Regression: linear models in statistics
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London
Springer
[2010]
|
| Schriftenreihe: | Springer undergraduate mathematics series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | xiii, 284 Seiten Illustrationen |
| ISBN: | 9781848829688 9781848829695 |
Internformat
MARC
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| 100 | 1 | |a Bingham, Nicholas H. |d 1945- |0 (DE-588)118095315 |4 aut | |
| 245 | 1 | 0 | |a Regression |b linear models in statistics |c N. H. Bingham ; John M. Fry |
| 264 | 1 | |a London |b Springer |c [2010] | |
| 264 | 4 | |c © 2010 | |
| 300 | |a xiii, 284 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer undergraduate mathematics series | |
| 650 | 4 | |a Regression analysis | |
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| 655 | 7 | |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-018702204 | ||
Datensatz im Suchindex
| _version_ | 1804140813362397184 |
|---|---|
| adam_text | Contents
1. Linear Regression........................................... 1
1.1
Introduction
............................................. 1
1.2
The Method of Least
Squares..............................
З
1.2.1
Correlation version
................................. 7
1.2.2
Large-sample limit
.................................. 8
1.3
The origins of regression
................................... 9
1.4
Applications of regression
.................................. 11
1.5
The Bivariate Normal Distribution
......................... 14
1.6
Maximum Likelihood and Least Squares
..................... 21
1.7
Sums of Squares
.......................................... 23
1.8
Two regressors
........................................... 26
Exercises
.................................................... 28
2.
The Analysis of Variance (ANOVA)
........................ 33
2.1
The Chi-Square Distribution
............................... 33
2.2
Change of variable formula and Jacobians
................... 36
2.3
The Fisher F-distribution
.................................. 37
2.4
Orthogonality
............................................ 38
2.5
Normal sample mean and sample variance
................... 39
2.6
One-Way Analysis of Variance
............................. 42
2.7
Two-Way ANOVA; No Replications
......................... 49
2.8
Two-Way ANOVA: Replications and Interaction
.............. 52
Exercises
.................................................... 56
3.
Multiple Regression
........................................ 61
3.1
The Normal Equations
.................................... 61
xi
x¡¡
Contents
3.2
Solution of the Normal Equations
.......................... 64
3.3
Properties of Least-Squares Estimators
...................... 70
3.4
Sum-of-Squares Decompositions
............................ 73
3.4.1
Coefficient of determination
.......................... 79
3.5
Chi-Square Decomposition
................................. 80
3.5.1
Idempotence, Trace and Rank
........................ 81
3.5.2
Quadratic forms in normal
variâtes
................... 82
3.5.3
Sums of Projections
................................ 82
3.6
Orthogonal Projections and Pythagoras s Theorem
........... 85
3.7
Worked examples
......................................... 89
Exercises
.................................................... 94
4.
Further Multilinear Regression
............................. 99
4.1
Polynomial Regression
.................................... 99
4.1.1
The Principle of Parsimony
..........................102
4.1.2
Orthogonal polynomials
.............................103
4.1.3
Packages
..........................................103
4.2
Analysis of Variance
......................................104
4.3
The Multivariate Normal Distribution
.......................105
4.4
The
Multinormal
Density
..................................
Ill
4.4.1
Estimation for the multivariate normal
................113
4.5
Conditioning and Regression
...............................115
4.6
Mean-square prediction
...................................121
4.7
Generalised least squares and weighted regression
.............123
Exercises
....................................................125
5.
Adding additional covariates and the Analysis
of Covariance
...............................................129
5.1
Introducing further explanatory variables
....................129
5.1.1
Orthogonal parameters
..............................133
5.2
ANCOVA
...............................................135
5.2.1
Nested Models
.....................................139
5.3
Examples
................................................140
Exercises
....................................................145
6.
Linear Hypotheses
..........................................149
6.1
Minimisation Under Constraints
............................149
6.2
Sum-of-Squares Decomposition and F-Test
...................152
6.3
Applications: Sequential Methods
...........................157
6.3.1
Forward selection
...................................157
6.3.2
Backward selection
.................................158
6.3.3
Stepwise regression
.................................159
Exercises
.......................... ........160
Contents xiii
7. Model
Checking
and Transformation
of Data
...............163
7.1
Deviations from Standard Assumptions
.....................163
7.2
Transformation of Data
...................................168
7.3
Variance-Stabilising Transformations
........................171
7.4
Multicollinearity
.........................................174
Exercises
....................................................177
8.
Generalised Linear Models
.................................181
8.1
Introduction
.............................................181
8.2
Definitions and examples
..................................183
8.2.1
Statistical testing and model comparisons
.............185
8.2.2
Analysis of residuals
................................187
8.2.3
Athletics times
.....................................188
8.3
Binary models
...........................................190
8.4
Count data, contingency tables and log-linear models
.........193
8.5
Over-dispersion and the Negative Binomial Distribution
.......197
8.5.1
Practical applications: Analysis of over-dispersed models
in R®
.............................................199
Exercises
....................................................200
9.
Other topics
................................................203
9.1
Mixed models
............................................203
9.1.1
Mixed models and Generalised Least Squares
..........206
9.2
Non-parametric regression
.................................211
9.2.1
Kriging
...........................................213
9.3
Experimental Design
......................................215
9.3.1
Optimality criteria
.................................215
9.3.2
Incomplete designs
.................................216
9.4
Time series
..............................................219
9.4.1
Cointegration
and spurious regression
.................220
9.5
Survival analysis
.........................................222
9.5.1
Proportional hazards
...............................224
9.6
p»n
..................................................225
Solutions
.......................................................227
Dramatis
Personae:
Who did what when
.......................269
Bibliography
....................................................271
Index
...........................................................279
The Springer Undergraduate Mathematics Series (SUMS) is designed for
undergraduates in the mathematical sciences. From core foundational material
to final year topics, SUMS books take a fresh and modern approach and are ideal
for self-study or for a one- or two-semester course. Each book includes numerous
examples, problems and fully-worked solutions.
N.
H. Bingham
·
John M. Fry
Regression
Regression is the branch of Statistics in which a dependent variable of interest is
modelled as a linear combination of one or more predictor variables, together with
a random error. The subject is inherently two- or higher- dimensional, thus an
understanding of Statistics in one dimension is essential.
Regression: Linear Modeb in Statistics fills the gap between introductory statistical theory
and more specialist sources
ofinformation.
In doing so, it provides the reader with a
number of worked examples, and exercises with full solutions.
The book begins with simple linear regression (one predictor variable), and analysis of
variance
(ANOVA),
and then further explores the area through inclusion of topics such
as multiple linear regression (several predictor variables) and analysis of covariance
(ANCOVA). The book concludes with special topics such as non-parametric regression
and mixed models, time series, spatial processes and design of experiments.
Aimed at
2nd
and
3rd
year undergraduates studying Statistics, Regression: Linear Models
in Statistics requires a basic knowledge of (one-dimensional) Statistics, as well as
Probability and standard Linear Algebra. Possible companions include John Haigh s
Probability Models, and T. S. Bh/th
&
E.F. Robertsons Basic Linear Algebra and Further
Linear Algebra.
ISBN
978-1-84882-968-8
|
| any_adam_object | 1 |
| author | Bingham, Nicholas H. 1945- Fry, John 1980- |
| author_GND | (DE-588)118095315 (DE-588)142838136 |
| author_facet | Bingham, Nicholas H. 1945- Fry, John 1980- |
| author_role | aut aut |
| author_sort | Bingham, Nicholas H. 1945- |
| author_variant | n h b nh nhb j f jf |
| building | Verbundindex |
| bvnumber | BV035843964 |
| classification_rvk | SK 830 SK 840 |
| ctrlnum | (OCoLC)449852100 (DE-599)DNB996986057 |
| dewey-full | 519.536 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.536 |
| dewey-search | 519.536 |
| dewey-sort | 3519.536 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| institution | BVB |
| isbn | 9781848829688 9781848829695 |
| language | English |
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| spelling | Bingham, Nicholas H. 1945- (DE-588)118095315 aut Regression linear models in statistics N. H. Bingham ; John M. Fry London Springer [2010] © 2010 xiii, 284 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Springer undergraduate mathematics series Regression analysis Lineares Regressionsmodell (DE-588)4127971-2 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Lineares Regressionsmodell (DE-588)4127971-2 s DE-604 Fry, John 1980- (DE-588)142838136 aut Erscheint auch als Online-Ausgabe 978-1-84882-969-5 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018702204&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018702204&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Bingham, Nicholas H. 1945- Fry, John 1980- Regression linear models in statistics Regression analysis Lineares Regressionsmodell (DE-588)4127971-2 gnd |
| subject_GND | (DE-588)4127971-2 (DE-588)4123623-3 |
| title | Regression linear models in statistics |
| title_auth | Regression linear models in statistics |
| title_exact_search | Regression linear models in statistics |
| title_full | Regression linear models in statistics N. H. Bingham ; John M. Fry |
| title_fullStr | Regression linear models in statistics N. H. Bingham ; John M. Fry |
| title_full_unstemmed | Regression linear models in statistics N. H. Bingham ; John M. Fry |
| title_short | Regression |
| title_sort | regression linear models in statistics |
| title_sub | linear models in statistics |
| topic | Regression analysis Lineares Regressionsmodell (DE-588)4127971-2 gnd |
| topic_facet | Regression analysis Lineares Regressionsmodell Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018702204&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018702204&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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