Page 20 - Applied statistics and probability for engineers

xvi Contents

10-2.1 Hypotheses Tests on the Difference in 11-7.1 Residual Analysis 453
Means, Variances Unknown 383 11-7.2 Coeficient of Determination
2
10-2.2 Type II Error and Choice of Sample (R ) 454
Size 389 11-8 Correlation 457
10-2.3 Conidence Interval on the Difference in 11-9 Regression on Transformed Variables 463
Means, Variances Unknown 390 11-10 Logistic Regression 467
10-3 A Nonparametric Test for the Difference in Two
Chapter 12 Multiple Linear Regression 477
Means 396
10-3.1 Description of the Wilcoxon Rank-Sum 12-1 Multiple Linear Regression Model 478
Test 397 12-1.1 Introduction 478
10-3.2 Large-Sample Approximation 398 12-1.2 Least Squares Estimation of the
10-3.3 Comparison to the t-Test 399 Parameters 481
10-4 Paired t-Test 400 12-1.3 Matrix Approach to Multiple Linear
10-5 Inference on the Variances of Two Normal Regression 483
Distributions 407 12-1.4 Properties of the Least Squares
10-5.1 F Distribution 407 Estimators 488
10-5.2 Hypothesis Tests on the Ratio of Two 12-2 Hypothesis Tests In Multiple Linear
Variances 409 Regression 497
10-5.3 Type II Error and Choice of Sample 12-2.1 Test for Signiicance
Size 411 of Regression 497
10-5.4 Conidence Interval on the Ratio of Two 12-2.2 Tests on Individual Regression
Variances 412 Coeficients and Subsets of
10-6 Inference on Two Population Coeficients 500
Proportions 414 12-3 Conidence Intervals In Multiple Linear
10-6.1 Large-Sample Tests on the Difference in Regression 506
Population Proportions 414 12-3.1 Conidence Intervals on Individual
10-6.2 Type II Error and Choice of Sample Regression Coeficients 506
Size 416 12-3.2 Conidence Interval on the Mean
10-6.3 Conidence Interval on the Difference in Response 507
Population Proportions 417 12-4 Prediction of New Observations 508
10-7 Summary Table and Road Map for Inference 12-5 Model Adequacy Checking 511
Procedures for Two Samples 420 12-5.1 Residual Analysis 511
12-5.2 Inluential Observations 514
Chapter 11 Simple Linear Regression
12-6 Aspects of Multiple Regression
and Correlation 427
Modeling 517
11-1 Empirical Models 428 12-6.1 Polynomial Regression Models 517
11-2 Simple Linear Regression 431 12-6.2 Categorical Regressors and Indicator
11-3 Properties of the Least Squares Variables 519
Estimators 440 12-6.3 Selection of Variables and Model
11-4 Hypothesis Tests in Simple Linear Building 522
Regression 441 12-6.4 Multicollinearity 529
11-4.1 Use of t-Tests 441 Chapter 13 Design and Analysis of Single-Factor
11-4.2 Analysis of Variance Approach to Test Experiments: The Analysis of Variance 539
Signiicance of Regression 443
11-5 Conidence Intervals 447 13-1 Designing Engineering Experiments 540
11-5.1 Conidence Intervals on the Slope and 13-2 Completely Randomized Single-Factor
Intercept 447 Experiment 541
11-5.2 Conidence Interval on the Mean 13-2.1 Example: Tensile Strength 541
Response 448 13-2.2 Analysis of Variance 542
11-6 Prediction of New Observations 449 13-2.3 Multiple Comparisons Following the
11-7 Adequacy of the Regression Model 452 ANOVA 549