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### Causal Forecasting

by Gordon Lloyd

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?

- Forecasting is a process of estimating the unknown

Business Applications

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

Methods of Forecasting

- Time Series Methods
- Causal Forecasting 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.

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

- Regression
- Econometric models
- Input-Output Models:

Regression Analysis Modeling

- Pros
- Increased accuracies
- Reliability
- Look at multiple factors of demand
- Cons
- Difficult to interpret
- Complicated math

Linear RegressionLine Formula

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

Linear Regression FormulasCorrelation

- 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
- Measures the percentage of variation in the dependent (y) variable that is attributed to the independent (x) variable

r = r²

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

# 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

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

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

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(1009046)-(1009046)²]

r = .8433

# 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

Excel Regression ExampleRegression 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 ExampleRegression 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

Excel Regression ExampleManual 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

Compare Excel to Manual RegressionManual Results

r = .8344

r² = .7111

Excel Results

r = .8344

r² = .7111

Compare Excel to Manual RegressionConclusion

- Causal forecasting is accurate and efficient
- When strong correlation exists the model is very 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
- 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

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