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El. knyga: Regression Graphics - Ideas for Studying Regressions through Graphics: Ideas for Studying Regressions Through Graphics [Wiley Online]

R. Dennis Cook (The University of Minnesota, St. Paul)

Formatas: 349 pages
Serija: Wiley Series in Probability and Statistics
Išleidimo metai: 19-Oct-1998
Leidėjas: Wiley-Interscience
ISBN-10: 470316934
ISBN-13: 9780470316931

Kitos knygos pagal šią temą:

Wiley Online
Kaina: 200,89 €*
* this price gives unlimited concurrent access for unlimited time

Formatas: 349 pages
Serija: Wiley Series in Probability and Statistics
Išleidimo metai: 19-Oct-1998
Leidėjas: Wiley-Interscience
ISBN-10: 470316934
ISBN-13: 9780470316931

Kitos knygos pagal šią temą:

More info about Wiley Online

Partnerių interneto svetainė: https://onlinelibrary.wiley.com/doi/book/10.1002/9780470316931

Developed from lecture notes for a one-quarter graduate course for students who had at least a year of mathematical statistics and two quarters of linear models under their hats. Focuses narrowly on new ideas for graphical representation of statistics made possible by the growing power of computers. Emphasizes a relatively new statistical context for regression and regression graphics that is intended to blend with rather than replace more traditional paradigms for regression analysis. Annotation c. by Book News, Inc., Portland, Or.

An exploration of regression graphics through computer graphics.

Recent developments in computer technology have stimulated new and exciting uses for graphics in statistical analyses. Regression Graphics, one of the first graduate-level textbooks on the subject, demonstrates how statisticians, both theoretical and applied, can use these exciting innovations. After developing a relatively new regression context that requires few scope-limiting conditions, Regression Graphics guides readers through the process of analyzing regressions graphically and assessing and selecting models. This innovative reference makes use of a wide range of graphical tools, including 2D and 3D scatterplots, 3D binary response plots, and scatterplot matrices. Supplemented by a companion ftp site, it features numerous data sets and applied examples that are used to elucidate the theory.

Other important features of this book include:
* Extensive coverage of a relatively new regression context based on dimension-reduction subspaces and sufficient summary plots
* Graphical regression, an iterative visualization process for constructing sufficient regression views
* Graphics for regressions with a binary response
* Graphics for model assessment, including residual plots
* Net-effects plots for assessing predictor contributions
* Graphics for predictor and response transformations
* Inverse regression methods
* Access to a Web site of supplemental plots, data sets, and 3D color displays.

An ideal text for students in graduate-level courses on statistical analysis, Regression Graphics is also an excellent reference for professional statisticians.

Preface

Introduction

(13)

C C & I

(3)

Construction

(1)

Characterization

(1)

Inference

(1)

Illustrations

(5)

Residuals versus fitted values

(2)

Residuals versus the predictors

(1)

Residuals versus the response

(2)

On things to come

(1)

Notational conventions

(4)

Problems

(1)

Introduction to 2D Scatterplots

(26)

Response plots in simple regression

(1)

New Zealand horse mussels

(5)

Transforming y via inverse response plots

(5)

Response transformations

(3)

Response transformations: Mussel data

(1)

Danish twins

(4)

Scatterplot matrices

(3)

Construction

(2)

Example

(1)

Regression graphics in the 1920s

(5)

Ezekiel's successive approximations

(2)

Bean's graphic method

(3)

Discussion

(3)

Problems

(2)

Constructing 3D Scatterplots

(7)

Getting an impression of 3D

(2)

Depth cuing

(1)

Scaling

(1)

Orthogonalization

(3)

Problems

(1)

Interpreting 3D Scatterplots

(31)

Haystacks

(2)

Structural dimensionality

(2)

One predictor

(1)

Two predictors

(1)

Many predictors

(1)

One-dimensional structure

(4)

Two-dimensional structure

(3)

Removing linear trends

(1)

Identifying semiparametric regression functions

(2)

Assessing structural dimensionality

(5)

A visual metaphor for structural dimension

(1)

A first method for deciding d = 1 or 2

(2)

Natural rubber

(2)

Assessment methods

(15)

Using independence

(1)

Using uncorrelated 2D views

(2)

Uncorrelated 2D views: Haystack data

(2)

Intraslice residuals

(2)

Intraslice orthogonalization

(1)

Mussels again

(1)

Discussion

(1)

Problems

(4)

Binary Response Variables

(23)

One predictor

(1)

Two predictors

(7)

Checking 0D structure

(1)

Checking 1D structure

(2)

Comparison with previous checking methods

(1)

Exploiting the binary response

(1)

Illustrations

(5)

Australian Institute of Sport

(3)

Kyphosis data

(2)

Three predictors

(3)

Checking 1D structure

(2)

Kyphosis data again

(1)

Visualizing a logistic model

(7)

Conditionally normal predictors

(3)

Other predictor distributions

(1)

Problems

(2)

Dimension-Reduction Subspaces

101

(19)

Overview

101

(2)

Dimension-reduction subspaces

103

(2)

Central subspaces

105

(3)

Guaranteeing S y/x by constraining

108

(4)

the distribution of x

108

(3)

the distribution of x

111

(1)

Importance of central subspaces

112

(2)

h-Level response plots

114

(6)

Problems

117

(3)

Graphical Regression

120

(23)

Introduction to graphical regression

120

(4)

Capturing Sy/x1

124

(3)

Example: Linear regression

125

(1)

Example: Sy/x1 = S (η1), but Sy/x2 ≠ S (η2)

126

(1)

Forcing Sy/x1 ⊂ S(η1)

127

(7)

Location regressions for the predictors

128

(1)

Elliptically contoured distributions

129

(2)

Elliptically contoured predictors

131

(3)

Improving resolution

134

(3)

Forcing Sy/x1 = S(η1)

137

(3)

Example: x1 independent of x2, but Sy/x1 ≠ S(η1)

137

(1)

Conditions for Sy/x1 = S(η1)

137

(2)

Marginal consistency assumption

139

(1)

Visual fitting with h-level response plots

140

(3)

Problems

142

(1)

Getting Numerical Help

143

(16)

Fitting with linear kernels

143

(4)

Isomerization data

145

(1)

Using the Li-Duan Proposition

146

(1)

Quadratic kernels

147

(3)

The predictor distribution

150

(3)

Reweighting for elliptical contours

153

(6)

Voronoi weights

154

(1)

Target distribution

155

(1)

Modifying the predictors

156

(2)

Problems

158

(1)

Graphical Regression Studies

159

(28)

Naphthalene data

159

(16)

Naphthoquinone, YN

161

(9)

Phthalic anhydride, YP

170

(5)

Wheat protein

175

(4)

Reaction yield

179

(5)

Discussion

184

(3)

Problems

184

(3)

Inverse Regression Graphics

187

(16)

Inverse regression function

187

(9)

Mean checking condition

191

(2)

Mean checking condition: Wheat protein

193

(1)

Mean checking condition: Mussel data

194

(2)

Inverse variance function

196

(7)

Variance checking condition

199

(1)

Variance checking condition: Ethanol data

200

(1)

Problems

201

(2)

Sliced Inverse Regression

203

(21)

Inverse regression subspace

203

(1)

SIR

204

(2)

Asymptotic distribution of Λd

206

(7)

Overview

206

(2)

The general case

208

(2)

Distribution of Λd with constraints

210

(3)

SIR: Mussel data

213

(3)

Minneapolis schools

216

(4)

Discussion

220

(4)

Problems

222

(2)

Principal Hessian Directions

224

(30)

Incorporating residuals

225

(2)

Connecting Se/z and Sezz when

227

(4)

E(z /ρTZ) = PρZ

227

(3)

E(z /ρTZ) = PρZ and Var(Z ρTZ) = Qρ

230

(1)

Z is normally distributed

231

(1)

Estimation and testing

231

(7)

Asymptotic distribution of Δk

232

(3)

An algorithm for inference on k

235

(1)

Asymptotic distribution of Δk with constraints

236

(2)

Testing e independent of z

238

(1)

pHd: Reaction yield

238

(5)

OLS and SIR

239

(1)

pHd test results

240

(1)

Subtracting β

241

(2)

Using stronger assumptions

243

(1)

pHd: Mussel data

243

(5)

pHd test results

244

(2)

Simulating the response

246

(1)

Using Voronoi weights

246

(2)

pHd: Haystacks

248

(1)

Discussion

249

(5)

pHd with the response

249

(1)

Additional developments

250

(1)

Problems

251

(3)

Studying Predictor Effects

254

(18)

Introduction to net-effect plots

254

(5)

Natural rubber: Net-effect plots

255

(1)

Joint normality

256

(1)

Slicing

257

(2)

Reducing brushing dimensions

259

(1)

Distributional indices

259

(7)

Example

260

(2)

Location dependence

262

(2)

Post-model net-effect plots

264

(1)

Bivariate SIR

265

(1)

Global net-effect plots

266

(6)

Tar

268

(1)

Minneapolis schools again

269

(1)

Problems

270

(2)

Predictor Transformations

272

(31)

CERES plots

273

(6)

Motivation

273

(1)

Estimating α1

274

(2)

Example

276

(3)

CERES plots when (x1 / x2) is

279

(4)

Constant

279

(1)

Linear in x2

280

(1)

Quadratic in x2

281

(2)

CERES plots in practice

283

(7)

Highly dependent predictors

284

(1)

Using many CERES plots

285

(4)

Transforming more than one predictor

289

(1)

Big Mac data

290

(4)

Added-variable plots

294

(2)

Environmental contamination

296

(7)

Assessing relative importance

297

(1)

Data analysis

298

(4)

Problems

302

(1)

Graphics for Model Assessment

303

(26)

Residual plots

304

(9)

Rationale

304

(1)

Isomerization data

305

(1)

Using residuals in graphical regression

306

(3)

pHd

309

(1)

Residual plots: Kyphosis data

309

(3)

Interpreting residual plots

312

(1)

Assessing model adequacy

313

(16)

Marginal regression functions

314

(2)

Marginal variance functions

316

(1)

Marginal model plots

317

(2)

Isomerization data again

319

(3)

Reaction yield data

322

(1)

Tomato tops

322

(3)

Marginal model plots: Kyphosis data

325

(2)

Problems

327

(2)

Bibliography

329

(10)

Author Index

339

(4)

Subject Index

343

R. DENNIS COOK is Professor, Department of Applied Statistics, University of Minnesota. He is the coauthor of An Introduction to Regression Graphics and numerous articles on regression and experimental design. He received his PhD in statistics from Kansas State University and is a Fellow of the American Statistical Association and the Institute of Mathematical Statistics.

Pastovi nuoroda: https://www.kriso.lt/db/9780470316931_pe.html

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El. knyga: Regression Graphics - Ideas for Studying Regressions through Graphics: Ideas for Studying Regressions Through Graphics [Wiley Online]

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