book

Best Fit Lines & Curves

Name: Best Fit Lines & Curves
Author: Alan Jones
ISBN: 9781351661447

by Alan Jones

October 2018

Intermediate to advanced

530 pages

14h 2m

English

Routledge

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Cover
Title
Copyright
Dedication
Contents
List of Figures
List of Tables
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 series1.2.1 Chapter context1.2.2 The lighter side (humour)1.2.3 Quotations1.2.4 Definitions1.2.5 Discussions and explanations with a mathematical slant for Formula-philes1.2.6 Discussions and explanations without a mathematical slant for Formula-phobes1.2.7 Caveat augur1.2.8 Worked examples1.2.9 Useful Microsoft Excel functions and facilities1.2.10 References to authoritative sources1.2.11 Chapter reviews1.3 Overview of chapters in this volume1.4 Elsewhere in the ‘Working Guide to Estimating & Forecasting’ series1.4.1 Volume I: Principles, Process and Practice of Professional Number Juggling1.4.2 Volume II: Probability, Statistics and Other Frightening Stuff1.4.3 Volume III: Best Fit Lines and Curves, and Some Mathe-Magical Transformations1.4.4 Volume IV: Learning, Unlearning and Re-learning curves1.4.5 Volume V: Risk, Opportunity, Uncertainty and Other Random Models1.5 Final thoughts and musings on this volume and seriesReferences
2 Linear and nonlinear properties (!) of straight lines
2.1 Basic linear properties2.1.1 Inter-relation between slope and intercept2.1.2 The difference between two straight lines is a straight line2.2 The Cumulative Value (nonlinear) property of a linear sequence2.2.1 The Cumulative Value of a Discrete Linear Function2.2.2 The Cumulative Value of a Continuous Linear Function2.2.3 Exploiting the Quadratic Cumulative Value of a straight line2.3 Chapter reviewReference

3 Trendsetting with some Simple Moving Measures
3.1 Going all trendy: The could and the should3.1.1 When should we consider trend smoothing?3.1.2 When is trend smoothing not appropriate?3.2 Moving Averages3.2.1 Use of Moving Averages3.2.2 When not to use Moving Averages3.2.3 Simple Moving Average3.2.4 Weighted Moving Average3.2.5 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 thinking3.2.8 Dealing with missing data3.2.9 Uncertainty Range around the Moving Average3.3 Moving Medians3.3.1 Choosing the Moving Median Interval3.3.2 Dealing with missing data3.3.3 Uncertainty Range around the Moving Median3.4 Other Moving Measures of Central Tendency3.4.1 Moving Geometric Mean3.4.2 Moving Harmonic Mean3.4.3 Moving Mode3.5 Exponential Smoothing3.5.1 An unfortunate dichotomy3.5.2 Choice of Smoothing Constant, or Choice of Damping Factor3.5.3 Uses for Exponential Smoothing3.5.4 Double and Triple Exponential Smoothing3.6 Cumulative Average and Cumulative Smoothing3.6.1 Use of Cumulative Averages3.6.2 Dealing with missing data3.6.3 Cumulative Averages with batch data3.6.4 Being slightly more creative – Cumulative Average on a sliding scale3.6.5 Cumulative Smoothing3.7 Chapter reviewReferences
4 Simple and Multiple Linear Regression
4.1 What is Regression Analysis?4.1.1 Least Squares Best Fit4.1.2 Two key sum-to-zero properties of Least Squares4.2 Simple Linear Regression4.2.1 Simple Linear Regression using basic Excel functions4.2.2 Simple Linear Regression using the Data Analysis Add-in Tool Kit in Excel4.2.3 Simple Linear Regression using advanced Excel functions4.3 Multiple Linear Regression4.3.1 Using categorical data in Multiple Linear Regression4.3.2 Multiple Linear Regression using the Data Analysis Add-in Tool Kit in Excel4.3.3 Multiple Linear Regression using advanced Excel functions4.4 Dealing with Outliers in Regression Analysis?4.5 How good is our Regression? Six key measures4.5.1 Coefficient of Determination (R-Square): A measure of linearity?!4.5.2 F-Statistic: A measure of chance occurrence4.5.3 t-Statistics: Measures of Relevance or Significant Contribution4.5.4 Regression through the origin4.5.5 Role of common sense as a measure of goodness of fit4.5.6 Coefficient of Variation as a measure of tightness of fit4.5.7 White's Test for heteroscedasticity ... and, by default, homoscedasticity4.6 Prediction and Confidence Intervals – Measures of uncertainty4.6.1 Prediction Intervals and Confidence Intervals: What's the difference?4.6.2 Calculating Prediction Limits and Confidence Limits for Simple Linear Regression4.6.3 Calculating Prediction Limits and Confidence Limits for Multi-Linear Regression4.7 Stepwise Regression4.7.1 Backward Elimination4.7.2 Forward Selection4.7.3 Backward or Forward Selection – Which should we use?4.7.4 Choosing the best model when we are spoilt for choice4.8 Chapter reviewReferences
5 Linear transformation: Making bent lines straight
5.1 Logarithms5.1.1 Basic properties of powers5.1.2 Basic properties of logarithms5.2 Basic linear transformation: Four Standard Function types5.2.1 Linear functions5.2.2 Logarithmic Functions5.2.3 Exponential Functions5.2.4 Power Functions5.2.5 Transforming with Microsoft Excel5.2.6 Is the transformation really better, or just a mathematical sleight of hand?5.3 Advanced linear transformation: Generalised Function types5.3.1 Transforming Generalised Logarithmic Functions5.3.2 Transforming Generalised Exponential Functions5.3.3 Transforming Generalised Power Functions5.3.4 Reciprocal Functions – Special cases of Generalised Power Functions5.3.5 Transformation options5.4 Finding the Best Fit Offset Constant5.4.1 Transforming Generalised Function Types into Standard Functions5.4.2 Using the Random-Start Bisection Method (Technique)5.4.3 Using Microsoft Excel's Goal Seek or Solver5.5 Straightening out Earned Value Analysis ... or EVM Disintegration5.5.1 EVM terminology5.5.2 Taking a simpler perspective5.6 Linear transformation based on Cumulative Value Disaggregation5.7 Chapter reviewReferences
6 Transforming Nonlinear Regression
6.1 Simple Linear Regression of a linear transformation6.1.1 Simple Linear Regression with a Logarithmic Function6.1.2 Simple Linear Regression with an Exponential Function6.1.3 Simple Linear Regression with a Power Function6.1.4 Reversing the transformation of Logarithmic, Exponential and Power Functions6.2 Multiple Linear Regression of a multi-linear transformation6.2.1 Multi-linear Regression using linear and linearised Logarithmic Functions6.2.2 Multi-Linear Regression using linearised Exponential and Power Functions6.3 Stepwise Regression and multi-linear transformations6.3.1 Stepwise Regression by Backward Elimination with linear transformations6.3.2 Stepwise Regression by Forward Selection with linear transformations6.4 Is the Best Fit really the better fit?6.5 Regression of Transformed Generalised Nonlinear Functions6.5.1 Linear Regression of a Transformed Generalised Logarithmic Function6.5.2 Linear Regression of a Transformed Generalised Exponential Function6.5.3 Linear Regression of a Transformed Generalised Power Function6.5.4 Generalised Function transformations: Avoiding the pitfalls and tripwires6.6 Pseudo Multi-linear Regression of Polynomial Functions6.6.1 Offset Quadratic Regression of the Cumulative of a straight line6.6.2 Example of a questionable Cubic Regression of three linear variables6.7 Chapter reviewReferences
7 Least Squares Nonlinear Curve Fitting without the logs
7.1 Curve Fitting by Least Squares ... without the logarithms7.1.1 Fitting data to Discrete Probability Distributions7.1.2 Fitting data to Continuous Probability Distributions7.1.3 Revisiting the Gamma Distribution Regression7.2 Chapter reviewReference
8 The ups and downs of Time Series Analysis
8.1 The bits and bats ... and buts of a Time Series8.1.1 Conducting a Time Series Analysis8.2 Alternative Time Series Models8.2.1 Additive/Subtractive Time Series Model8.2.2 Multiplicative Time Series Model8.3 Classical Decomposition: Determining the underlying trend8.3.1 See-Saw ... Regression flaw?8.3.2 Moving Average Seasonal Smoothing8.3.3 Cumulative Average Seasonal Smoothing8.3.4 What happens when our world is not perfect? Do any of these trends work?8.3.5 Exponential trends and seasonal funnels8.3.6 Meandering trends8.4 Determining the seasonal variations by Classical Decomposition8.4.1 The Additive/Subtractive Model8.4.2 The Multiplicative Model8.5 Multi-Linear Regression: A holistic approach to Time Series?8.5.1 The Additive/Subtractive Linear Model8.5.2 The Additive/Subtractive Exponential Model8.5.3 The Multiplicative Linear Model8.5.4 The Multiplicative Exponential Model8.5.5 Multi-Linear Regression: Reviewing the options to make an informed decision8.6 Excel Solver technique for Time Series Analysis8.6.1 The Perfect World scenario8.6.2 The Real World scenario8.6.3 Wider examples of the Solver technique8.7 Chapter reviewReference
Glossary of estimating and forecasting terms
Legend for Microsoft Excel Worked Example Tables in Greyscale
Index

Content preview from Best Fit Lines & Curves

2 Linear and nonlinear properties (!) of straight lines

Q: When is a straight line not a straight line? A: When it has been bent!

Now we might well be thinking ‘Why would we want to do that as we have already intimated that straight lines are easier to extrapolate or project than curves?’ However, in the case of sequential linear relationships, we don’t have to bend straight lines because they already possess the property that their Cumulative Values always form a Quadratic Function (i.e. a Polynomial of Order 2) – a distinctly curved line. Furthermore, the Quadratic will have coefficients or parameters that are simple functions of the slope and intercept of the straight line.

Before we delve into this perhaps lesser known property, let’s remind ...

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Best Fit Lines & Curves

by Alan Jones

2 Linear and nonlinear properties (!) of straight lines

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.