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Copyright 2006 John Wiley & Sons, Inc. Beni Asllani University of Tennessee at Chattanooga Forecasting Operations Management - 5 th Edition Chapter 11 Roberta Russell & Bernard W. Taylor, III

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Copyright 2006 John Wiley & Sons, Inc.11-2 Lecture Outline Strategic Role of Forecasting in Supply Chain Management and TQM Components of Forecasting Demand Time Series Methods Forecast Accuracy Regression Methods

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Copyright 2006 John Wiley & Sons, Inc.11-3 Forecasting Predicting the Future Qualitative forecast methods subjective subjective Quantitative forecast methods based on mathematical formulas based on mathematical formulas

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Copyright 2006 John Wiley & Sons, Inc.11-4 Forecasting and Supply Chain Management Accurate forecasting determines how much inventory a company must keep at various points along its supply chain Continuous replenishment supplier and customer share continuously updated data supplier and customer share continuously updated data typically managed by the supplier typically managed by the supplier reduces inventory for the company reduces inventory for the company speeds customer delivery speeds customer delivery Variations of continuous replenishment quick response quick response JIT (just-in-time) JIT (just-in-time) VMI (vendor-managed inventory) VMI (vendor-managed inventory) stockless inventory stockless inventory

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Copyright 2006 John Wiley & Sons, Inc.11-5 Forecasting and TQM Accurate forecasting customer demand is a key to providing good quality service Continuous replenishment and JIT complement TQM eliminates the need for buffer inventory, which, in turn, reduces both waste and inventory costs, a primary goal of TQM smoothes process flow with no defective items meets expectations about on-time delivery, which is perceived as good-quality service

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Copyright 2006 John Wiley & Sons, Inc.11-6 Types of Forecasting Methods Depend on time frame time frame demand behavior demand behavior causes of behavior causes of behavior

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Copyright 2006 John Wiley & Sons, Inc.11-7 Time Frame Indicates how far into the future is forecast Short- to mid-range forecast Short- to mid-range forecast typically encompasses the immediate future typically encompasses the immediate future daily up to two years daily up to two years Long-range forecast Long-range forecast usually encompasses a period of time longer than two years usually encompasses a period of time longer than two years

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Copyright 2006 John Wiley & Sons, Inc.11-8 Demand Behavior Trend a gradual, long-term up or down movement of demand a gradual, long-term up or down movement of demand Random variations movements in demand that do not follow a pattern movements in demand that do not follow a pattern Cycle an up-and-down repetitive movement in demand an up-and-down repetitive movement in demand Seasonal pattern an up-and-down repetitive movement in demand occurring periodically an up-and-down repetitive movement in demand occurring periodically

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Copyright 2006 John Wiley & Sons, Inc.11-9 Time (a) Trend Time (d) Trend with seasonal pattern Time (c) Seasonal pattern Time (b) Cycle Demand Demand Demand Demand Random movement Forms of Forecast Movement

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Copyright 2006 John Wiley & Sons, Inc.11-10 Forecasting Methods Qualitative use management judgment, expertise, and opinion to predict future demand use management judgment, expertise, and opinion to predict future demand Time series statistical techniques that use historical demand data to predict future demand statistical techniques that use historical demand data to predict future demand Regression methods attempt to develop a mathematical relationship between demand and factors that cause its behavior attempt to develop a mathematical relationship between demand and factors that cause its behavior

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Copyright 2006 John Wiley & Sons, Inc.11-11 Qualitative Methods Management, marketing, purchasing, and engineering are sources for internal qualitative forecasts Delphi method involves soliciting forecasts about technological advances from experts

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Copyright 2006 John Wiley & Sons, Inc.11-12 Forecasting Process 6. Check forecast accuracy with one or more measures 4. Select a forecast model that seems appropriate for data 5. Develop/compute forecast for period of historical data 8a. Forecast over planning horizon 9. Adjust forecast based on additional qualitative information and insight 10. Monitor results and measure forecast accuracy 8b. Select new forecast model or adjust parameters of existing model 7. Is accuracy of forecast acceptable? 1. Identify the purpose of forecast 3. Plot data and identify patterns 2. Collect historical data No Yes

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Copyright 2006 John Wiley & Sons, Inc.11-13 Time Series Assume that what has occurred in the past will continue to occur in the future Relate the forecast to only one factor - time Include moving average exponential smoothing linear trend line

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Copyright 2006 John Wiley & Sons, Inc.11-14 Moving Average Naive forecast demand the current period is used as next period’s forecast demand the current period is used as next period’s forecast Simple moving average stable demand with no pronounced behavioral patterns stable demand with no pronounced behavioral patterns Weighted moving average weights are assigned to most recent data

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Copyright 2006 John Wiley & Sons, Inc.11-15 Moving Average: Naïve Approach Jan120 Feb90 Mar100 Apr75 May110 June50 July75 Aug130 Sept110 Oct90 ORDERS MONTHPER MONTH -1209010075110507513011090 Nov - FORECAST

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Copyright 2006 John Wiley & Sons, Inc.11-16 Simple Moving Average MA n = n i = 1 DiDiDiDi n where n =number of periods in the moving average D i =demand in period i

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Copyright 2006 John Wiley & Sons, Inc.11-17 3-month Simple Moving Average Jan120 Feb90 Mar100 Apr75 May110 June50 July75 Aug130 Sept110 Oct90 Nov- ORDERS MONTHPER MONTH MA 3 = 3 i = 1 DiDiDiDi 3 = 90 + 110 + 130 3 = 110 orders for Nov –––103.388.395.078.378.385.0105.0110.0MOVINGAVERAGE

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Copyright 2006 John Wiley & Sons, Inc.11-18 5-month Simple Moving Average Jan120 Feb90 Mar100 Apr75 May110 June50 July75 Aug130 Sept110 Oct90 Nov- ORDERS MONTHPER MONTH MA 5 = 5 i = 1 DiDiDiDi 5 = 90 + 110 + 130+75+50 5 = 91 orders for Nov –––––99.085.082.088.095.091.0MOVINGAVERAGE

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Copyright 2006 John Wiley & Sons, Inc.11-19 Smoothing Effects 150 150 – 125 125 – 100 100 – 75 75 – 50 50 – 25 25 – 0 0 – ||||||||||| JanFebMarAprMayJuneJulyAugSeptOctNov Actual Orders Month 5-month 3-month

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Copyright 2006 John Wiley & Sons, Inc.11-20 Weighted Moving Average WMA n = i = 1 Wi DiWi DiWi DiWi Di where W i = the weight for period i, between 0 and 100 percent W i = 1.00 Adjusts moving average method to more closely reflect data fluctuations

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Copyright 2006 John Wiley & Sons, Inc.11-21 Weighted Moving Average Example MONTH WEIGHT DATA August 17%130 September 33%110 October 50%90 WMA 3 = 3 i = 1 Wi DiWi DiWi DiWi Di = (0.50)(90) + (0.33)(110) + (0.17)(130) = 103.4 orders November Forecast

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Copyright 2006 John Wiley & Sons, Inc.11-22 Averaging method Weights most recent data more strongly Reacts more to recent changes Widely used, accurate method Exponential Smoothing

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Copyright 2006 John Wiley & Sons, Inc.11-23 F t +1 = D t + (1 - )F t where: F t +1 =forecast for next period D t =actual demand for present period F t =previously determined forecast for present period =weighting factor, smoothing constant Exponential Smoothing (cont.)

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Copyright 2006 John Wiley & Sons, Inc.11-24 Effect of Smoothing Constant 0.0 1.0 If = 0.20, then F t +1 = 0.20 D t + 0.80 F t If = 0, then F t +1 = 0 D t + 1 F t 0 = F t Forecast does not reflect recent data If = 1, then F t +1 = 1 D t + 0 F t = D t Forecast based only on most recent data

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Copyright 2006 John Wiley & Sons, Inc.11-25 F 2 = D 1 + (1 - )F 1 = (0.30)(37) + (0.70)(37) = 37 F 3 = D 2 + (1 - )F 2 = (0.30)(40) + (0.70)(37) = 37.9 F 13 = D 12 + (1 - )F 12 = (0.30)(54) + (0.70)(50.84) = 51.79 Exponential Smoothing (α=0.30) PERIODMONTHDEMAND 1Jan37 2Feb40 3Mar41 4Apr37 5May 45 6Jun50 7Jul 43 8Aug 47 9Sep 56 10Oct52 11Nov55 12Dec 54

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Copyright 2006 John Wiley & Sons, Inc.11-26 FORECAST, F t + 1 PERIODMONTHDEMAND( = 0.3)( = 0.5) 1Jan37–– 2Feb4037.0037.00 3Mar4137.9038.50 4Apr3738.8339.75 5May 4538.2838.37 6Jun5040.2941.68 7Jul 4343.2045.84 8Aug 4743.1444.42 9Sep 5644.3045.71 10Oct5247.8150.85 11Nov5549.0651.42 12Dec 5450.8453.21 13Jan–51.7953.61 Exponential Smoothing (cont.)

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Copyright 2006 John Wiley & Sons, Inc.11-27 70 70 – 60 60 – 50 50 – 40 40 – 30 30 – 20 20 – 10 10 – 0 0 – ||||||||||||| 12345678910111213 Actual Orders Month Exponential Smoothing (cont.) = 0.50 = 0.30

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Copyright 2006 John Wiley & Sons, Inc.11-28 AF t +1 = F t +1 + T t +1 where T = an exponentially smoothed trend factor T t +1 = (F t +1 - F t ) + (1 - ) T t where T t = the last period trend factor = a smoothing constant for trend Adjusted Exponential Smoothing

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Copyright 2006 John Wiley & Sons, Inc.11-29 Adjusted Exponential Smoothing (β=0.30) PERIODMONTHDEMAND 1Jan37 2Feb40 3Mar41 4Apr37 5May 45 6Jun50 7Jul 43 8Aug 47 9Sep 56 10Oct52 11Nov55 12Dec 54 T 3 = (F 3 - F 2 ) + (1 - ) T 2 = (0.30)(38.5 - 37.0) + (0.70)(0) = 0.45 AF 3 = F 3 + T 3 = 38.5 + 0.45 = 38.95 T 13 = (F 13 - F 12 ) + (1 - ) T 12 = (0.30)(53.61 - 53.21) + (0.70)(1.77) = 1.36 AF 13 = F 13 + T 13 = 53.61 + 1.36 = 54.96

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Copyright 2006 John Wiley & Sons, Inc.11-30 Adjusted Exponential Smoothing: Example FORECASTTRENDADJUSTED PERIODMONTHDEMANDF t +1 T t +1 FORECAST AF t +1 1Jan3737.00–– 2Feb4037.000.0037.00 3Mar4138.500.4538.95 4Apr3739.750.6940.44 5May 4538.370.0738.44 6Jun5038.370.0738.44 7Jul 4345.841.9747.82 8Aug 4744.420.9545.37 9Sep 5645.711.0546.76 10Oct5250.852.2858.13 11Nov5551.421.7653.19 12Dec 5453.211.7754.98 13Jan–53.611.3654.96

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Copyright 2006 John Wiley & Sons, Inc.11-31 Adjusted Exponential Smoothing Forecasts 70 70 – 60 60 – 50 50 – 40 40 – 30 30 – 20 20 – 10 10 – 0 0 – ||||||||||||| 12345678910111213 Actual Demand Period Forecast ( = 0.50) Adjusted forecast ( = 0.30)

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Copyright 2006 John Wiley & Sons, Inc.11-32 y = a + bx where a = intercept b = slope of the line x = time period y = forecast for demand for period x Linear Trend Line b = a = y - b x where n =number of periods x == mean of the x values y == mean of the y values xy - nxy x 2 - nx 2 x n y n

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Copyright 2006 John Wiley & Sons, Inc.11-33 Least Squares Example x (PERIOD) y (DEMAND) xyx 2 173371 240804 3411239 43714816 54522525 65030036 74330149 84737664 95650481 1052520100 1155605121 1254648144 785573867650

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Copyright 2006 John Wiley & Sons, Inc.11-34 x = = 6.5 y = = 46.42 b = = =1.72 a = y - bx = 46.42 - (1.72)(6.5) = 35.2 3867 - (12)(6.5)(46.42) 650 - 12(6.5) 2 xy - nxy x 2 - nx 2 78 12 557 12 Least Squares Example (cont.)

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Copyright 2006 John Wiley & Sons, Inc.11-35 Linear trend line y = 35.2 + 1.72 x Forecast for period 13 y = 35.2 + 1.72(13)= 57.56 units 70 70 – 60 60 – 50 50 – 40 40 – 30 30 – 20 20 – 10 10 – 0 0 – ||||||||||||| 12345678910111213 Actual Demand Period Linear trend line

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Copyright 2006 John Wiley & Sons, Inc.11-36 Seasonal Adjustments Repetitive increase/ decrease in demand Use seasonal factor to adjust forecast Seasonal factor = S i = DiDiDDDiDiDD

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Copyright 2006 John Wiley & Sons, Inc.11-37 Seasonal Adjustment (cont.) 2002 12.68.66.317.545.0 2003 14.110.37.518.250.1 2004 15.310.68.119.653.6 Total 42.029.521.955.3148.7 DEMAND (1000’S PER QUARTER) YEAR1234Total S 1 = = = 0.28 D1D1DDD1D1DD 42.0148.7 S 2 = = = 0.20 D2D2DDD2D2DD 29.5148.7 S 4 = = = 0.37 D4D4DDD4D4DD 55.3148.7 S 3 = = = 0.15 D3D3DDD3D3DD 21.9148.7

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Copyright 2006 John Wiley & Sons, Inc.11-38 Seasonal Adjustment (cont.) SF 1 = (S 1 ) (F 5 ) = (0.28)(58.17) = 16.28 SF 2 = (S 2 ) (F 5 ) = (0.20)(58.17) = 11.63 SF 3 = (S 3 ) (F 5 ) = (0.15)(58.17) = 8.73 SF 4 = (S 4 ) (F 5 ) = (0.37)(58.17) = 21.53 y = 40.97 + 4.30 x = 40.97 + 4.30(4) = 58.17 For 2005

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Copyright 2006 John Wiley & Sons, Inc.11-39 Forecast Accuracy Forecast error difference between forecast and actual demand MAD mean absolute deviation MAPD mean absolute percent deviation Cumulative error Average error or bias

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Copyright 2006 John Wiley & Sons, Inc.11-40 Mean Absolute Deviation (MAD) where t = period number t = period number D t = demand in period t D t = demand in period t F t = forecast for period t F t = forecast for period t n = total number of periods n = total number of periods = absolute value D t - F t n MAD =

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Copyright 2006 John Wiley & Sons, Inc.11-41 MAD Example 13737.00–– 24037.003.003.00 34137.903.103.10 43738.83-1.831.83 54538.286.726.72 65040.299.699.69 74343.20-0.200.20 84743.143.863.86 95644.3011.7011.70 105247.814.194.19 115549.065.945.94 125450.843.153.15 55749.3153.39 PERIODDEMAND, D t F t ( =0.3)(D t - F t ) |D t - F t | D t - F t n MAD= = = 4.85 53.39 11

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Copyright 2006 John Wiley & Sons, Inc.11-42 Other Accuracy Measures Mean absolute percent deviation (MAPD) MAPD = |D t - F t | D t Cumulative error E = e t Average error E = etetnnetetnnn

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Copyright 2006 John Wiley & Sons, Inc.11-43 Comparison of Forecasts FORECASTMADMAPDE(E) Exponential smoothing ( = 0.30)4.859.6%49.314.48 Exponential smoothing ( = 0.50)4.048.5%33.213.02 Adjusted exponential smoothing3.817.5%21.141.92 ( = 0.50, = 0.30) Linear trend line2.294.9%––

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Copyright 2006 John Wiley & Sons, Inc.11-44 Forecast Control Tracking signal monitors the forecast to see if it is biased high or low 1 MAD ≈ 0.8 б Control limits of 2 to 5 MADs are used most frequently Tracking signal = = (D t - F t ) MADEMAD

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Copyright 2006 John Wiley & Sons, Inc.11-45 Tracking Signal Values 13737.00––– 24037.003.003.003.00 34137.903.106.103.05 43738.83-1.834.272.64 54538.286.7210.993.66 65040.299.6920.684.87 74343.20-0.2020.484.09 84743.143.8624.344.06 95644.3011.7036.045.01 105247.814.1940.234.92 115549.065.9446.175.02 125450.843.1549.324.85 DEMANDFORECAST,ERROR E = PERIODD t F t D t - F t (D t - F t )MAD TS 3 = = 2.00 6.10 3.05 Tracking signal for period 3 –1.002.001.623.004.255.016.007.198.189.2010.17TRACKINGSIGNAL

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Copyright 2006 John Wiley & Sons, Inc.11-46 Tracking Signal Plot 3 3 – 2 2 – 1 1 – 0 0 – -1 -1 – -2 -2 – -3 -3 – ||||||||||||| 0123456789101112 Tracking signal (MAD) Period Exponential smoothing ( = 0.30) Linear trend line

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Copyright 2006 John Wiley & Sons, Inc.11-47 Statistical Control Charts = = = = (D t - F t ) 2 n - 1 Using we can calculate statistical control limits for the forecast error Control limits are typically set at 3

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Copyright 2006 John Wiley & Sons, Inc.11-48 Statistical Control Charts Errors 18.39 18.39 – 12.24 12.24 – 6.12 6.12 – 0 0 – -6.12 -6.12 – -12.24 -12.24 – -18.39 -18.39 – ||||||||||||| 0123456789101112 Period UCL = +3 LCL = -3

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Copyright 2006 John Wiley & Sons, Inc.11-49 Regression Methods Linear regression a mathematical technique that relates a dependent variable to an independent variable in the form of a linear equation Correlation a measure of the strength of the relationship between independent and dependent variables

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Copyright 2006 John Wiley & Sons, Inc.11-50 Linear Regression y = a + bx a = y - b x b = where a =intercept b =slope of the line x == mean of the x data y == mean of the y data xy - nxy x 2 - nx 2 x n y n

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Copyright 2006 John Wiley & Sons, Inc.11-51 Linear Regression Example xy (WINS)(ATTENDANCE) xyx 2 436.3145.216 640.1240.636 641.2247.236 853.0424.064 644.0264.036 745.6319.249 539.0195.025 747.5332.549 49346.72167.7311

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Copyright 2006 John Wiley & Sons, Inc.11-52 Linear Regression Example (cont.) x = = 6.125 y = = 43.36 b = = = 4.06 a = y - bx = 43.36 - (4.06)(6.125) = 18.46 49 8 346.9 8 xy - nxy 2 x 2 - nx 2 (2,167.7) - (8)(6.125)(43.36) (311) - (8)(6.125) 2

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Copyright 2006 John Wiley & Sons, Inc.11-53 ||||||||||| 012345678910 60,000 60,000 – 50,000 50,000 – 40,000 40,000 – 30,000 30,000 – 20,000 20,000 – 10,000 10,000 – Linear regression line, y = 18.46 + 4.06 x Wins, x Attendance, y Linear Regression Example (cont.) y = 18.46 + 4.06 x y = 18.46 + 4.06(7) = 46.88, or 46,880 Regression equation Attendance forecast for 7 wins

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Copyright 2006 John Wiley & Sons, Inc.11-54 Correlation and Coefficient of Determination Correlation, r Measure of strength of relationship Varies between -1.00 and +1.00 Coefficient of determination, r 2 Percentage of variation in dependent variable resulting from changes in the independent variable

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Copyright 2006 John Wiley & Sons, Inc.11-55 Computing Correlation n xy - x y [ n x 2 - ( x ) 2 ] [ n y 2 - ( y ) 2 ] r = Coefficient of determination r 2 = (0.947) 2 = 0.897 r = (8)(2,167.7) - (49)(346.9) [(8)(311) - (49 )2 ] [(8)(15,224.7) - (346.9) 2 ] r = 0.947

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Copyright 2006 John Wiley & Sons, Inc.11-56 Multiple Regression Study the relationship of demand to two or more independent variables y = 0 + 1 x 1 + 2 x 2 … + k x k where 0 =the intercept 1, …, k =parameters for the independent variables x 1, …, x k =independent variables

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Copyright 2006 John Wiley & Sons, Inc.11-57 Copyright 2006 John Wiley & Sons, Inc. All rights reserved. Reproduction or translation of this work beyond that permitted in section 117 of the 1976 United States Copyright Act without express permission of the copyright owner is unlawful. Request for further information should be addressed to the Permission Department, John Wiley & Sons, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, or damages caused by the use of these programs or from the use of the information herein.

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