Causal Forecasting
by Gordon Lloyd
What will be covered?
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
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

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
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

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 Regression
Line Formula
y = a + bx
y = the dependent variable
a = the intercept
b = the slope of the line
x = the independent variable
Linear Regression
Formulas
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
Correlation

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
Week
1
2
3
4
5
6
7
8
9
10
Total
# of
Housing starts
x
11
15
22
19
17
26
18
18
29
16
191
Yards of
Concrete Ordered
y
xy
x²
225
2475
121
250
3750
225
336
7392
484
310
5890
361
325
5525
289
463
12038 676
249
4482
324
267
4806
324
379
10991 841
300
4800
256
3104
62149
3901
y²
50625
62500
112896
96100
105625
214369
62001
71289
143641
90000
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
Coefficient of
Determination
r = .8433
r² = (.8433)²
r² = .7111
Excel Regression Example
# of Housing
Starts
Week
1
2
3
4
5
6
7
8
9
10
x
11
15
22
19
17
26
18
18
29
16
# of Yards
of Concrete
Ordered
y
225
250
336
310
325
463
249
267
379
300
Excel Regression Example
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.8433
R Square
0.7111
Adjusted R Square
Standard Error
0.6750
40.5622
Observations
10
ANOVA
df
SS
MS
Regression
1
32402.05
32402.0512
Residual
8
13162.35
1645.2936
Total
9
45564.40
Coefficients
Standard Error
t Stat
F
19.6938
P-value
Significance F
0.0022
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 Example
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
0.8433
0.7111
0.6750
40.5622
10
ANOVA
df
Regression
Residual
Total
Intercept
X Variable 1
1
8
9
Coefficients
94.2052
11.3191
Compare Excel to Manual
Regression
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
Excel Correlation and
Coefficient of Determination
Regression Statistics
Multiple R
0.8433
R Square
0.7111
Compare Excel to Manual
Regression

Manual Results
r = .8344
r² = .7111

Excel Results
r = .8344
r² = .7111
Conclusion



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,

Armstrong, University of Pennsylvania
www.uoguelph.ca/~dsparlin/forecast.htm,

Principles of Forecasting, A Handbook for
Researchers and Practitioners, Edited by J. Scott
Forecasting