Home Page Icon
Home Page
Table of Contents for
Contents
Close
Contents
by Alan R. Jones
Best Fit Lines & Curves
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 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 and 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
Reference
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 functions
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 Microsoft 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 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
Reference
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
Reference
Glossary of estimating and forecasting terms
Legend for Microsoft Excel Worked Example Tables in Greyscale
Index
Search in book...
Toggle Font Controls
Playlists
Add To
Create new playlist
Name your new playlist
Playlist description (optional)
Cancel
Create playlist
Sign In
Email address
Password
Forgot Password?
Create account
Login
or
Continue with Facebook
Continue with Google
Sign Up
Full Name
Email address
Confirm Email Address
Password
Login
Create account
or
Continue with Facebook
Continue with Google
Prev
Previous Chapter
Dedication
Next
Next Chapter
List of Figures
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 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 and 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
Reference
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 functions
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 Microsoft 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 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
Reference
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
Reference
Glossary of estimating and forecasting terms
Legend for Microsoft Excel Worked Example Tables in Greyscale
Index
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 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 and 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
Reference
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 functions
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 Microsoft 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 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
Reference
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
Reference
Glossary of estimating and forecasting terms
Legend for Microsoft Excel Worked Example Tables in Greyscale
Index
i
ii
iii
iv
v
vi
vii
viii
ix
x
xi
xii
xiii
xiv
xv
xvi
xvii
xviii
xix
xx
xxi
xxx
xxxi
xxxii
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
Guide
Cover
Title
Copyright
Dedication
Contents
List of Figures
List of Tables
Foreword
Start of Content
Glossary of estimating and forecasting terms
Legend for Microsoft Excel Worked Example Tables in Greyscale
Index
Add Highlight
No Comment
..................Content has been hidden....................
You can't read the all page of ebook, please click
here
login for view all page.
Day Mode
Cloud Mode
Night Mode
Reset