Table Of Content“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. Thank-
fully, 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 estimat-
ing using experientially based models to analyse the most appropriate, repeatable, trans-
parent 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 author’s
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 estimat-
ing 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 publi-
cations 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.
Alan’s 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 under-
standing 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 Jones’s “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
Best Fit Lines and Curves, and Some
Mathe-Magical Transformations
Best Fit Lines and Curves, and Some Mathe-Magical Transformations (Volume III of the Work-
ing 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 rela-
tionships 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, accoun-
tants, project risk specialists as well as students of cost engineering.
Alan Jones is Principal Consultant at Estimata Limited, an estimating consultancy
service. He is a Certified Cost Estimator/Analyst (US) and Certified Cost Engineer
(CCE) (UK). Prior to setting up his own business, he has enjoyed a 40-year career in
the UK aerospace and defence industry as an estimator, culminating in the role of Chief
Estimator at BAE Systems. Alan 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 (. . . that was slightly more recent, being only two decades ago).
Oh, how time flies when you are enjoying yourself.
Working Guides to Estimating & Forecasting
Alan R. Jones
As engineering and construction projects get bigger, more ambitious and increasingly
complex, the ability of organisations to work with realistic estimates of cost, risk or sched-
ule has become fundamental. Working with estimates requires technical and mathemat-
ical skills from the estimator but it also requires an understanding of the processes, the
constraints and the context by those making investment and planning decisions. You can
only forecast the future with confidence if you understand the limitations of your forecast.
The Working Guides to Estimating & Forecasting introduce, explain and illustrate the
variety and breadth of numerical techniques and models that are commonly used to
build estimates. Alan Jones defines the formulae that underpin many of the techniques;
offers justification and explanations for those whose job it is to interpret the estimates;
advice on pitfalls and shortcomings; and worked examples. These are often tabular in
form to allow you to reproduce the examples in Microsoft Excel. Graphical or pictorial
figures are also frequently used to draw attention to particular points as the author advo-
cates that you should always draw a picture before and after analysing data.
The five volumes in the Series provide expert applied advice for estimators, engineers,
accountants, project risk specialists as well as students of cost engineering, based on the
author’s thirty-something years’ experience as an estimator, project planner and controller.
Volume I Principles, Process and Practice of Professional Number Juggling
Alan R. Jones
Volume II Probability, Statistics and Other Frightening Stuff
Alan R. Jones
Volume III Best Fit Lines and Curves, and Some Mathe-Magical
Transformations
Alan R. Jones
Volume IV Learning, Unlearning and Re-learning Curves
Alan R. Jones
Volume V Risk, Opportunity, Uncertainty and Other Random Models
Alan R. Jones
Best Fit Lines and Curves,
and Some Mathe-Magical
Transformations
Alan R. Jones
First published 2019
by Routledge
2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN
and by Routledge
711 Third Avenue, New York, NY 10017
Routledge is an imprint of the Taylor & Francis Group, an informa business
© 2019 Alan R. Jones
The right of Alan Jones to be identified as authors of this work has been asserted by him in
accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988.
All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form
or by any electronic, mechanical, or other means, now known or hereafter invented, including
photocopying and recording, or in any information storage or retrieval system, without
permission in writing from the publishers.
Trademark notice: Product or corporate names may be trademarks or registered trademarks, and
are used only for identification and explanation without intent to infringe.
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library
Library of Congress Cataloging-in-Publication Data
Names: Jones, Alan (Alan R.), 1953- author.
Title: Best fit lines and curves : and some mathe-magical transformations / Alan Jones.
Description: Abingdon, Oxon ; New York, NY : Routledge, 2018. |
Series: Working guides to estimating & forecasting ; volume 3 |
Includes bibliographical references and index.
Identifiers: LCCN 2017059102 (print) | LCCN 2018000657 (ebook) |
ISBN 9781315160085 (eBook) | ISBN 9781138065000 (hardback : alk. paper)
Subjects: LCSH: Industrial engineering—Statistical methods. | Regression analysis. |
Costs, Industrial—Estimates. | Costs, Industrial—Statistical methods.
Classification: LCC T57.35 (ebook) | LCC T57.35 .J66 2018 (print) |
DDC 519.5/6—dc23
LC record available at https://lccn.loc.gov/2017059102
ISBN: 9781138065000 (hbk)
ISBN: 9781315160085 (ebk)
Typeset in Bembo
by Apex CoVantage, LLC
To my family:
Lynda, Martin, Gareth and Karl
Thank you for your support and forbearance, and for understanding
why I wanted to do this.
My thanks also to my friends and former colleagues at BAE Systems and the wider
Estimating Community for allowing me the opportunity to learn, develop and practice
my profession, . . . and for suffering my brand of humour over the years.
In particular, a special thanks to Tracey C, Mike C, Mick P and Andy L for your
support, encouragement and wise counsel. (You know who you are!)
Contents
List of Figures xv
List of Tables xxi
Foreword xxxi
1 Introduction and objectives 1
1.1 Why write this book? Who might find it useful? Why five volumes? 1
1.1.1 Why write this series? Who might find it useful? 1
1.1.2 Why five volumes? 2
1.2 Features you’ll find in this book and others in this series 2
1.2.1 Chapter context 3
1.2.2 The lighter side (humour) 3
1.2.3 Quotations 3
1.2.4 Definitions 3
1.2.5 Discussions and explanations with a mathematical
slant for Formula-philes 4
1.2.6 Discussions and explanations without a mathematical
slant for Formula-phobes 5
1.2.7 Caveat augur 5
1.2.8 Worked examples 6
1.2.9 Useful Microsoft Excel functions and facilities 6
1.2.10 References to authoritative sources 7
1.2.11 Chapter reviews 7
1.3 Overview of chapters in this volume 7
1.4 Elsewhere in the ‘Working Guide to Estimating & Forecasting’ series 8
1.4.1 Volume I: Principles, Process and Practice of Professional
Number Juggling 9
1.4.2 Volume II: Probability, Statistics and Other Frightening Stuff 10
1.4.3 Volume III: Best Fit Lines and Curves, and
Some Mathe-Magical Transformations 11
