METODE PERAMALAN Pertemuan 16 Matakuliah : J1186 - Analisis Kuantitatif Bisnis Tahun : 2009/2010 METODE PERAMALAN Pertemuan 16

Framework Metode Peramalan Regresi Aplikasi Model (Model Regresi Sederhana dan Regresi Berganda) Koefisien Determinasi Interpretasi Hasil dan Analisis Model Bina Nusantara University

d). Linear Trend Line Rumus Umum: Y = a + bx dimana: a = intersep b = kemiringan x = periode waktu Y = ramalan untuk periode Bina Nusantara University

Linear Trend Projection Model b > 0 a Y b < 0 a X Bina Nusantara University

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 Bina Nusantara University

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 = 5.4 + 2.6x Small errors! Bina Nusantara University

Kesalahan Peramalan Kesalahan Peramalan = Ukuran yang digunakan: Mean Absolute Deviation (MAD) Mean Squared Error (MSE) Pilih metode peramalan yang menghasilkan MAD atau MSE terkecil Bina Nusantara University

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 Bina Nusantara University

Linear Regression Model Y a Y b X i =  Error  i Observed value Y a b X =  Regression line Error ^ i i X Bina Nusantara University

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. Bina Nusantara University

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. Bina Nusantara University

Koefisien Korelasi Bina Nusantara University

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) 1 1 0.6 1.00 2 1 1.3 1.00 3 2 2.0 1.00 4 2 2.7 1.90 5 4 3.4 1.99 This slide begins an example of choosing a model. Bina Nusantara University

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 = 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% Bina Nusantara University

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 = 5.05 / 5 = 1.01 MAD = Σ |Error| / n = 3.11 / 5 = 0.622 MAPE = Σ[|Error|/Actual]/n = 1.0525/5 = 0.2105 = 21% Bina Nusantara University

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% 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?) Bina Nusantara University