ebook ebooks e-book e-books downloaden bei MyEbooks.ch downloaden

Regression Linear Models in Statistics

:	N. H. Bingham, John M. Fry
:	Regression Linear Models in Statistics
:	Springer Verlag London Limited
:	9781848829695
:	1
:	CHF 31.70
:

:	Sonstiges
:	English

:	293
:	DRM
:	PC/MAC/eReader/Tablet
:	PDF

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 Models in Statistics fills the gap between introductory statistical theory and more specialist sources of information. 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. Blyth& E.F. Robertsons' Basic Linear Algebra and Further Linear Algebra.

	Preface	373
	8	373
	Contents	12
	1. Linear Regression	16
	1.1 Introduction	16
	1.2 The Method of Least Squares	18
	1.2.1 Correlation version	22
	1.2.2 Large-sample limit	23
	1.3 The origins of regression	24
	1.4 Applications of regression	26
	1.5 The Bivariate Normal Distribution	29
	1.6 Maximum Likelihood and Least Squares	36
	1.7 Sums of Squares	38
	1.8 Two regressors	41
	Exercises	43
	2. The Analysis of Variance (ANOVA)	48
	2.1 The Chi-Square Distribution	48
	2.2 Change of variable formula and Jacobians	51
	2.3 The Fisher F-distribution	52
	2.4 Orthogonality	53
	2.5 Normal sample mean and sample variance	54
	2.6 One-Way Analysis of Variance	57
	2.7 Two-Way ANOVA	No Replications
	2.8 Two-Way ANOVA: Replications and Interaction	67
	Exercises	71
	3. Multiple Regression	75
	3.1 The Normal Equations	75
	3.2 Solution of the Normal Equations	78
	3.3 Properties of Least-Squares Estimators	84
	3.4 Sum-of-Squares Decompositions	87
	3.4.1 Coefficient of determination	93
	3.5 Chi-Square Decomposition	94
	3.5.1 Idempotence, Trace and Rank	95
	3.5.2 Quadratic forms in normal variates	96
	3.5.3 Sums of Projections	96
	3.6 Orthogonal Projections and Pythagoras's Theorem	99
	3.7 Worked examples	103
	Exercises	108
	4. Further Multilinear Regression	112
	4.1 Polynomial Regression	112
	4.1.1 The Principle of Parsimony	115
	4.1.2 Orthogonal polynomials	116
	4.1.3 Packages	116
	4.2 Analysis of Variance	117
	4.3 The Multivariate Normal Distribution	118
	4.4 The Multinormal Density	124
	4.4.1 Estimation for the multivariate normal	126
	4.5 Conditioning and Regression	128
	4.6 Mean-square prediction	134
	4.7 Generalised least squares and weighted regression	136
	Exercises	138
	5. Adding additional covariates and the Analysisof Covariance	141
	5.1 Introducing further explanatory variables	141
	5.1.1 Orthogonal parameters	145
	5.2 ANCOVA	147
	Interactions	148
	5.2.1 Nested Models	151
	Update	151
	Akaike Information Criterion (AIC)	152
	Step	152
	5.3 Examples	152
	Exercises	157
	6. Linear Hypotheses	161
	6.1 Minimisation Under Constraints	161
	6.2 Sum-of-Squares Decomposition and F-Test	164
	6.3 Applications: Sequential Methods	169
	6.3.1 Forward selection	169
	6.3.2 Backward selection	170
	6.3.3 Stepwise regression	171
	Exercises	172
	7. Model Checking and Transformation of Data	175
	7.1 Deviations from Standard Assumptions	175
	Residual Plots	175
	Scatter Plots	175
	Non-constant Variance	176
	Unaccounted-for Structure	176
	Outliers	176
	Detecting outliers via residual analysis	177
	Influential Data Points	178
	Cook's distance	179
	Non-additive or non-Gaussian errors	180
	Correlated Errors	180
	7.2 Transformation of Data	180
	Dimensional Analysis	183
	7.3 Variance-Stabilising Transformations	183
	Taylor's Power Law	184
	Delta Method	185
	7.4 Multicollinearity	186
	Regression Diagnostics	189
	Exercises	189
	8. Generalised Linear Models	193
	8.1 Introduction	193
	8.2 Definitions and examples	195
	8.2.1 Statistical testing and model comparisons	197
	8.2.2 Analysis of residuals	199
	8.2.3 Athletics times	200
	8.3 Binary models	202
	8.4 Count data, contingency tables and log-linear models	205
	8.5 Over-dispersion and the Negative Binomial Distribution	209
	8.5.1 Practical applications: Analysis of over-dispersed models in R	209
	211	209
	Exercises	212
	9. Other topics	214
	9.1 Mixed models	214
	9.1.1 Mixed models and Generalised Least Squares	217
	9.2 Non-parametric regression	222
	9.2.1 Kriging	224
	9.3 Experimental Design	226
	9.3.1 Optimality criteria	226
	9.3.2 Incomplete designs	227
	9.4 Time series	230
	9.4.1 Cointegration and spurious regression	231
	9.5 Survival analysis	233
	9.5.1 Proportional hazards	235
	9.6 p	235
	9.6 p	235
	236	235
	Solutions	237
	Dramatis Personae: Who did what when	279
	Bibliography	281
	Index	288