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Causal Forecasting

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Causal Forecasting

by Gordon Lloyd

- What is forecasting?
- Methods of forecasting
- What is Causal Forecasting?
- When is Causal Forecasting Used?
- Methods of Causal Forecasting
- Example of Causal Forecasting

- Forecasting is a process of estimating the unknown

- Basis for most planning decisions
- Scheduling
- Inventory
- Production
- Facility Layout
- Workforce
- Distribution
- Purchasing
- Sales

- Time Series Methods
- Causal Forecasting Methods
- Qualitative Methods

- Causal forecasting methods are based on the relationship between the variable to be forecasted and an independent variable.

- Know or believe something caused demand to act a certain way
- Demand or sales patterns that vary drastically with planned or unplanned events

- Regression
- Econometric models
- Input-Output Models:

- Pros
- Increased accuracies
- Reliability
- Look at multiple factors of demand

- Cons
- Difficult to interpret
- Complicated math

y = a + bx

y = the dependent variable

a = the intercept

b = the slope of the line

x = the independent variable

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

- Measures the strength of the relationship between the dependent and independent variable

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

- 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

- Concrete Company
- Forecasting Concrete Usage
- How many yards will poured during the week

- Forecasting Inventory
- Cement
- Aggregate
- Additives

- Forecasting Work Schedule

# of Yards of

Week Housing starts Concrete Ordered

xy xy x²y²

111225 2475 12150625

215250 3750 22562500

322336 7392 484112896

419310 5890 36196100

517325 5525 289105625

626463 12038 676214369

718249 4482 32462001

818267 4806 32471289

929379 10991 841143641

1016 300 4800 25690000

Total 191 310462149 39011009046

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

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

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

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

r = .8433

r² = (.8433)²

r² = .7111

# 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

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

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

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

Regression Statistics

Multiple R

0.8433

R Square

0.7111

Manual Results

r = .8344

r² = .7111

Excel Results

r = .8344

r² = .7111

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

- 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