INDEX

A

Added-variable plot, 95, 109

Adjusted multiple correlation coefficient, 285

AIC, 287, 290–291, 295, 308, 320, 327, 343

bias corrected, 287

Akaike Information Criteria, 287

Analysis of covariance, 12, 15

Analysis of variance, 12, 15, 67, 140

ANOVA, 140

multiple regression, 67

simple regression, 71

Assumption

constant variance, 86

Homogeneity, 86

independent-errors, 87

linearity, 31, 86

normality, 37, 86

Autocorrelation, 18, 87, 180, 197, 201

B

Backward elimination, 289

Bayes Information Criteria, 287

Best linear unbiased estimator, 61, 83

BIC, 287, 290–291, 295, 308, 320, 327

Binary

response data, 195

response variable, 318, 321

variable, 12

BLUE, 61, 83

C

Centering, 239

Classification, 336

Coefficient of determination, 42, 61

Collinearity-influential observations, 246

Collinearity, 18, 88, 222

Computer repair data, 26, 30–31, 35, 42

Concordance Index, 328

Condition number, 244, 276, 288

Confidence

interval, 38

interval for β_j, 63

region, 37

Constant variance assumption, 86

Cook's Distance, 103

Corrected sums of squares and products matrix, 60

Correlated errors, 141

Correlation coefficient, 21, 24, 240

between Y and , 40, 61

population, 36

sample, 36, 39

Correlation matrix, 117, 241, 243, 250, 252

, 83

Covariance, 21, 23

Cross-sectional data, 128, 214–215

Cumulative distribution function, 319

D

Data set

advertising, 234, 236

air pollution, 300, 302

Anscombe's quartet, 24

bacteria deaths, 155

bankruptcy, 320, 322

brain, 171–172

cigarette consumption, 1, 79–80, 312

college expense, 182

computer repair (expanded), 116

computer repair, 26–27

consumer expenditure, 198, 216

corn yields, 147

cost of education, 182

diabetes, 330, 332

DJIA, 216

domestic immigration, 6

education expenditure, 141, 143, 185

Egyptian skulls, 6

equal educational opportunity, 223

examination, 75–76

exponential growth, 108

field goal kicking, 339

fuel consumption, 256

Hald, 265–266

Hamilton, 95

hard disk prices, 177

heights of husbands and wives, 47–48, 78

homicide, 296

housing starts, 206

import, 229, 260

injury incidents, 161

labor force, 47

Longley, 275–276

magazine advertising, 174

milk production, 3

new drugs, 343

New York rivers, 10, 6, 99, 101, 105

newspapers, 48

nonlinear, 24

oil production, 176, 216

PCB, 348

preemployment testing, 132

presidential election, 148–150, 176, 255, 312

quantitative sensory testing, 14

real estate, 309

right-to-work laws, 4

salary survey, 122–123

Scottish Hills Races, 111

ski sales, 140–141, 210–211

Space Shuttle, 339

students information, 147–148

supervised workers, 164, 180

supervisor performance, 54–55, 63–64, 292

wind chill factor, 175

Data

collection, 11

re-expression, 13

transformation, 13

Degrees of freedom, 33, 58, 89

DFITS, 104

Discriminant analysis, 336

Distance

Cook's, 103

orthogonal, 29

perpendicular, 29

vertical, 29

Distribution

binomial, 342

chi-square, 323

gamma, 342

inverse Gaussian, 342

Poisson, 160, 164, 342

Dose-response curve, 180, 194

Draftsman's matrix, 94

Dummy variable, 121

Durbin-Watson statistic, 200

E

Eigenvalues, 243

Eigenvector, 243

Externally studentized residual, 90

F

F-test, 65

Fitted

regression equation, 37

value, 15, 30, 57

Fitting

models to data, 14

Forecast interval, 38

Forward selection, 289

Full model, 65

Function

cumulative distribution, 319

intrinsically nonlinear, 13

linear, 13

linearizable, 13

link, 343

logistic, 195

nonlinear, 13, 195

G

Generalized linear models, xv, 341

Goodness-of-fit index, 42

H

Hadi's influence measure, 105

Hat matrix, 83, 89

Heteroscedasticity, 86, 159, 179

High leverage, 100, 265

Homogeneity (Homoscedasticity), 86, 159

I

Independent-errors assumption, 87

Indicator variable, 118, 121, 211

Influence measures, 103

Welsch and Kuh (DFITS), 106

Cook's Distance, 103, 106, 117

Hadi's, 105–106, 117

Welsch and Kuh (DFITS), 104, 106

Influential observations, 91, 98

Interaction effects, 125

Intercept, 57

Internally studentized residual, 90

Interpretation of regression coefficients, 58

Iterative process, 16

L

L-R plot, 107

Ladder of transformation, 171

Lagged variables, 215

Least squares, 14

estimates, 30

line, 30

method, 29–30, 57

properties, 60

weighted, 18, 167, 180

Leverage-residual plot, 107

Leverage values, 89

Linearity assumption, 31, 86

Link function, 343

Logistic regression, xv, 342

binary, xv, 18

multinomial, xv, 18

polytomous, 329

ordered response variable, xv, 18

Logistic

distribution, 319

function, 176, 195

models, 180, 195

regression, 12, 15, 18, 140, 317, 319

regression diagnostics, 323

response function, 318

Logit, 320

link function, 342

model, xv, 195, 343

transformation, 319

M

Masking problem, 101

Matrix, 241

corrected sums of squares and products, 60

correlation, 241, 243, 250, 252

draftsman's, 94

hat, 89

plot, 94, 117

projection, 89

variance-covariance, 241, 257

Maximum likelihood, 14, 320, 342

Maximum likelihood method, 335, 330

Model

fitting, 14

full, 65

no-intercept, 183, 186

probit, 195, 319

random walk, 219

reduced, 65

through the origin, 42

Multicollinearity, 68, 222

Multinomial logit model, 329

Multiple correlation coefficient, 61, 67, 70, 87, 285

Multiple regression, 15, 54, 61

ANOVA table, 67

assumptions, 60

Multiplicative effect, 125

Multivariate regression, 14–15

N

Nested models, 65, 326

No-intercept model, 42, 183, 186

Nominal model, 335

Nonlinear regression, 15

Nonparametric statistics, 200

Normal

equations, 57, 82

property of, 160

scores, 97

Normality assumption, 33, 86

Normalizing transformations, 153

O

Odds ratio, 319

One-sample t-test, 44

Ordered response category, 334

Ordered response variable, xv, 18

Ordinal logistic regression, 334

Ordinal model, 335

Orthogonal

predictors, 221, 239

regression, 29

Outliers, 100, 265

P

P-R plot, 107

P-value for

F-test, 66

t-test, 63

P-value

for t-test, 34

Parameter estimation, 14

Parsimony, 69

Partial

regression coefficients, 53, 58

regression plot, 110

residual plot, 110

Plot

added-variable, 95, 109

L-R, 107

matrix, 94, 117

P-R, 107

partial regression, 110

partial residual, 110

potential-residual, 107, 117

residual plus component, 95

sequence, 199

Poisson regression, xv, 18, 342

Potential-residual plot, 107, 117

Predicted value, 15

Prediction

errors, 219

interval, 38

Principal components, 14, 239, 243, 255, 257

Probit model, 195, 319

Projection matrix, 83, 89

Proportional odds model, 329, 334–335

Pure error, 184

R

R², 41, 61

Random walk model, 219

Reduced model, 65

Regression

assumptions, 86

coefficients, 2, 28, 53

definition, 1

elements of, 7

examples of, 3

line, 30

linear, 15

logistic, 12, 15, 18

model through the origin, 42

multiple, 13, 15, 17, 54, 61

multivariate, 14–15

nonlinear, 15

parameters, 2, 28

partial coefficients, 53

Poisson, xv, 18, 342

ridge, 268

robust, 115

simple, 13, 15, 17, 54, 63, 71, 74

sum of squares, 40

trivial models, 44

univariate, 14–15

Relationship between simple and multiple regression coefficients, 76

Residual

adjusted, 105

internally studentized, 90

mean square, 44, 285

ordinary least squares, 30, 57

plots, 90

plus component plot, 95, 109–110

standardized, 89

sum of squares, 33, 40, 89

Ridge

bias of estimators, 278

method, 14

parameter, 268

regression, 268

trace, 268–269

variance of estimators, 278

Robust regression, xv, 115, 341, 345

S

Sample

mean, 22

standard deviation, 44

variance, 44

Sampling distribution of

, 37

, 33, 37

Scaling, 239

unit length, 240

Sequence plot, 199

Shrinkage estimators, 269

Simple regression, 15, 54, 63, 71, 74

ANOVA table, 71

Simultaneous confidence region, 37

Standard deviation, 33

sample, 23, 44

Standard error of , 83

estimate, 33

Standard normal distribution, 90

Standardized

deviance residuals, 323

Personian residuals, 323

residual, 89

variables, 240

Standardizing, 240

Stepwise method, 289

Stimulus-response relationships, 195

Sum of squared residuals, 58

Swamping problem, 101

T

Test

t-, 44

Durbin-Watson, 200

F-, 65–68, 70

one-sample t, 44

runs, 200

t-, 33–34, 63–64, 67, 72

two-sample t, 45

Time series data, 130, 199, 214

Total

mean square error, 277–279

sum of squares, 40

variance, 268

variance of OLS estimators, 269

variance of ridge estimators, 268

Transformation, 13, 18, 32

ladder of, 171

to achieve linearity, 153

to achieve normality, 153

variance-stabilizing, 153

Trivial regression models, 44

Two-sample t-test, 45

U

Uniqueness of LS solution, 30, 57

Univariate regression, 14–15

V

Variable

binary, 12, 318, 321

dependent, 1

dummy, 12, 121

explanatory, 1

independent, 2

indicator, 12, 118, 121, 211

lagged, 215

predictor, 1

qualitative, 12, 18

quantitative, 12

regressor, 2

response, 1

role of, 313

selection, 18

selection procedures, 281

standardized, 240

Variance-covariance matrix, 241, 257

Variance-stabilizing transformations, 153

Variance

inflation factor, 236, 278, 288

of ridge estimators, 278

sample, 44

W

Wald Test, 321

Web site

book's, 3, xiv

Case book, 2

DASL, 3

Electronic Dataset Service, 3

Weighted

least squares, 18, 167, 180

leverages, 323

Welsch and Kuh measure, 104