Best fit lines and curves, and some mathe-magical transformations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London
Routledge, Taylor & Francis Group
2019
|
| Series: | Working guides to estimating & forecasting
volume 3 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xxxii, 497 Seiten |
| ISBN: | 9781138065000 |
Staff View
MARC
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| 245 | 1 | 0 | |a Best fit lines and curves, and some mathe-magical transformations |c Alan R. Jones |
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Record in the Search Index
| _version_ | 1804178886008766464 |
|---|---|
| adam_text | 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 6c 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
11
12
13
14
15
15
18
19
21
21
26
34
43
44
45
45
45
47
48
49
49
50
54
58
66
68
70
71
81
83
84
84
85
87
87
88
89
89
Contents
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
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
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 MovingAverage 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 MovingAverage
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 Flarmonic Mean
3.4.3 Moving Mode
3.5 Exponential Smoothing
3.5,1 An unfortunate dichotomy
Contents
xi
3*5.2 Choice of Smoothing Constant, or Choice of
Damping Factor 92
3.5.3 Uses for Exponential Smoothing 94
3.5.4 Double and Triple Exponential Smoothing 95
3.6 Cumulative Average and Cumulative Smoothing 96
3.6.1 Use of Cumulative Averages 97
3.6.2 Dealing with missing data 101
3.6.3 Cumulative Averages with batch data 103
3.6.4 Being slightly more creative — Cumulative Average
on a sliding scale 103
3.6.5 Cumulative Smoothing 105
3.7 Chapter review 110
References 112
4 Simple and Multiple Linear Regression 113
4.1 What is Regression Analysis? 113
4.1.1 Least Squares Best Fit 115
4.1.2 Two key sum-to-zero properties of Least Squares 120
4.2 Simple Linear Regression 122
4.2.1 Simple Linear Regression using basic Excel functions 123
4.2.2 Simple Linear Regression using the Data Analysis
Add-in Tool Kit in Excel 125
4.2.3 Simple Linear Regression using advanced Excel functions 127
4.3 Multiple Linear Regression 129
4.3.1 Using categorical data in Multiple Linear Regression 131
4.3.2 Multiple Linear Regression using the Data Analysis
Add-in Tool Kit in Excel 133
4.3.3 Multiple Linear Regression using advanced Excel functions 136
4.4 Dealing with Outliers in Regression Analysis? 138
4.5 How good is our Regression? Six key measures 140
4.5.1 Coefficient of Determination (R-Square):
A measure of linearity?! 141
4.5.2 F-Statistic: A measure of chance occurrence 149
4.5.3 t-Statistics: Measures of Relevance or Significant Contribution 156
4.5.4 Regression through the origin 162
4.5.5 Role of common sense as a measure of goodness of fit 171
4.5.6 Coefficient of Variation as a measure of tightness of fit 172
4.5.7 Whites Test for heteroscedasticity ... and,
by default, homoscedasticity 174
4.6 Prediction and Confidence Intervals — Measures of uncertainty 179
4.6.1 Prediction Intervals and Confidence Intervals:
Whats the difference?
180
Contents
xii
4.6.2 Calculating Prediction Limits and Confidence
Limits for Simple Linear Regression 182
4.6.3 Calculating Prediction Limits and Confidence
Limits for Multi-Linear Regression 185
4.7 Stepwise Regression 193
4.7.1 Backward Elimination 197
4.7.2 Forward Selection 201
4.7.3 Backward or Forward Selection — Which should we use? 206
4.7.4 Choosing the best model when we are spoilt for choice 208
4.8 Chapter review 209
References 210
5 Linear transformation: Making bent lines straight 211
5.1 Logarithms 212
5.1.1 Basic properties of powers 213
5.1.2 Basic properties of logarithms 216
5.2 Basic linear transformation: Four Standard Function types 222
5.2.1 Linear functions 223
5.2.2 Logarithmic Functions 225
5.2.3 Exponential Functions 230
5.2.4 Power Functions 233
5.2.5 Transforming with Microsoft Excel 237
5.2.6 Is the transformation really better, or just a
mathematical sleight of hand? 242
5.3 Advanced linear transformation: Generalised Function types 244
5.3.1 Transforming Generalised Logarithmic Functions 245
5.3.2 Transforming Generalised Exponential Functions 249
5.3.3 Transforming Generalised Power Functions 250
5.3.4 Reciprocal Functions - Special cases of Generalised
Power Functions 253
5.3.5 Transformation options 254
5.4 Finding the Best Fit Offset Constant 257
5.4.1 Transforming Generalised Function Types into
Standard Functions 259
5.4.2 Using the Random-Start Bisection Method (Technique) 260
5.4.3 Using Microsoft Excel’s Goal Seek or Solver 263
5.5 Straightening out Earned Value Analysis ... or EVM Disintegration 271
5.5.1 EVM terminology 271
5.5.2 Taking a simpler perspective 274
5.6 Linear transformation based on Cumulative Value Disaggregation 279
5.7 Chapter review 281
References 283
Contents
xiii
6 Transforming Nonlinear Regression 284
6.1 Simple Linear Regression of a linear transformation 284
6.1.1 Simple Linear Regression with a Logarithmic Function 288
6.1.2 Simple Linear Regression with an Exponential Function 291
6.1.3 Simple Linear Regression with a Power Function 298
6.1.4 Reversing the transformation of Logarithmic,
Exponential and Power Functions 299
6.2 Multiple Linear Regression of a multi-linear transformation 300
6.2.1 Multi-linear Regression using linear and linearised
Logarithmic Functions 302
6.2.2 Multi-Linear Regression using linearised Exponential
and Power Functions 312
6.3 Stepwise Regression and multi-linear transformations 323
6.3.1 Stepwise Regression by Backward Elimination with linear
transformations 323
6.3.2 Stepwise Regression by Forward Selection with
linear transformations 330
6.4 Is the Best Fit really the better fit? 333
6.5 Regression of Transformed Generalised
Nonlinear Functions 337
6.5.1 Linear Regression of a Transformed Generalised
Logarithmic Function 342
6.5.2 Linear Regression of a Transformed Generalised
Exponential Function 348
6.5.3 Linear Regression of a Transformed Generalised
Power Function 351
6.5.4 Generalised Function transformations: Avoiding the
pitfalls and tripwires 357
6.6 Pseudo Multi-linear Regression of Polynomial Functions 359
6.6.1 Offset Quadratic Regression of the Cumulative of
a straight line 361
6.6.2 Example of a questionable Cubic Regression of three
linear variables 368
6.7 Chapter review 378
References 379
7 Least Squares Nonlinear Curve Fitting without the logs 380
7.1 Curve Fitting by Least Squares . .. without the logarithms 381
7.1.1 Fitting data to Discrete Probability Distributions 381
7.1.2 Fitting data to Continuous Probability Distributions 391
7.1.3 Revisiting the Gamma Distribution Regression 399
7.2 Chapter review 406
Reference 406
XIV
Contents
8 The ups and downs of Time Series Analysis 407
8.1 The bits and bats . .. and buts of a Time Series 408
8.1-1 Conducting a Time Series Analysis 411
8.2 Alternative Time Series Models 411
8.2.1 Additive/Subtractive Time Series Model 412
8-2.2 Multiplicative Time Series Model 413
8.3 Classical Decomposition: Determining the underlying trend 415
8.3.1 See-Saw . .. Regression flaw? 416
8.3.2 Moving Average Seasonal Smoothing 420
8.3.3 Cumulative Average Seasonal Smoothing 422
8.3.4 What happens when our world is not perfect?
Do any of these trends work? 424
8.3.5 Exponential trends and seasonal funnels 430
8.3.6 Meandering trends 436
8.4 Determining the seasonal variations by
Classical Decomposition 437
8.4.1 The Additive/Subtractive Model 438
8.4.2 The Multiplicative Model 440
8.5 Multi-Linear Regression: A holistic approach to
Time Series? 443
8.5.1 The Additive/Subtractive Linear Model 444
8.5.2 The Additive/Subtractive Exponential Model 449
8.5.3 The Multiplicative Linear Model 452
8.5.4 The Multiplicative Exponential Model 456
8.5.5 Multi-Linear Regression: Reviewing the options to
make an informed decision 460
8.6 Excel Solver technique for Time Series Analysis 461
8.6.1 The Perfect World scenario 462
8.6.2 The Real World scenario 465
8.6.3 Wider examples of the Solver technique 468
8.7 Chapter review 468
Reference 469
Glossary of estimating and forecasting terms 470
Legend for Microsoft Excel Worked Example Tables in Greyscale 489
Index 491
|
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| physical | xxxii, 497 Seiten |
| publishDate | 2019 |
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| publisher | Routledge, Taylor & Francis Group |
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| spelling | Jones, Alan R. 1953- Verfasser (DE-588)1161098445 aut Best fit lines and curves, and some mathe-magical transformations Alan R. Jones London Routledge, Taylor & Francis Group 2019 xxxii, 497 Seiten txt rdacontent n rdamedia nc rdacarrier Working guides to estimating & forecasting volume 3 Industrial engineering Statistical methods Regression analysis Costs, Industrial Estimates Costs, Industrial Statistical methods Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf Kostenschätzung (DE-588)4114297-4 gnd rswk-swf Regressionsanalyse (DE-588)4129903-6 s Zeitreihenanalyse (DE-588)4067486-1 s Kostenschätzung (DE-588)4114297-4 s b DE-604 Erscheint auch als Online-Ausgabe Jones, Alan (Alan R.), 1953- author Best fit lines and curves Abingdon, Oxon ; New York, NY : Routledge, 2018 978-1-315-16008-5 Working guides to estimating & forecasting volume 3 (DE-604)BV045215706 3 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030580042&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jones, Alan R. 1953- Best fit lines and curves, and some mathe-magical transformations Working guides to estimating & forecasting Industrial engineering Statistical methods Regression analysis Costs, Industrial Estimates Costs, Industrial Statistical methods Regressionsanalyse (DE-588)4129903-6 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd Kostenschätzung (DE-588)4114297-4 gnd |
| subject_GND | (DE-588)4129903-6 (DE-588)4067486-1 (DE-588)4114297-4 |
| title | Best fit lines and curves, and some mathe-magical transformations |
| title_auth | Best fit lines and curves, and some mathe-magical transformations |
| title_exact_search | Best fit lines and curves, and some mathe-magical transformations |
| title_full | Best fit lines and curves, and some mathe-magical transformations Alan R. Jones |
| title_fullStr | Best fit lines and curves, and some mathe-magical transformations Alan R. Jones |
| title_full_unstemmed | Best fit lines and curves, and some mathe-magical transformations Alan R. Jones |
| title_short | Best fit lines and curves, and some mathe-magical transformations |
| title_sort | best fit lines and curves and some mathe magical transformations |
| topic | Industrial engineering Statistical methods Regression analysis Costs, Industrial Estimates Costs, Industrial Statistical methods Regressionsanalyse (DE-588)4129903-6 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd Kostenschätzung (DE-588)4114297-4 gnd |
| topic_facet | Industrial engineering Statistical methods Regression analysis Costs, Industrial Estimates Costs, Industrial Statistical methods Regressionsanalyse Zeitreihenanalyse Kostenschätzung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030580042&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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