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Matakuliah
Tahun
: J1186 - Analisis Kuantitatif Bisnis
: 2009/2010
METODE PERAMALAN
Pertemuan 16
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Framework
• Metode Peramalan Regresi
• Aplikasi Model (Model Regresi Sederhana dan Regresi
Berganda)
• Koefisien Determinasi
• Interpretasi Hasil dan Analisis Model
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d). Linear Trend Line
Rumus Umum:
Y = a + bx
dimana:
a = intersep
x = periode waktu
b = kemiringan
Y = ramalan untuk periode
b
N  xy   x y
a 
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N  x 2  ( x) 2
y
N

b x
N
4
Linear Trend Projection Model
Yi  a  bX i
b>0
Y
a
b<0
a
X
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Contoh : Linear Trend Projection
Perio
d
1(x)
2
3
4
5
x=3
Sales
(y)
xy
8
11
13
15
19
y=13.2
8
22
39
60
95
xy=224
224  5  3 13.2
 2.6
2
55  5  3
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b
a
x2
1
4
9
16
25
x2=55
66
15
 2.6  5.4
5
5
6
Lanjutan
Period Sales
(x)
(y)
1
8
2
11
3
13
4
15
5
19
6
M
A
10.67
13.00
15.67
MA
Err.
ES
ES
Err. TP
11
11
4.33 12 3.0 15.8 -0.8
6.00 13.5 5.5 18.4 0.6
16.25
21.0
TP = Trend Projection: Y = 5.4 + 2.6x
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TP
Err.
Small errors!
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Kesalahan Peramalan
Kesalahan Peramalan =
( Dt
Ukuran yang digunakan:
1. Mean Absolute Deviation (MAD)
 Ft )
(D

MAD 
t
Ft )
n
2. Mean Squared Error (MSE)
MSE 
2
(
D
F
)
 t t
n
Pilih metode peramalan yang menghasilkan MAD atau MSE terkecil
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Model Regresi Linear
Shows linear relationship between dependent & explanatory variables
– Example: Sales & advertising (not time)
Y-intercept
^
Y
Dependent
(response) variable
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Slope
= a
b X
i
Independent (explanatory)
variable
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Linear Regression Model
Y
Yi = a
b Xi
Error
Error
Regression line
Y^i = a
Observed value
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b Xi
X
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Interpretasi Koefisien Regresi
• Slope (b):
– Y changes by b units for each 1 unit increase in X.
– If b = +2, then sales (Y) is forecast to increase by 2 for
each 1 unit increase in advertising (X).
• Y-intercept (a):
– Average value of Y when X = 0.
– If a = 4, then average sales (Y) is expected to be 4 when
advertising (X) is 0.
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Koefisien Determinasi
• Answers: ‘How strong is the linear relationship between the
variables?’
• Coefficient of correlation - r
– Measures degree of association; ranges from -1 to +1
• Coefficient of determination - r2
– Amount of variation explained by regression equation.
• Used to evaluate quality of linear relationship.
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Koefisien Korelasi
r
n
n
n
i 
i 
i 
n  x i yi   x i  yi
 n   n   n   n  
n  x i    x i   n  yi    yi  
 i     i 
 i   
 i 
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Selecting Forecasting Model Example
You’re a marketing analyst for Hasbro Toys. You’ve forecast
sales with a linear regression model & exponential
smoothing. Which model do you use?
Year
1
2
3
4
5
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Linear Regression
Actual
Model
Sales
Forecast
1
1
2
2
4
0.6
1.3
2.0
2.7
3.4
Exponential
Smoothing
Forecast (.9)
1.00
1.00
1.00
1.90
1.99
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Linear Regression
Year
Y
F’cast
Error
Error2
|Error|
1
1
0.6
0.4
0.16
0.4
2
1
1.3
-0.3
0.09
0.3
3
2
2.0
0.0
0.00
0.0
4
2
2.7
-0.7
0.49
0.7
5
4
3.4
0.6
0.36
0.6
Total
i
0.0
1.10
2.0
MSE = Σ Error2 / n = 1.10 / 5 = 0.220
MAD = Σ |Error| / n = 2.0 / 5 = 0.400
MAPE = Σ[|Error|/Actual]/n = 1.2/5 = 0.24 = 24%
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Model Eksponential Smoothing
Year
Yi
F’cast
1.00
1.00
1.00
1.90
1.99
Error Error2
1
1
0.0
0.00
2
1
0.0
0.00
3
2
1.0
1.00
4
2
0.1
0.01
5
4
2.01 4.04
Total
0.3
5.05
MSE = Σ Error2 / n = 5.05 / 5 = 1.01
|Error|
0.0
0.0
1.0
0.1
2.01
3.11
MAD = Σ |Error| / n = 3.11 / 5 = 0.622
MAPE = Σ[|Error|/Actual]/n = 1.0525/5 = 0.2105 = 21%
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Mana Yang Terbaik???
Linear Regression :
MSE = Σ Error2 / n = 1.10 / 5 = 0.220
MAD = Σ |Error| / n = 2.0 / 5 = 0.400
MAPE = Σ[|Error|/Actual]/n = 1.2/5 = 0.24 = 24%
Exponential Smoothing:
MSE = Σ Error2 / n = 5.05 / 5 = 1.01
MAD = Σ |Error| / n = 3.11 / 5 = 0.622
MAPE = Σ[|Error|/Actual]/n = 1.0525/5 = 0.2105 = 21%
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