regresi time series
TRANSCRIPT
![Page 1: regresi time series](https://reader036.vdocuments.us/reader036/viewer/2022081416/5571fa374979599169919934/html5/thumbnails/1.jpg)
Metode Peramalan
1. Pendahuluan2. Naïve Models dan Moving Average Methods 3. Exponential Smoothing Methods4. Regresi dan Trend Analysis5. Regresi Berganda dan Time Series Regresi6. Metode Dekomposisi7. Model ARIMA Box-Jenkins8. Studi Kasus : Model ARIMAX (Analisis Intervensi,
Fungsi Transfer dan Neural Networks)
![Page 2: regresi time series](https://reader036.vdocuments.us/reader036/viewer/2022081416/5571fa374979599169919934/html5/thumbnails/2.jpg)
Kaitan Pola Data dan Metode Regresi (Trend Analysis)
Time Series Patterns
Stationer Trend Effect Seasonal Effect Cyclic Effect
Regresi untuk Trend Linear
Regresi untuk Seasonal Data
Regresi untuk Cyclic Effect
![Page 3: regresi time series](https://reader036.vdocuments.us/reader036/viewer/2022081416/5571fa374979599169919934/html5/thumbnails/3.jpg)
Problem 1: Regresi Linear Sederhana
Harga Produk
Biaya Iklan, Jumlah Outlet,
Area Pema-saran dan faktor lain yang
dapat dikontrol dalam kondisi
TETAP
Sales Produk
Bagaimana pengaruh harga terhadap sales suatu produk ? Dapatkah meramal sales suatu produk berdasarkan harganya ?
Harga Pesaing, Selera Konsumen, Kondisi Ekonomi Nasional (inflasi dll) dan faktor lain yang tidak dapat dikontrol
dalam kondisi TETAP
Process (Model Regresi)Input
(X)Output
(Y)
Z1, Z2, …, Zq
F1, F2, …, Fq
Uncontrollable Factors
Controllable Factors
![Page 4: regresi time series](https://reader036.vdocuments.us/reader036/viewer/2022081416/5571fa374979599169919934/html5/thumbnails/4.jpg)
Tahap-tahap dalam Analisis Regresi
1. Plot data identifikasi bentuk hubungan secara grafik
2. Koefisien Korelasi identifikasi hubungan linear dengan suatu angka
3. Pendugaan (estimasi) model regresi4. Evaluasi (diagnostic check) kesesuain model regresi5. Prediksi (forecast) suatu nilai Y pada suatu X
tertentu
n
ii
n
ii
n
iii
xy
yyxx
yyxx
r
1
2
1
2
1
)()(
))((
, -1 rxy 1
![Page 5: regresi time series](https://reader036.vdocuments.us/reader036/viewer/2022081416/5571fa374979599169919934/html5/thumbnails/5.jpg)
Problem 1: Data hasil pengamatan … (continued)
MingguSales
(ribu unit)Harga
(ribu rupiah)
1. 10 1.3
2. 6 2.0
3. 5 1.7
4. 12 1.5
5. 10 1.6
6. 15 1.2
7. 5 1.6
8. 12 1.4
9. 17 1.0
10. 20 1.1
Pengamatan dilakukan dengan mengambil secara random data 10
minggu penjualan
Plot antara Harga dan Sales
![Page 6: regresi time series](https://reader036.vdocuments.us/reader036/viewer/2022081416/5571fa374979599169919934/html5/thumbnails/6.jpg)
Problem 1: MINITAB output … (continued)
MTB > Correlation 'Harga' 'Sales'.
Pearson correlation of Harga and Sales = -0.863P-Value = 0.001
MTB > Regress 'Sales' 1 'Harga'
The regression equation isSales = 32.1 – 14.5 Harga
Predictor Coef SE Coef T PConstant 32.136 4.409 7.29 0.000Harga -14.539 3.002 -4.84 0.001
S = 2.725 R-Sq = 74.6% R-Sq(adj) = 71.4%
Analysis of Variance
Source DF SS MS F PRegression 1 174.18 174.18 23.45 0.001Residual Error 8 59.42 7.43Total 9 233.60
![Page 7: regresi time series](https://reader036.vdocuments.us/reader036/viewer/2022081416/5571fa374979599169919934/html5/thumbnails/7.jpg)
Problem 1: MINITAB output … (continued)
Plot data, garis regresi dan ramalan Sales dari
Harga
![Page 8: regresi time series](https://reader036.vdocuments.us/reader036/viewer/2022081416/5571fa374979599169919934/html5/thumbnails/8.jpg)
Problem 2: Regresi Linear Berganda
Harga Produ
k
Jumlah Outlet, Area Pemasaran dan faktor faktor lain yang dapat dikontrol dalam kondisi TETAP
Sales Produk
Bagaimana pengaruh harga dan biaya iklan terhadap sales suatu produk ? Lebih baikkah ketepatan ramalannya ?
Harga Pesaing, Selera Konsumen, Kondisi Ekonomi Nasional (inflasi dll) dan faktor lain yang tidak dapat dikontrol
dalam kondisi TETAP
Process (Model Regresi)Input
(X)Output
(Y)
Z1, Z2, …, Zq
F1, F2, …, Fq
Uncontrollable Factors
Controllable Factors
Biaya Iklan
![Page 9: regresi time series](https://reader036.vdocuments.us/reader036/viewer/2022081416/5571fa374979599169919934/html5/thumbnails/9.jpg)
Problem 2: Data hasil pengamatan … (continued)
MingguSales (ribu unit)
Harga (ribu rupiah)
Biaya Iklan (juta rupiah)
1. 10 1.3 9
2. 6 2.0 7
3. 5 1.7 5
4. 12 1.5 14
5. 10 1.6 15
6. 15 1.2 12
7. 5 1.6 6
8. 12 1.4 10
9. 17 1.0 15
10. 20 1.1 21
Pengamatan dilakukan dengan mengambil secara random data 10
minggu penjualanPlot antara Harga, Iklan dg
Sales
![Page 10: regresi time series](https://reader036.vdocuments.us/reader036/viewer/2022081416/5571fa374979599169919934/html5/thumbnails/10.jpg)
Problem 2: MINITAB output … (continued)
MTB > Correlation 'Sales'-'Iklan'.
Correlations: Sales, Harga, Iklan
Sales HargaHarga -0.863 0.001
Iklan 0.891 -0.654 0.001 0.040
Cell Contents: Pearson correlation
P-Value
MTB > Regress 'Sales' 2 'Harga' 'Iklan'
The regression equation isSales = 16.4 - 8.25 Harga + 0.585 Iklan
Predictor Coef SE Coef T PConstant 16.406 4.343 3.78 0.007Harga -8.248 2.196 -3.76 0.007Iklan 0.5851 0.1337 4.38 0.003
S = 1.507 R-Sq = 93.2% R-Sq(adj) = 91.2%
Analysis of Variance
Source DF SS MS F PRegression 2 217.70 108.85 47.92 0.000Residual 7 15.90 2.27Total 9 233.60
![Page 11: regresi time series](https://reader036.vdocuments.us/reader036/viewer/2022081416/5571fa374979599169919934/html5/thumbnails/11.jpg)
Problem 2: MINITAB output … (continued)
R2 = 74.6%
R2 = 79.5%
R2 = 93.2%
![Page 12: regresi time series](https://reader036.vdocuments.us/reader036/viewer/2022081416/5571fa374979599169919934/html5/thumbnails/12.jpg)
Problem 3: Regresi dengan Variabel Dummy
Nilai TES
BAKAT pekerja
Usia, Pendidikan, Ruang kerja,
Mesin dan faktor faktor lain yang dapat dikontrol dalam kondisi
TETAP
Produktifitas pekerja
Bagaimana pengaruh TES BAKAT dan GENDER thd produktifitas ? Dapatkah produktifitas pekerja diramal dari tes bakat dan jenis kelaminnya?
Emosi (suasana hati) pekerja dan faktor lain yang tidak dapat dikontrol dalam
kondisi TETAP
Process (Model Regresi)Input
(X)Output
(Y)
Z1, Z2, …, Zq
F1, F2, …, Fq
Uncontrollable Factors
Controllable Factors
JENIS KELAMIN pekerja
![Page 13: regresi time series](https://reader036.vdocuments.us/reader036/viewer/2022081416/5571fa374979599169919934/html5/thumbnails/13.jpg)
Problem 2: Data hasil pengamatan … (continued)
Pengamatan dilakukan dengan mengambil secara random data 15
pekerja
Plot antara Tes Bakat dan Produk-tifitas, antara pekerja PRIA dan
WANITA
![Page 14: regresi time series](https://reader036.vdocuments.us/reader036/viewer/2022081416/5571fa374979599169919934/html5/thumbnails/14.jpg)
Problem 3: MINITAB output … (continued)
MTB > Correlation 'Tes Bakat' 'Dummy' 'Produktifitas'.
Tes Bakat DummyProduktifitas 0.876 -0.021 0.000 0.940
MTB > Regress 'Produktifitas' 2 'Tes Bakat' 'Dummy'
The regression equation isProduktifitas = - 4.14 + 0.120 Tes Bakat + 2.18 Dummy
Predictor Coef SE Coef T PConstant -4.1372 0.8936 -4.63 0.001Tes Bakat 0.12041 0.01015 11.86 0.000Dummy 2.1807 0.4503 4.84 0.000
S = 0.7863 R-Sq = 92.1% R-Sq(adj) = 90.8%
![Page 15: regresi time series](https://reader036.vdocuments.us/reader036/viewer/2022081416/5571fa374979599169919934/html5/thumbnails/15.jpg)
Problem 3: MINITAB output … (continued)
![Page 16: regresi time series](https://reader036.vdocuments.us/reader036/viewer/2022081416/5571fa374979599169919934/html5/thumbnails/16.jpg)
Problem 3: Plot hasil regresi … (continued)
WANITA
PRIA
![Page 17: regresi time series](https://reader036.vdocuments.us/reader036/viewer/2022081416/5571fa374979599169919934/html5/thumbnails/17.jpg)
Model-model Time Series Regression
1. Model Regresi untuk LINEAR TREND Yt = a + b.t + error t = 1, 2, … (dummy waktu)
2. Model Regresi untuk Data SEASONAL (variasi konstan)
Yt = a + b1 D1 + … + bS-1 DS-1 + error
dengan : D1, D2, …, DS-1 adalah dummy waktu dalam satu periode seasonal.
3. Model Regresi untuk Data dengan LINEAR TREND dan SEASONAL (variasi konstan)
Yt = a + b.t + c1 D1 + … + cS-1 DS-1 + error
Gabungan model 1 dan 2.
![Page 18: regresi time series](https://reader036.vdocuments.us/reader036/viewer/2022081416/5571fa374979599169919934/html5/thumbnails/18.jpg)
Problem 4: Regresi Trend Linear (Video Store case)
Time Series Plot data Sales
![Page 19: regresi time series](https://reader036.vdocuments.us/reader036/viewer/2022081416/5571fa374979599169919934/html5/thumbnails/19.jpg)
Problem 4: Hasil Regresi Trend dg MINITAB … (continued)
![Page 20: regresi time series](https://reader036.vdocuments.us/reader036/viewer/2022081416/5571fa374979599169919934/html5/thumbnails/20.jpg)
Problem 4: Hasil Regresi Trend dg MINITAB … (continued)
![Page 21: regresi time series](https://reader036.vdocuments.us/reader036/viewer/2022081416/5571fa374979599169919934/html5/thumbnails/21.jpg)
Problem 5: Regresi Data Seasonal … (Data Electrical Usage)
Time Series Plot (Data seasonal)
![Page 22: regresi time series](https://reader036.vdocuments.us/reader036/viewer/2022081416/5571fa374979599169919934/html5/thumbnails/22.jpg)
Problem 5: Hasil regresi dengan MINITAB …
MTB > Regress 'Kilowatts' 3 'Kuartal-1'-'Kuartal-3'
The regression equation isKilowatts = 722 + 281 Kuartal.1 - 97.4 Kuartal.2 - 202 Kuartal.3
Predictor Coef SE Coef T PConstant 721.60 13.79 52.32 0.000Kuartal.1 281.20 19.51 14.42 0.000Kuartal.2 -97.40 19.51 -4.99 0.000Kuartal.3 -202.20 19.51 -10.37 0.000
S = 30.84 R-Sq = 97.7% R-Sq(adj) = 97.3%
Analysis of VarianceSource DF SS MS F PRegression 3 646802 215601 226.65 0.000Residual Error 16 15220 951Total 19 662022
![Page 23: regresi time series](https://reader036.vdocuments.us/reader036/viewer/2022081416/5571fa374979599169919934/html5/thumbnails/23.jpg)
Problem 5: Struktur dummy dan hasil regresinya …
Dummy Variable
![Page 24: regresi time series](https://reader036.vdocuments.us/reader036/viewer/2022081416/5571fa374979599169919934/html5/thumbnails/24.jpg)
Problem 5: Hasil regresi dengan MINITAB …
Time Series Plot (Data dan Ramalannya)
Forecast
![Page 25: regresi time series](https://reader036.vdocuments.us/reader036/viewer/2022081416/5571fa374979599169919934/html5/thumbnails/25.jpg)
Problem 6: Regresi Data Trend Linear dan Seasonal …
Time Series Plot (Data trend dan
seasonal)
![Page 26: regresi time series](https://reader036.vdocuments.us/reader036/viewer/2022081416/5571fa374979599169919934/html5/thumbnails/26.jpg)
Problem 6: Hasil regresi dengan MINITAB …
Dummy Variable
![Page 27: regresi time series](https://reader036.vdocuments.us/reader036/viewer/2022081416/5571fa374979599169919934/html5/thumbnails/27.jpg)
Problem 6: Hasil regresi dengan MINITAB …
MTB > Regress 'Sales' 4 't' 'Kuartal.1'-'Kuartal.3'
The regression equation isSales = 413 + 19.7 t + 130 Kuartal.1 - 108 Kuartal.2 - 228 Kuartal.3
16 cases used 4 cases contain missing values
Predictor Coef SE Coef T PConstant 412.81 26.99 15.30 0.000t 19.719 2.012 9.80 0.000Kuartal.1 130.41 26.15 4.99 0.000Kuartal.2 -108.06 25.76 -4.19 0.001Kuartal.3 -227.78 25.52 -8.92 0.000
S = 35.98 R-Sq = 96.3% R-Sq(adj) = 95.0%
Analysis of Variance
Source DF SS MS F PRegression 4 371967 92992 71.82 0.000Residual Error 11 14243 1295Total 15 386211
![Page 28: regresi time series](https://reader036.vdocuments.us/reader036/viewer/2022081416/5571fa374979599169919934/html5/thumbnails/28.jpg)
Problem 6: Hasil regresi dengan MINITAB …
Time Series Plot (Data dan Ramalannya)
Forecast
![Page 29: regresi time series](https://reader036.vdocuments.us/reader036/viewer/2022081416/5571fa374979599169919934/html5/thumbnails/29.jpg)
Perbandingan ketepatan ramalan antar metode …
ModelKriteria kesalahan
ramalan
MSE MAD MAPE
Double M.A.
66.6963
6.68889
0.9557
Holt’s Method
28.7083
4.4236 0.6382
Regresi Trend
21.6829
3.73048
0.5382Holt’s Method :
Alpha (level): 0.202284Gamma (trend):
0.234940
Kasus Sales Video Store
ModelKriteria kesalahan
ramalan
MSE MAD MAPE
Winter’s Method
4372.69
52.29 9.67
Regresi Trend &
Seasonal
890.215
23.2969
4.3122
Kasus Sales Data Kuartalan
Winter’s Method :Alpha (level): 0.4Gamma (trend): 0.1Delta (seasonal):
0.3