The text considers Simple Linear Regression and ask what is it doing? how good is it? how accurate is it? and how can we use it to create estimates? The book considers all this and looks at how you can exploit this transformability and use the capability of Simple Linear Regression.
Best Fit Lines and Curves, and Some Mathe-Magical Transformations (Volume III of the Working Guides to Estimating & Forecasting series) concentrates on techniques for finding the Best Fit Line or Curve to some historical data allowing us to interpolate or extrapolate the implied relationship that will underpin our prediction. A range of simple Moving Measures are suggested to smooth the underlying trend and quantify the degree of noise or scatter around that trend. The advantages and disadvantages are discussed and a simple way to offset the latent disadvantage of most Moving Measure Techniques is provided.
Simple Linear Regression Analysis, a more formal numerical technique that calculates the line of best fit subject to defined goodness of fit criteria. Microsoft Excel is used to demonstrate how to decide whether the line of best fit is a good fit, or just a solution in search of some data. These principles are then extended to cover multiple cost drivers, and how we can use them to quantify 3-Point Estimates.
With a deft sleight of hand, certain commonly occurring families of non-linear relationships can be transformed mathe-magically into linear formats, allowing us to exploit the powers of Regression Analysis to find the Best Fit Curves. The concludes with an exploration of the ups and downs of seasonal data (Time Series Analysis). Supported by a wealth of figures and tables, this is a valuable resource for estimators, engineers, accountants, project risk specialists as well as students of cost engineering.
Recenzijos
"In the Working Guides to Estimating and Forecasting Alan has managed to capture the full spectrum of relevant topics with simple explanations, practical examples and academic rigor, while injecting humour into the narrative." Dale Shermon, Chairman, Society of Cost Analysis and Forecasting (SCAF).
"If estimating has always baffled you, this innovative well illustrated and user friendly book will prove a revelation to its mysteries. To confidently forecast, minimise risk and reduce uncertainty we need full disclosure into the science and art of estimating. Thankfully, and at long last the "Working Guides to Estimating & Forecasting" are exactly that, full of practical examples giving clarity, understanding and validity to the techniques. These are comprehensive step by step guides in understanding the principles of estimating using experientially based models to analyse the most appropriate, repeatable, transparent and credible outcomes. Each of the five volumes affords a valuable tool for both corporate reference and an outstanding practical resource for the teaching and training of this elusive and complex subject. I wish I had access to such a thorough reference when I started in this discipline over 15 years ago, I am looking forward to adding this to my library and using it with my team." - Tracey L Clavell, Head of Estimating & Pricing, BAE Systems Australia
"At last, a comprehensive compendium on these engineering math subjects, essential to both the new and established "cost engineer"! As expected the subjects are presented with the authors usual wit and humour on complex and daunting "mathematically challenging" subjects. As a professional trainer within the MOD Cost Engineering community trying to embed this into my students, I will be recommending this series of books as essential bedtime reading." - Steve Baker, Senior Cost Engineer, DE&S MOD
"Alan has been a highly regarded member of the Cost Estimating and forecasting profession for several years. He is well known for an ability to reduce difficult topics and cost estimating methods down to something that is easily digested. As a master of this communication he would most often be found providing training across the cost estimating and forecasting tools and at all levels of expertise. With this 5-volume set, Working Guides to Estimating and Forecasting, Alan has brought his normal verbal training method into a written form. Within their covers Alan steers away from the usual dry academic script into establishing an almost 1:1 relationship with the reader. For my money a recommendable read for all levels of the Cost Estimating and forecasting profession and those who simply want to understand what is in the blackbox just a bit more." - Prof Robert Mills, Margin Engineering, Birmingham City University. MACOSTE, SCAF, ICEAA.
"Finally, a book to fill the gap in cost estimating and forecasting! Although other publications exist in this field, they tend to be light on detail whilst also failing to cover many of the essential aspects of estimating and forecasting. Jones covers all this and more from both a theoretical and practical point of view, regularly drawing on his considerable experience in the defence industry to provide many practical examples to support his comments. Heavily illustrated throughout, and often presented in a humorous fashion, this is a must read for those who want to understand the importance of cost estimating within the broader field of project management." - Dr Paul Blackwell, Lecturer in Management of Projects, The University of Manchester, UK.
"Alan Jones provides a useful guidebook and navigation aid for those entering the field of estimating as well as an overview for more experienced practitioners. His humorous asides supplement a thorough explanation of techniques to liven up and illuminate an area which has little attention in the literature, yet is the basis of robust project planning and successful delivery. Alans talent for explaining the complicated science and art of estimating in practical terms is testament to his knowledge of the subject and to his experience in teaching and training." - Therese Lawlor-Wright, Principal Lecturer in Project Management at the University of Cumbria
"Alan Jones has created an in depth guide to estimating and forecasting that I have not seen historically. Anyone wishing to improve their awareness in this field should read this and learn from the best." Richard Robinson, Technical Principal for Estimating, Mott MacDonald
"The book series of Working Guides to Estimating and Forecasting is an essential read for students, academics and practitioners who interested in developing a good understanding of cost estimating and forecasting from real-life perspectives". Professor Essam Shehab, Professor of Digital Manufacturing and Head of Cost Engineering, Cranfield University, UK.
"In creating the Working Guides to Estimating and Forecasting, Alan has captured the core approaches and techniques required to deliver robust and reliable estimates in a single series. Some of the concepts can be challenging, however, Alan has delivered them to the reader in a very accessible way that supports lifelong learning. Whether you are an apprentice, academic or a seasoned professional, these working guides will enhance your ability to understand the alternative approaches to generating a well-executed, defensible estimate, increasing your ability to support competitive advantage in your organisation." - Professor Andrew Langridge, Royal Academy of Engineering Visiting Professor in Whole Life Cost Engineering and Cost Data Management, University of Bath, UK.
"Alan Joness "Working Guides to Estimating and Forecasting" provides an excellent guide for all levels of cost estimators from the new to the highly experienced. Not only does he cover the underpinning good practice for the field, his books will take you on a journey from cost estimating basics through to how estimating should be used in manufacturing the future reflecting on a whole life cycle approach. He has written a must-read book for anyone starting cost estimating as well as for those who have been doing estimates for years. Read this book and learn from one of the best." - Linda Newnes, Professor of Cost Engineering, University of Bath, UK.
Foreword, 1 Introduction and Objectives, 1.1 Why write this book? Who
might find it useful? Why Five Volumes? 1.1.1 Why write this series? Who
might find it useful? 1.1.2 Why Five Volumes? 1.2 Features you'll find in
this book and others in this series, 1.2.1
Chapter Context, 1.2.2 The Lighter
Side (humour), 1.2.3 Quotations, 1.2.4 Definitions, 1.2.5 Discussions and
Explanations with a Mathematical Slant for Formula-philes, 1.2.6 Discussions
and Explanations without a Mathematical Slant for Formula-phobes, 1.2.7
Caveat Augur, 1.2.8 Worked Examples, 1.2.9 Useful Microsoft Excel Functions
and Facilities, 1.2.10 References to Authoritative Sources, 1.2.11
Chapter
Reviews, 1.3 Overview of
Chapters in this Volume, 1.4 Elsewhere in the
'Working Guide to Estimating & Forecasting' Series, 1.4.1 Volume I:
Principles, Process and Practice of Professional Number Juggling, 1.4.2
Volume II: Probability, Statistics and other Frightening Stuff, 1.4.3 Volume
III: Best Fit Lines & Curves, and some Mathe-Magical Transformations, 1.4.4
Volume IV: Learning, Unlearning and Re-Learning Curves, 1.4.5 Volume V: Risk,
Opportunity, Uncertainty and Other Random Models, 1.5 Final Thoughts and
Musings on this Volume and Series, References, , 2 Linear and Nonlinear
Properties (!) of Straight Lines, 2.1 Basic Linear Properties, 2.1.1
Inter-relation between Slope and Intercept, 2.1.2 The Difference between Two
Straight Lines is a Straight Line, 2.2 The Cumulative Value (Nonlinear)
Property of a Linear Sequence, 2.2.1 The Cumulative Value of a Discrete
Linear Function, 2.2.2 The Cumulative Value of a Continuous Linear Function,
2.2.3 Exploiting the Quadratic Cumulative Value of a Straight Line, 2.3
Chapter Review, References, , 3 Trendsetting with Some Simple Moving
Measures, 3.1 Going All Trendy: The Could and The Should, 3.1.1 When should
we consider trend smoothing?, 3.1.2 When is trend smoothing not appropriate?,
3.2 Moving Averages, 3.2.1 Use of Moving Averages, 3.2.2 When not to use
Moving Averages, 3.2.3 Simple Moving Average, 3.2.4 Weighted Moving Average,
3.2.5 Choice of Moving Average Interval: Is there a better way than guessing?
3.2.6 Can we take the Moving Average of a Moving Average?, 3.2.7 A Creative
Use for Moving Averages - A Case of Forward Thinking, 3.2.8 Dealing with
Missing Data, 3.2.9 Uncertainty Range around the Moving Average, 3.3 Moving
Medians, 3.3.1 Choosing the Moving Median Interval, 3.3.2 Dealing with
Missing Data, 3.3.3 Uncertainty Range around the Moving Median, 3.4 Other
Moving Measures of Central Tendency, 3.4.1 Moving Geometric Mean, 3.4.2
Moving Harmonic Mean, 3.4.3 Moving Mode, 3.5 Exponential Smoothing, 3.5.1 An
Unfortunate Dichotomy, 3.5.2 Choice of Smoothing Constant, or Choice of
Damping Factor, 3.5.3 Uses for Exponential Smoothing, 3.5.4 Double and Triple
Exponential Smoothing, 3.6 Cumulative Average and Cumulative Smoothing, 3.6.1
Use of Cumulative Averages, 3.6.2 Dealing with Missing Data, 3.6.3 Cumulative
Averages with Batch Data, 3.6.4 Being slightly more Creative - Cumulative
Average on a Sliding Scale, 3.6.5 Cumulative Smoothing, 3.7
Chapter Review,
References, , 4 Simple and Multiple Linear Regression, 4.1 What is Regression
Analysis?, 4.1.1 Least Squares Best Fit, 4.1.2 Two Key Sum-to-Zero Properties
of Least Squares, 4.2 Simple Linear Regression, 4.2.1 Simple Linear
Regression using Basic Excel Functions, 4.2.2 Simple Linear Regression using
the Data Analysis Add-in Tool Kit in Excel, 4.2.3 Simple Linear Regression
using Advanced Excel Functions, 4.3 Multiple Linear Regression, 4.3.1 Using
Categorical Data in Multiple Linear Regression, 4.3.2 Multiple Linear
Regression using the Data Analysis Add-in Tool Kit in Excel, 4.3.3 Multiple
Linear Regression using Advanced Excel Function, 4.4 Dealing with Outliers in
Regression Analysis?, 4.5 How Good is our Regression? Six Key Measures, 4.5.1
Coefficient of Determination (R-Square): A Measure of Linearity?!, 4.5.2
F-Statistic: A Measure of Chance Occurrence, 4.5.3 t-Statistics: Measures of
Relevance or Significant Contribution, 4.5.4 Regression through the Origin,
4.5.5 Role of Common Sense as a Measure of Goodness of Fit, 4.5.6 Coefficient
of Variation as a Measure of Tightness of Fit, 4.5.7 White's Test for
Heteroscedasticity ... and By Default Homoscedasticity, 4.6 Prediction and
Confidence Intervals - Measures of Uncertainty, 4.6.1 Prediction Intervals
and Confidence Intervals: What's the Difference?, 4.6.2 Calculating
Prediction Limits and Confidence Limits for Simple Linear Regression, 4.6.3
Calculating Prediction Limits and Confidence Limits for Multi-Linear
Regression, 4.7 Stepwise Regression, 4.7.1 Backward Elimination, 4.7.2
Forward Selection, 4.7.3 Backward or Forward Selection - Which should we
use?, 4.7.4 Choosing the Best Model when we are Spoilt for Choice, 4.8
Chapter Review, References, , 5 Linear Transformation: Making Bent Lines
Straight, 5.1 Logarithms, 5.1.1 Basic Properties of Powers, 5.1.2 Basic
Properties of Logarithms, 5.2 Basic Linear Transformation: Four Standard
Function Types, 5.2.1 Linear Functions, 5.2.2 Logarithmic Functions, 5.2.3
Exponential Functions, 5.2.4 Power Functions, 5.2.5 Transforming with Excel,
5.2.6 Is the Transformation Really Better, or Just a Mathematical Sleight of
Hand?, 5.3 Advanced Linear Transformation: Generalised Function Types, 5.3.1
Transforming Generalised Logarithmic Functions, 5.3.2 Transforming
Generalised Exponential Functions, 5.3.3 Transforming Generalised Power
Functions, 5.3.4 Reciprocal Functions - Special Cases of a Generalised Power
Functions, 5.3.5 Transformation Options, 5.4 Finding the Best Fit Offset
Constant, 5.4.1 Transforming Generalised Function Types into Standard
Functions, 5.4.2 Using the Random-Start Bisection Method (Technique), 5.4.3
Using Microsoft Excel's Goal Seek or Solver, 5.5 Straightening Out Earned
Value Analysis or EVM Disintegration, 5.5.1 EVM Terminology, 5.5.2 Taking a
Simpler Perspective, 5.6 Linear Transformation Based on Cumulative Value
Disaggregation, 5.7
Chapter Review, References, , 6 Transforming Nonlinear
Regression, 6.1 Simple Linear Regression of a Linear Transformation, 6.1.1
Simple Linear Regression with a Logarithmic Function, 6.1.2 Simple Linear
Regression with an Exponential Function, 6.1.3 Simple Linear Regression with
a Power Function, 6.1.4 Reversing the Transformation of Logarithmic,
Exponential and Power Functions, 6.2 Multiple Linear Regression of a
Multi-linear Transformation, 6.2.1 Multi-linear Regression using Linear and
Linearised Logarithmic Functions, 6.2.2 Multi-linear Regression using
Linearised Exponential and Power Functions, 6.3 Stepwise Regression and
Multi-Linear Transformations, 6.3.1 Stepwise Regression by Backward
Elimination with Linear Transformations, 6.3.2 Stepwise Regression by Forward
Selection with Linear Transformations, 6.4 Is the Best Fit Really the Better
Fit?, 6.5 Regression of Transformed Generalised Nonlinear Functions, 6.5.1
Linear Regression of a Transformed Generalised Logarithmic Function, 6.5.2
Linear Regression of a Transformed Generalised Exponential Function, 6.5.3
Linear Regression of a Transformed Generalised Power Function, 6.5.4
Generalised Function Transformations: Avoiding the Pitfalls and Tripwires,
6.6 Pseudo Multi-linear Regression of Polynomial Functions, 6.6.1 Offset
Quadratic Regression of the Cumulative of a Straight Line, 6.6.2 Example of a
Questionable Cubic Regression of Three Linear Variables, 6.7
Chapter Review,
References, 7 Least Squares Nonlinear Curve Fitting without the Logs, 7.1
Curve Fitting by Least Squares without the Logarithms, 7.1.1 Fitting Data
to Discrete Probability Distributions, 7.1.2 Fitting data to Continuous
Probability Distributions, 7.1.3 Revisiting the Gamma Distribution
Regression, 7.2
Chapter Review, References, , 8 The Ups and Downs of Time
Series Analysis, 8.1 The Bits and Bats and Buts of a Time Series, 8.1.1
Conducting a Time Series Analysis, 8.2 Alternative Time Series Models, 8.2.1
Additive/Subtractive Time Series Model, 8.2.2 Multiplicative Time Series
Model, 8.3 Classical Decomposition: Determining the Underlying Trend, 8.3.1
See-Saw Regression Flaw?, 8.3.2 Moving Average Seasonal Smoothing, 8.3.3
Cumulative Average Seasonal Smoothing, 8.3.4 What happens when our world is
not perfect? Do any of these trends work?, 8.3.5 Exponential Trends and
Seasonal Funnels, 8.3.6 Meandering Trends, 8.4 Determining the Seasonal
Variations by Classical Decomposition, 8.4.1 The Additive/Subtractive Model,
8.4.2 The Multiplicative Model, 8.5 Multi-Linear Regression: A Holistic
Approach to Time Series?, 8.5.1 The Additive/Subtractive Linear Model, 8.5.2
The Additive/Subtractive Exponential Model, 8.5.3 The Multiplicative Linear
Model, 8.5.4 The Multiplicative Exponential Model, 8.5.5 Multi-linear
Regression: Reviewing the Options to Make an Informed Decision, 8.6 Excel
Solver Technique for Time Series Analysis, 8.6.1 The Perfect World Scenario,
8.6.2 The Real World Scenario, 8.6.3 Wider examples of the Solver Technique,
8.7
Chapter Review, References, Glossary of Estimating Terms, Index
Alan R. Jones is Principal Consultant at Estimata Limited, aconsultancy service specialising in Estimating Skills Training. He is a Certified Cost Estimator/Analyst (US) and Certified Cost Engineer (CCE) (UK). Prior to setting up his own business, he enjoyed a 40-year career in the UK aerospace and defence industry as an estimatorAlan is a Fellow of the Association of Cost Engineers and a member of the International Cost Estimating and Analysis Association. Historically (some four decades ago), Alan was a graduate in Mathematics from Imperial College of Science and Technology in London, and was an MBA Prize-winner at the Henley Management College.
