2. METODE PERAMALAN Pertemuan 16
Matakuliah : J Analisis Kuantitatif Bisnis
Tahun : 2009/2010
METODE PERAMALAN Pertemuan 16

3. Framework Metode Peramalan Regresi
Aplikasi Model (Model Regresi Sederhana dan Regresi Berganda)
Koefisien Determinasi
Interpretasi Hasil dan Analisis Model
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4. d). Linear Trend Line Rumus Umum: Y = a + bx dimana:
a = intersep b = kemiringan
x = periode waktu Y = ramalan untuk periode
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5. Linear Trend Projection Model
b > 0 a Y
b < 0 a X
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6. Contoh : Linear Trend Projection
Period
(x) 1 8 2 11 3 13 4 15 5 19
Sales
(y) xy 60 95 22 39
xy=224 x2 9 16 25
x2=55
x=3
y=13.2
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7. Lanjutan Period (x) MA ES 1 2 3 4 5 8 11 13 15 19 Err. 6 10.67 13.00
15.67 12
13.5
16.25
4.33
6.00
Sales
(y)
3.0
5.5 TP
21.0
18.4
15.8
-0.8
0.6
TP = Trend Projection: Y = x
Small errors!
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8. Kesalahan Peramalan Kesalahan Peramalan = Ukuran yang digunakan:
Mean Absolute Deviation (MAD)
Mean Squared Error (MSE)
Pilih metode peramalan yang menghasilkan MAD atau MSE terkecil
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9. Model Regresi Linear
Shows linear relationship between dependent & explanatory variables
Example: Sales & advertising (not time)
Y-intercept
Slope ^ Y = a  b X i i
Dependent (response) variable
Independent (explanatory) variable
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10. Linear Regression ModelY a Y b X i = 
Error  i
Observed value Y a b X = 
Regression line
Error ^ i i X
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11. 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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12. 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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13. Koefisien Korelasi
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14. 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?
Linear Regression Exponential
Actual Model Smoothing
Year Sales Forecast Forecast (.9)
This slide begins an example of choosing a model.
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15. Linear Regression 1.10 Year Y i F’cast 1 0.6 0.4 0.16 2 1.3 -0.3 0.09
2.0
0.0
0.00 4
2.7
-0.7
0.49
0.7 5
3.4
0.36
Total
Error
Error2
|Error|
1.10
MSE = Σ Error2 / n = / 5 =
MAD = Σ |Error| / n = / 5 =
MAPE = Σ[|Error|/Actual]/n = 1.2/5 = = 24%
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16. Model Eksponential Smoothing
Year Y i
F’cast 1
1.00
0.0
0.00 2 3
1.0 4
1.90
0.1
0.01 5
2.01
4.04
Total
0.3
5.05
3.11
Error
Error2
|Error|
1.99
MSE = Σ Error2 / n = / 5 =
MAD = Σ |Error| / n = / 5 =
MAPE = Σ[|Error|/Actual]/n = /5 = = 21%
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17. Mana Yang Terbaik??? Linear Regression :
MSE = Σ Error2 / n = / 5 =
MAD = Σ |Error| / n = / 5 =
MAPE = Σ[|Error|/Actual]/n = 1.2/5 = = 24%
Exponential Smoothing:
MSE = Σ Error2 / n = / 5 =
MAD = Σ |Error| / n = / 5 =
MAPE = Σ[|Error|/Actual]/n = /5 = = 21%
This slide presents the result of the calculations of MSE and MAD for the Linear and Exponential Smoothing models.
Students should be asked to choose the “better” model.
Students should also be asked to consider the differences between the values calculated for the error measures for a given model, and between the two models. Do these differences tell us more than simply that one model is preferable to the other? (For example, is the exponential smoothing model 22 times better than the linear model?)
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