2b. forecasting linear trend
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The document discusses techniques for trend forecasting, including linear and nonlinear trends. It provides the equation for a linear trend forecasting model, which uses data points over time to calculate the values of a and b in the equation Ft = a + bt. An example is given showing how to calculate a and b from a dataset and use the linear trend equation to forecast future time periods. Sources of errors in forecasting are also listed, such as an inadequate model, irregular variations in the data, and incorrect use of forecasting techniques.
2b. forecasting linear trend
- 1. 3-1 Forecasting Forecasting McGraw-Hill/Irwin Operations Management, Eighth Edition, by William J. Stevenson Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved.
- 2. 3-2 Forecasting Techniques for TrendTechniques for Trend • Analysis of trend involves developing an equation that will suitably describe trend. • The trend component may be linear or it may not.
- 3. 3-3 Forecasting Common Nonlinear TrendsCommon Nonlinear Trends Parabolic Exponential Growth
- 4. 3-4 Forecasting Linear Trend EquationLinear Trend Equation • Ft = Forecast for period t • t = Specified number of time periods • a = Value of Ft at t = 0 • b = Slope of the line • y = a + bt Ft = a + bt 0 1 2 3 4 5 t Ft
- 5. 3-5 Forecasting Calculating a and bCalculating a and b b = n (ty) - t y n t2 - ( t)2 a = y - b t n ∑∑∑ ∑∑ ∑∑
- 6. 3-6 Forecasting Linear Trend Equation ExampleLinear Trend Equation Example t y Week t 2 Sales ty 1 1 150 150 2 4 157 314 3 9 162 486 4 16 166 664 5 25 177 885 Σ t = 15 Σ t 2 = 55 Σ y = 812 Σ ty = 2499 (Σ t) 2 = 225
- 7. 3-7 Forecasting Linear Trend CalculationLinear Trend Calculation y = 143.5 + 6.3t a = 812 - 6.3(15) 5 = b = 5 (2499) - 15(812) 5(55) - 225 = 12495-12180 275-225 = 6.3 143.5
- 8. 3-8 Forecasting Sources of Forecast errorsSources of Forecast errors • Model may be inadequate • Irregular variations • Incorrect use of forecasting technique