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15-1 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Forecasting Chapter 15

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15-2 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall ■Forecasting Components ■Time Series Methods ■Forecast Accuracy ■Time Series Forecasting Using Excel ■Time Series Forecasting Using QM for Windows ■Regression Methods Chapter Topics

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15-3 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall ■A variety of forecasting methods are available for use depending on the time frame of the forecast and the existence of patterns. ■Time Frames: Short-range (one to two months) Medium-range (two months to one or two years) Long-range (more than one or two years) ■Patterns: Trend Random variations Cycles Seasonal pattern Forecasting Components

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15-4 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Trend - A long-term movement of the item being forecast. Random variations - movements that are not predictable and follow no pattern. Cycle - A movement, up or down, that repeats itself over a lengthy time span. Seasonal pattern - Oscillating movement in demand that occurs periodically in the short run. Forecasting Components Patterns (1 of 2)

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15-5 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Figure 15.1 (a) Trend; (b) Cycle; (c) Seasonal; (d) Trend with Season Forecasting Components Patterns (2 of 2)

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15-6 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Forecasting Components Forecasting Methods 1.Times Series - Statistical techniques that use historical data to predict future behavior. 2.Regression Methods - Regression (or causal ) methods that attempt to develop a mathematical relationship between the item being forecast and factors that cause it to behave the way it does. 3.Qualitative Methods - Methods using judgment, expertise and opinion to make forecasts.

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15-7 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Forecasting Components Qualitative Methods “Jury of executive opinion,” a qualitative technique, is the most common type of forecast for long-term strategic planning. Performed by individuals or groups within an organization, sometimes assisted by consultants and other experts, whose judgments and opinions are considered valid for the forecasting issue. Usually includes specialty functions such as marketing, engineering, purchasing, etc., in which individuals have experience and knowledge of the forecasted item. Supporting techniques include the Delphi Method, market research, surveys, and technological forecasting.

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15-8 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Time Series Methods Overview Statistical techniques that make use of historical data collected over a long period of time. Methods assume that what has occurred in the past will continue to occur in the future. Forecasts based on only one factor - time.

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15-9 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Time Series Methods Moving Average (1 of 6) Moving average uses values from the recent past to develop forecasts. This dampens random increases and decreases. Useful for forecasting relatively stable items that do not display any trend or seasonal pattern. Formula for moving average (MA):

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15-10 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Example: Instant Paper Clip Supply Company wants to forecast orders for the month of November. Develop three-month and five-month moving averages using the data. Time Series Methods Moving Average (2 of 6) Table 15.1 Orders for 10-month period

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15-11 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Example: Instant Paper Clip Supply Company wants to forecast orders for the month of November. Three-month moving average: Five-month moving average: Time Series Methods Moving Average (3 of 6)

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15-12 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Table 15.1 Three- and 5-month moving averages Time Series Methods Moving Average (4 of 6)

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15-13 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Figure 15.2 Three- and 5-month moving averages Time Series Methods Moving Average (5 of 6)

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15-14 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Time Series Methods Moving Average (6 of 6) Longer-period moving averages react more slowly to changes in demand than do shorter-period moving averages. The appropriate number of periods to use often requires trial-and- error experimentation. A moving average does not react well to changes (trends, seasonal effects, etc.) but is easy to use and inexpensive. Good for short-term forecasting.

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15-15 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall In a weighted moving average, weights are assigned to the most recent data. Determining precise weights and the number of periods requires trial-and-error experimentation. Time Series Methods Weighted Moving Average

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15-16 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Exponential smoothing weights recent past data more strongly than more distant data. Two forms: simple exponential smoothing and adjusted exponential smoothing. Simple exponential smoothing: F t + 1 = D t + (1 - )F t where: F t + 1 = the forecast for the next period D t = actual demand in the present period F t = the previously determined forecast for the present period = a weighting factor (smoothing constant). Time Series Methods Exponential Smoothing (1 of 11)

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15-17 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall The most commonly used values of are between 0.10 and Determination of is usually judgmental and subjective and often based on trial-and -error experimentation. Time Series Methods Exponential Smoothing (2 of 11)

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15-18 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Example: PM Computer Services (see Table 15.4). Exponential smoothing forecasts using smoothing constant of.30. Forecast for period 2 (February): F 2 = D 1 + (1- )F 1 = (.30)(.37) + (1-.30)(.37) = 37 units Forecast for period 3 (March): F 3 = D 2 + (1- )F 2 = (.30)(.40) + (1-.30)(37) = 37.9 units Time Series Methods Exponential Smoothing (3 of 11)

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15-19 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Table 15.4 Exponential smoothing forecasts, =.30 and =.50 Time Series Methods Exponential Smoothing (4 of 11)

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15-20 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall The forecast that uses the higher smoothing constant (.50) reacts more strongly to changes in demand than does the forecast with the lower constant (.30). Both forecasts lag behind actual demand. Both forecasts tend to be consistently lower than actual demand. Low smoothing constants are appropriate for stable data without trend; higher constants appropriate for data with trends. Time Series Methods Exponential Smoothing (5 of 11)

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15-21 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Figure 15.3 Exponential smoothing forecasts Time Series Methods Exponential Smoothing (6 of 11)

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15-22 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall ■ Adjusted exponential smoothing: exponential smoothing with a trend adjustment factor added. FormulaAF t + 1 = F t T t+1 where: T = an exponentially smoothed trend factor T t (F t F t ) + (1 - )T t T t = the last period trend factor = smoothing constant for trend ( a value between zero and one). ■ Reflects the weight given to the most recent trend data. ■ Determined subjectively. ■ Time Series Methods Exponential Smoothing (7 of 11)

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15-23 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Example: PM Computer Services exponentially smoothed forecasts with =.50 and =.30 (see Table 15.5 next slide). Adjusted forecast for period 3: T 3 = (F 3 - F 2 ) + (1 - )T 2 = (.30)( ) + (.70)(0) = 0.45 AF 3 = F 3 + T 3 = = Time Series Methods Exponential Smoothing (8 of 11)

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15-24 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Table 15.5 Adjusted exponentially smoothed forecast values Time Series Methods Exponential Smoothing (9 of 11)

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15-25 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall ■ The adjusted forecast is consistently higher than the simple exponentially smoothed forecast. ■ It is more reflective of the generally increasing trend of the data. Time Series Methods Exponential Smoothing (10 of 11)

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15-26 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Figure 15.4 Adjusted exponentially smoothed forecast Time Series Methods Exponential Smoothing (11 of 11)

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15-27 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall ■ When demand displays an obvious trend over time, a least squares regression line, or linear trend line, can be used to forecast. ■ Formula: Time Series Methods Linear Trend Line (1 of 5)

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15-28 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Example: PM Computer Services (see Table 15.6) Time Series Methods Linear Trend Line (2 of 5)

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15-29 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Table 15.6 Least squares calculations Time Series Methods Linear Trend Line (3 of 5)

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15-30 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall ■ A trend line does not adjust to a change in the trend as does the exponential smoothing method. ■ This limits its use to shorter time frames in which the trend will not change. Time Series Methods Linear Trend Line (4 of 5)

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15-31 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Figure 15.5 Linear trend line Time Series Methods Linear Trend (5 of 5)

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15-32 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall ■ A seasonal pattern is a repetitive up-and-down movement in demand. ■ Seasonal patterns can occur on a quarterly, monthly, weekly, or daily basis. ■ A seasonally adjusted forecast can be developed by multiplying the normal forecast by a seasonal factor. ■ A seasonal factor can be determined by dividing the actual demand for each seasonal period by total annual demand: S i =D i / D Time Series Methods Seasonal Adjustments (1 of 4)

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15-33 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall ■ Seasonal factors lie between zero and one and represent the portion of total annual demand assigned to each season. ■ Seasonal factors are multiplied by annual demand to provide adjusted forecasts for each period. Time Series Methods Seasonal Adjustments (2 of 4)

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15-34 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall S 1 = D 1 / D = 42.0/148.7 = 0.28 S 2 = D 2 / D = 29.5/148.7 = 0.20 S 3 = D 3/ D = 21.9/148.7 = 0.15 S 4 = D 4 / D = 55.3/148.7 = 0.37 Table 15.7 Demand for turkeys at Wishbone Farms Example: Wishbone Farms Time Series Methods Seasonal Adjustments (3 of 4)

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15-35 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Multiply forecasted demand for an entire year by seasonal factors to determine the quarterly demand. Forecast for entire year (trend line for data in Table 15.7): y = x = (4) = Seasonally adjusted forecasts: SF 1 = (S 1 )(F 5 ) = (.28)(58.17) = SF 2 = (S 2 )(F 5 ) = (.20)(58.17) = SF 3 = (S 3 )(F 5 ) = (.15)(58.17) = 8.73 SF 4 = (S 4 )(F 5 ) = (.37)(58.17) = Time Series Methods Seasonal Adjustments (4 of 4)

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15-36 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Forecasts will always deviate from actual values. Difference between forecasts and actual values are referred to as forecast error. We would like forecast error to be as small as possible. If forecast error is large, either the technique being used is the wrong one, or the parameters need adjusting. Measures of forecast errors: Mean Absolute deviation (MAD) Mean absolute percentage deviation (MAPD) Cumulative error (E bar) Average error, or bias (E) Forecast Accuracy Overview

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15-37 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall MAD is the average absolute difference between the forecast and actual demand. The most popular and simplest-to-use measures of forecast error. Formula: Forecast Accuracy Mean Absolute Deviation (1 of 7)

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15-38 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Example: PM Computer Services (see Table 15.8). Compare accuracies of different forecasts using MAD: Forecast Accuracy Mean Absolute Deviation (2 of 7)

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15-39 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Table 15.8 Computational values for MAD and error Forecast Accuracy Mean Absolute Deviation (3 of 7)

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15-40 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall The lower the value of MAD relative to the magnitude of the data, the more accurate the forecast. When viewed alone, MAD is difficult to assess. MAD must be considered in light of magnitude of the data. Forecast Accuracy Mean Absolute Deviation (4 of 7)

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15-41 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Can be used to compare the accuracy of different forecasting techniques working on the same set of demand data (PM Computer Services): Exponential smoothing ( =.50): MAD = 4.04 Adjusted exponential smoothing ( =.50, =.30): MAD = 3.81 Linear trend line: MAD = 2.29 The linear trend line has the lowest MAD; increasing from.30 to.50 improved the smoothed forecast. Forecast Accuracy Mean Absolute Deviation (5 of 7)

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15-42 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall A variation on MAD is the mean absolute percent deviation (MAPD). Measures the absolute error as a percentage of demand rather than per period. Eliminates the problem of interpreting the measure of accuracy relative to the magnitude of the demand and forecast values. Formula: Forecast Accuracy Mean Absolute Deviation (6 of 7)

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15-43 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall MAPD for other three forecasts: Exponential smoothing ( =.50): MAPD = 8.5% Adjusted exponential smoothing ( =.50, =.30): MAPD = 8.1% Linear trend: MAPD = 4.9% Forecast Accuracy Mean Absolute Deviation (7 of 7)

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15-44 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Cumulative error is the sum of the forecast errors (E = e t ). A relatively large positive value indicates the forecast is biased low, a large negative value indicates the forecast is biased high. If the preponderance of errors are positive, the forecast is consistently low; and vice versa. The cumulative error for a trend line is always almost zero, and is therefore not a good measure for this method. The cumulative error for PM Computer Services can be read directly from Table E = e t = 49.31, indicating the forecasts are frequently below actual demand. Forecast Accuracy Cumulative Error (1 of 2)

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15-45 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Cumulative error for other forecasts: Exponential smoothing ( =.50): E = Adjusted exponential smoothing ( =.50, =.30): E = Average error (bias) is the per-period average of cumulative error. Average error for the exponential smoothing forecast: A large positive value of average error indicates a forecast is biased low; a large negative error indicates it is biased high. Forecast Accuracy Cumulative Error (2 of 2)

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15-46 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Results consistent for all forecasts: Larger value of alpha is preferable. Adjusted forecast is more accurate than exponential smoothing. Linear trend is more accurate than all the others. Table 15.9 Comparison of forecasts for PM Computer Services Forecast Accuracy Example Forecasts by Different Measures

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15-47 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Exhibit 15.1 Time Series Forecasting Using Excel (1 of 4) =G21/11 =B3*B8+(1-B3)*C8 =C9+D9 =B9-E9 =ABS(B9-E9) =SUM(F9:F20)

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15-48 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Exhibit 15.2 Time Series Forecasting Using Excel (2 of 4) To access this window, click on “Data” on the toolbar ribbon and then the “Data Analysis” add-in

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15-49 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Exhibit 15.3 Time Series Forecasting Using Excel (3 of 4) Demand values = 0.5 Cells in which the forecasted values will be placed

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15-50 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Exhibit 15.4 Time Series Forecasting Using Excel (4 of 4)

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15-51 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Exhibit 15.5 Exponential Smoothing Forecast with Excel QM Click “Add-Ins” to access forecasting macros Input problem data in cells B7 and B10:B21

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15-52 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Time Series Forecasting Solution with QM for Windows (1 of 2) Exhibit 15.6

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15-53 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Exhibit 15.7 Time Series Forecasting Solution with QM for Windows (2 of 2)

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15-54 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Time series techniques relate a single variable being forecast to time. Regression is a forecasting technique that measures the relationship of one variable to one or more other variables. The simplest form of regression is linear regression. Regression Methods Overview

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15-55 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Linear regression relates demand (dependent variable ) to an independent variable. Regression Methods Linear Regression

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15-56 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall State University Athletic Department. Regression Methods Linear Regression Example (1 of 3)

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15-57 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Regression Methods Linear Regression Example (2 of 3)

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15-58 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Figure 15.6 Linear regression line Regression Methods Linear Regression Example (3 of 3)

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15-59 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Correlation is a measure of the strength of the relationship between independent and dependent variables. Formula: Value lies between +1 and -1. Value of zero indicates little or no relationship between variables. Values near 1.00 and indicate a strong linear relationship. Regression Methods Correlation (1 of 2)

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15-60 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Value for State University example: Since the value is close to one, we have evidence of a strong linear relationship. Regression Methods Correlation (2 of 2)

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15-61 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall The coefficient of determination is the percentage of the variation in the dependent variable that results from the independent variable. Computed by squaring the correlation coefficient, r. For the State University example: r =.948, r 2 =.899 This value indicates that 89.9% of the amount of variation in attendance can be attributed to the number of wins by the team, with the remaining 10.1% due to other, unexplained, factors. Regression Methods Coefficient of Determination

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15-62 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Regression Analysis with Excel (1 of 6) Exhibit 15.8 =INTERCEPT(B5:B12,A5:A12) =CORREL(B5:B12,A5:A12)

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15-63 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Regression Analysis with Excel (2 of 6) Exhibit 15.9 Click on “Insert” to access “Charts” Click on “Scatter”

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15-64 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Exhibit Regression Analysis with Excel (3 of 6)

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15-65 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Exhibit Regression Analysis with Excel (4 of 6)

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15-66 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Exhibit Regression Analysis with Excel (5 of 6)

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15-67 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Exhibit Regression Analysis with QM for Windows (6 of 6)

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15-68 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Multiple Regression with Excel (1 of 4) Multiple regression relates demand to two or more independent variables. General form: y = 0 + 1 x 1 + 2 x k x k where 0 = the intercept 1... k = parameters representing contributions of the independent variables x 1... x k = independent variables

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15-69 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall State University example revisited; does the addition of promotional and advertising expenditures to wins improve the prediction of attendance? Multiple Regression with Excel (2 of 4)

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15-70 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Exhibit Multiple Regression with Excel (3 of 4) r 2, the coefficient of determination Regression equation coefficients for x 1 and x 2

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15-71 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Exhibit Multiple Regression with Excel (4 of 4) Includes x 1 and x 2 columns

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15-72 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Problem Statement: For the data below, develop an exponential smoothing forecast using =.40, and an adjusted exponential smoothing forecast using =.40 and =.20. Compare the accuracy of the forecasts using MAD and cumulative error. Example Problem Solution Computer Software Firm (1 of 4)

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15-73 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Step 1: Compute the Exponential Smoothing Forecast. F t+1 = D t + (1 - )F t Step 2: Compute the Adjusted Exponential Smoothing Forecast AF t+1 = F t +1 + T t+1 T t+1 = (F t +1 - F t ) + (1 - )T t Example Problem Solution Computer Software Firm (2 of 4)

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15-74 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Example Problem Solution Computer Software Firm (3 of 4)

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15-75 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Step 3: Compute the MAD Values Step 4: Compute the Cumulative Error. E(F t ) = E(AF t ) = Example Problem Solution Computer Software Firm (4 of 4)

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15-76 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall For the following data: Develop a linear regression model Determine the strength of the linear relationship using correlation. Determine a forecast for lumber given 10 building permits in the next quarter. Example Problem Solution Building Products Store (1 of 5)

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15-77 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Example Problem Solution Building Products Store (2 of 5)

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15-78 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Step 1: Compute the Components of the Linear Regression Equation. Example Problem Solution Building Products Store (3 of 5)

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15-79 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Step 2: Develop the Linear regression equation. y = a + bx, y = x Step 3: Compute the Correlation Coefficient. Example Problem Solution Building Products Store (4 of 5)

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15-80 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Example Problem Solution Building Products Store (5 of 5) Step 4: Calculate the forecast for x = 10 permits. Y = a + bx = (10) = or 1,386 board ft Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall

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15-81 Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Printed in the United States of America.

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