. What will be covered? What is forecasting? What is forecasting? Methods of forecasting Methods of forecasting What

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

Page 18: Causal Forecasting by Gordon Lloyd. What will be covered? What is forecasting? What is forecasting? Methods of forecasting Methods of forecasting What

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

Page 19: Causal Forecasting by Gordon Lloyd. What will be covered? What is forecasting? What is forecasting? Methods of forecasting Methods of forecasting What

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

Page 20: Causal Forecasting by Gordon Lloyd. What will be covered? What is forecasting? What is forecasting? Methods of forecasting Methods of forecasting What

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

Page 21: Causal Forecasting by Gordon Lloyd. What will be covered? What is forecasting? What is forecasting? Methods of forecasting Methods of forecasting What

Coefficient of Coefficient of DeterminationDetermination

r = .8433r = .8433

r² = (.8433)²r² = (.8433)²

r² = .7111r² = .7111

Page 22: Causal Forecasting by Gordon Lloyd. What will be covered? What is forecasting? What is forecasting? Methods of forecasting Methods of forecasting What

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

Page 23: Causal Forecasting by Gordon Lloyd. What will be covered? What is forecasting? What is forecasting? Methods of forecasting Methods of forecasting What

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

Page 24: Causal Forecasting by Gordon Lloyd. What will be covered? What is forecasting? What is forecasting? Methods of forecasting Methods of forecasting What

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

Page 25: Causal Forecasting by Gordon Lloyd. What will be covered? What is forecasting? What is forecasting? Methods of forecasting Methods of forecasting What

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

Page 26: Causal Forecasting by Gordon Lloyd. What will be covered? What is forecasting? What is forecasting? Methods of forecasting Methods of forecasting What

Excel Correlation and Excel Correlation and Coefficient of Coefficient of DeterminationDetermination

Multiple R 0.8433R Square 0.7111

Regression Statistics

Page 27: Causal Forecasting by Gordon Lloyd. What will be covered? What is forecasting? What is forecasting? Methods of forecasting Methods of forecasting What

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

Page 28: Causal Forecasting by Gordon Lloyd. What will be covered? What is forecasting? What is forecasting? Methods of forecasting Methods of forecasting What

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

Page 29: Causal Forecasting by Gordon Lloyd. What will be covered? What is forecasting? What is forecasting? Methods of forecasting Methods of forecasting What

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


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