Transcript Forecasting-2 Forecasting -2.2 Regression Analysis Ardavan Asef-Vaziri Chapter 7 Demand Forecasting in a Supply Chain Ardavan Asef-Vaziri 6/4/2009 Exponential Smoothing 1

Forecasting-2
Forecasting -2.2
Regression Analysis
Ardavan Asef-Vaziri
Chapter 7
Demand Forecasting
in a Supply Chain
Ardavan Asef-Vaziri
6/4/2009
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Associative (Causal) Forecasting -Regression
The primary method for associative forecasting is
Regression Analysis.
The relationship between a dependent variable and one
or more independent variables.
The independent variables are also referred to as
predictor variables.
We only discuss linear regression between two
variables.
We consider the relationship between the dependent
variable (demand) and the independent variable
(time).
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Regression Method
Ft  b0  b1t
Computed
relationship
50
40
30
20
10
0
0
5
10
15
20
25
Least Squares Line minimizes sum of squared deviations
around the line
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0.92 Correlation Coefficient (-1 and +1) we want it close to +1
0.84 Coefficient of Determination: Large (0 to 1) we want close to 1
0.82 To know if the line had + or - slope we look at X Varaible 1 or Multiple R
4.07 Standard Error is the standard deviation of our forecast
12 Something similar to 1.25MAD
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
ANOVA
SS
df
1
10
11
Regression
Residual
Total
Intercept
X Variable 1
Ardavan Asef-Vaziri
873.0
165.9
1038.9
MS
873.0
16.6
F
Significance F
52.61 2.74837E-05
Upper 95%
Lower 95%
P-value
t Stat
Coefficients Standard Error
2.686944916 1.883208505 0.089052275 -0.926808842 11.04696388
5.06
0.219632305 7.253137252 2.74837E-05 1.103651983 2.082394529
1.59
We want is less that .05
Y=5.06+1.59t
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Regression: Chart the Data
Period
1
2
3
4
5
6
7
8
9
10
Demand
117
126
210
222
262
310
278
338
379
388
Demand
450
400
350
300
250
Demand
200
150
100
50
0
0
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2
4
6
8
10
12
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Regression: The Same as Solver but This Time Data Analysis
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Data/Data Analysis/ Regression
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6/4/2009
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Regression: Tools / Data Analysis / Regression
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Regression Output
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
0.98
0.95
0.95
22.21
10
Correlation Coefficient +↑. Close to + 1
Coefficient of Determination ↑ Close to 1
Standard Deviation of Forecast ↓
If the first period is 1, next period is 10+1 = 11
ANOVA
Regression
Residual
Total
df
1
8
9
SS
77771
3945
81716
MS
77771
493
F
158
Significance F
1.51524E-06
Intercept
X Variable 1
Coefficients
94.13
30.70
Standard Error
15.17
2.44
t Stat
6.21
12.56
P-value
0.000258
0.000002
Lower 95%
59.15
25.07
Upper 95%
129.12
36.34
P-value ↓ less than 0.05
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Regression Output
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
0.98
0.95
0.95
22.21
10
ANOVA
Regression
Residual
Total
df
1
8
9
SS
77771
3945
81716
MS
77771
493
F
158
Significance F
1.51524E-06
Intercept
X Variable 1
Coefficients
94.13
30.70
Standard Error
15.17
2.44
t Stat
6.21
12.56
P-value
0.000258
0.000002
Lower 95%
59.15
25.07
Upper 95%
129.12
36.34
Ft = 94.13 +30.71t
What is your forecast for the next period.
F11 = 94.13 +30.71(11) = 431.7
Mean Forecast = 431.7, Standard Deviation of Forecast = 22.21
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