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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?.

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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

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 Examplea = 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 RegressionMultiple R

0.8433

R Square

0.7111

Excel Correlation and Coefficient of Determinationr = .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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