1. Ch 5-1 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Cost Analysis and Estimating for Engineering and Management Chapter 5 Forecasting

2. Ch 5-2 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Overview l Working with Data  Graphing, Statistics  Regression / Curve Fitting  Confidence / Correlation l Time Series  Moving Averages, Smoothing l Cost Indexes

3. Ch 5-3 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Business Forecasting l Prediction  Price of Material  Cost/Amount of Labor  Market Demand/Price l Term  Short  2 Years  Medium 2 - 5 Years  Long Range > 5 Years

4. Ch 5-4 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Graphical Analysis l Descriptive Statistics  Collect/Organize/Analyze Data  Summarize/Present  Draw Conclusions/Make Decisions l Raw Data Communicates Little Information

5. Ch 5-5 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Simplifying Data Price, ($/roll)ObsRel FreqCum Freq 12.35–12.7510.003 12.75–13.1560.0190.022 13.15–13.55330.1020.124 13.55–13.95510.1570.281 13.95–14.351210.3730.654 14.35–14.75500.1540.808 14.75–15.15440.1360.944 15.15–15.65130.0400.984 15.65–16.0550.0161.000 3241.000

6. Ch 5-6 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Graphical Presentation

7. Ch 5-7 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Frequency Curves

8. Ch 5-8 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Mean l Average Eq 5.1

9. Ch 5-9 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Median & Mode l Median  All Data from Lowest to Highest  Number in the Middle l Mode  Data Value(s) that Appear the Most Often

10. Ch 5-10 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Standard Deviation l Amount of Data Spread Around the Mean l Variance Is the Square of the Standard Deviation Eq 5.2

11. Ch 5-11 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Graph the Data l Pure Statistics Can Be Misleading l Any Set of Numbers  Will Have Mean, Std Dev, etc.  May or May Not Be Relevant l Plot the Data  Visual Interpretation  Apply “Judgment”

12. Ch 5-12 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Mathematical Model l Draw Line Through Data l Half of Points Above Line, Half Below l Straight Line y = a + bx Determine a and b from Graph

13. Ch 5-13 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Example

14. Ch 5-14 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Why Graph? l Visual Analysis of What Is Happening l Non-Linearity May Be Exposed l Incorporates “Reasonableness” l Mathematical Methods Can Assist in Establishing the “Best Fit” Line Through the Data

15. Ch 5-15 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Regression Analysis Finds Dependent y for Given x If x Is Time  Called Trend Line  Used for Forecasting

16. Ch 5-16 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Least Squares l Minimize Variation (Error) Between  Observed (Real) Values  Fitted Curve (Predicted) Values l Minimize  Sum of the Squares of the Errors

17. Ch 5-17 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Normal vs. Student-t Distribution

18. Ch 5-18 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Distribution Applied to Regression

19. Ch 5-19 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Mathematical Calculations l Error l Sum of the Squares Eq 5.4 Eq 5.5

20. Ch 5-20 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management The Least Squares Equation l y = a + bx The Least Squares Line Goes Through ( X, Y ) Eq 5.8 Eq 5.9

21. Ch 5-21 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Example Year x Index y x2 x2 xy y  2 2 0870084.8752.1254.516 1891 87.2641.7363.013 290418089.6540.3460.120 392927692.043-0.0430.002 4931637294.432-1.4322.051 ………………… 1051524101511337 63.168

22. Ch 5-22 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Example Calculations Find a and b Y = 84.875 + 2.389 X

23. Ch 5-23 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Confidence Limits

24. Ch 5-24 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management l Variance Around Regression Line l Degrees of Freedom Equations Eq 5.19 Eq 5.11

25. Ch 5-25 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Confidence Limits l Based on Student-t Tables l Regression Line Passes Through y  Variation of y Equals Constant Variation of regression line Eq 5.14

26. Ch 5-26 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management In General l Variance of y Due to Variance of y l Variance Applied to y Eq 5.15 Eq 5.16

27. Ch 5-27 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Compounded Variance l Variance of Predicted Value Eq 5.17 Eq 5.18 Eq 5.19

28. Ch 5-28 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Confidence vs Prediction l Confidence Interval  Variation Around Expected Y Value l Prediction Interval  Variation Around a Single Y Value  Greater In Magnitude

29. Ch 5-29 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Variance from Intercept X = 0 at Intercept a Eq 5.20 Eq 5.22 Eq 5.21 Eq 5.23

30. Ch 5-30 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Confidence Intervals

31. Ch 5-31 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Non-Linear Relationships l Curvilinear Regression Exponential Eq 5.24 Power Eq 5.25 Polynomial Eq 5.26

32. Ch 5-32 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Non-Linear Calculations l Convert to Log Representation For y = ab x ( Exponential Function ) Eq 5.27 Eq 5.28

33. Ch 5-33 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Another Version For y = ax b (Power Function) Eq 5.29 Eq 5.30

34. Ch 5-34 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Example xylog xlog y(log x) 2 log x log y 105101.00002.70761.00002.7076 302101.47712.32222.18193.4302 1001902.00002.27884.00004.5575 1501252.17612.09694.73544.5631 300712.47711.85136.13614.5858 9.130311.256718.053419.8441

35. Ch 5-35 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Finding a and b Eq 5.29 Eq 5.30

36. Ch 5-36 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Polynomial Regression l Linear Relationship Unknown Eq 5.31

37. Ch 5-37 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Correlation

38. Ch 5-38 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Correlation l Sometimes There Isn’t Any l Quantitative Measure -1  r  1 l Farther from 0, Stronger Correlation Eq 5.33

39. Ch 5-39 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Multiple Linear Regression l More than 1 Independent Variable l Graphical Representation Difficult l Mathematical Form Eq 5.34

40. Ch 5-40 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Finding Constants l Solve Simultaneously Eq 5.35

41. Ch 5-41 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Regression Assumptions The Values of x Are Controlled l Regression is Linear l Deviations are Mutually Independent Deviations Are Not a Function of x l Deviations Are Normally Distributed l Model Contains ALL Relevant Variables

42. Ch 5-42 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Time Series Models l Used for Forecasting l Fundamentals  Consistent Data Collection  Types of Behavior  Moving Average  Smoothing l Data Added on Revolving Basis

43. Ch 5-43 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Time Series Data l Collected at Successive Periods l Usually Equally Spaced l Is the Underlying Process  Constant  Variable  Trend-Cycle  Seasonal  Regular

44. Ch 5-44 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Typical Time Series Models

45. Ch 5-45 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Moving Average l Places More Reliance on Recent Data l Recent Data Better Predicts Future N Determines Rate of Response Eq 5.36

46. Ch 5-46 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Smoothing l “Weighted” Moving Average l Exponential Smoothing Eq 5.38

47. Ch 5-47 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Smoothing Constant  Variations in  values Drift in data Small,  = 0Little,  = 0.5Large,  = 1 None ModerateVery smallSmallModerate LargeSmallModerateLarge

48. Ch 5-48 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Cost Index l Dimensionless Number l Represents Change in Cost l Over a Period of Time l Relative to a “Benchmark” Period l What is Costed Remains Constant l Used to Forecast

49. Ch 5-49 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Using Cost Index Compares Known Cost at Period r Using Current I c and Reference I r Indexes Eq 5.39

50. Ch 5-50 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Figuring Cost Indexes l Benchmark Cost Used as Denominator l Index for Benchmark Period = 1 or 100 l Costs for Other Periods Divided by Benchmark Cost

51. Ch 5-51 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Rate of Change l Differences Between Periods  Percent Change Current index, period 5106.8 Less previous index, period 4102.3 Index point change+4.5 Divide by previous index102.3 Equals+0.044 = + 4.4%

52. Ch 5-52 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Change Rate l Figuring Average Rate of Change l Using Rate of Change to Find Index Eq 5.40 Eq 5.41

53. Ch 5-53 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Composite Index Material0*123 Laser glass$26,117$24,027$22,345$21,228 Steel tubing1913200821292278 Al extrusion418426439456 Printed circuits637643656657 Harness cable2103212421342305 Glass tubing4317418741034185 Total$35,505$33,415$31,806$31,119 Index, %100.094.189.687.6 * Benchmark Period

54. Ch 5-54 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Indexes l Basis Changes (Qty, Qual, Mix, etc) l Technology Creep l Kinds of Indexes  Material  Labor Geographical l Index Specific for Time and Location

55. Ch 5-55 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Caveats l Results Depend on Good Data l Cause and Effect Relationship l Eliminating Spurious Data l Backcast Period  Forecast Period l Limit Number of Variables l Use Judgment l Test for “Reasonableness”

56. Ch 5-56 © 2004 Pearson Education, Inc. Pearson Prentice Hall, Pearson Education, Upper Saddle River, NJ 07458 Ostwald and McLaren / Cost Analysis and Estimating for Engineering and Management Summary l Objective - Forecasting l Methods for Working with Data  Graphing, Statistics, Regression l Data In Time Periods (Time Series) l Cost Indexes  Applications, Calculations, Caveats