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Tables of Contents for Linear Statistical Models
Chapter/Section Title
Page #
Page Count
Introduction to Regression Analysis
1
10
Statistical Studies
2
1
Regression Analysis
3
1
Some Examples of Regression Analysis
4
4
Data Employed in Regression Studies
8
1
Cause-and-Effect Relationships
9
1
Upcoming Chapters
9
2
Populations, Samples, and Probability Distributions
11
33
Populations
12
2
Probability
14
2
Random Samples and Sample Statistics
16
4
Continuous Probability Distributions
20
2
The Normal Probability Distribution
22
12
Medians, Quartiles, Box Plots, and Trimmed Means
34
3
The t-Distribution and the F-Distribution
37
7
Exercises
39
5
Basic Statistical Inference
44
62
Confidence Intervals for a Population Mean
45
14
Hypothesis Testing for a Population Mean
59
18
Comparing Two Population Means by Using Independent Samples
77
11
Paired Difference Experiments
88
18
Exercises
93
13
The Simple Linear Regression Model
106
34
Description of the Model
106
10
The Least Squares Point Estimates
116
5
Point Estimates and Point Predictions
121
4
Model Assumptions, the Mean Square Error, and the Standard Error
125
15
Exercises
129
11
Inference in Simple Linear Regression
140
75
Sampling Properties Concerning b1, b0, s2, and s
141
3
A Confidence Interval for the Slope
144
6
Testing the Significance of the Independent Variable
150
9
Statistical Inference for the Intercept
159
2
A Confidence Interval for a Mean Value of the Dependent Variable
161
3
A Prediction Interval for an Individual Value of the Dependent Variable
164
6
An Example Using SAS
170
4
Simple Coefficients of Determination and Correlation
174
9
An F-Test for the Simple Linear Regression Model
183
4
An F-Test of Lack of Fit
187
4
Regression Analysis Through the Origin
191
4
Using SAS
195
20
Exercises
196
19
The Assumptions Behind Regression Analysis
215
61
Residual Plots
216
3
The Assumption of Correct Functional Form
219
9
The Population of Error Terms
228
1
Inference Assumption 1: Constant Variance
229
6
Inference Assumption 2: Independence
235
9
Inference Assumption 3: Normal Populations
244
5
Outlying and Influential Observations
249
2
Using SAS
251
25
Exercises
252
24
Matrix Algebra
276
19
Matrices and Vectors
276
2
The Transpose of a Matrix
278
1
Sums and Differences of Matrices
279
1
Matrix Multiplication
280
4
The Identity Matrix
284
1
Linear Dependence and Linear Independence
285
1
The Inverse of a Matrix
286
2
Some Regression-Related Matrix Calculations
288
7
Exercises
290
5
Multiple Regression: I
295
92
The Linear Regression Model
296
13
The Least Squares Point Estimates
309
8
Point Estimates and Point Predictions
317
5
The Regression Assumptions, the Standard Error, and Residual Analysis
322
6
Multiple Coefficients of Determination and Correlation
328
4
An F-Test for the Overall Model
332
2
Statistical Inference for βj
334
6
Confidence Intervals and Prediction Intervals
340
5
Using SAS
345
42
Exercises
346
41
Multiple Regression: II
387
49
Interaction
387
18
An F-Test for a Portion of a Model and the Partial Coefficient of Determination
405
5
Inferences for a Single Population
410
3
Using SAS
413
23
Exercises
415
21
Some Problems and Remedies
436
61
The Problem of Multicollinearity
437
20
The Standardized Regression Model
457
3
Ridge Regression
460
4
Diagnostic Statistics for Identifying Outlying and Influential Observations
464
13
Partial Leverage Residual Plots
477
4
Using SAS
481
16
Exercises
483
14
Model Building
497
57
Comparing Regression Models Using R2, s, Prediction Interval Length, and Corrected R2
498
14
Advanced Model Comparison Methods: The C Statistic and the PRESS Statistic
512
12
Stepwise Regression, Forward Selection, Backward Elimination, and Maximum R2 Improvement
524
11
Model Validation
535
1
Using SAS
536
18
Exercises
537
17
Dummy Variables and Advanced Statistical Inferences
554
77
Using Dummy Variables to Model Qualitative Independent Variables
555
27
Statistical Inferences for a Linear Combination of Regression Parameters
582
8
Simultaneous Confidence Intervals
590
8
Using SAS
598
33
Exercises
599
32
Remedies for Violations of the Regression Assumptions
631
98
Transformations to Achieve Linearity
632
12
Handling Nonconstant Error Variances and Weighted Least Squares
644
18
Binary Dependent Variables and Logistic Regression
662
11
Modeling Deterministic Time Series Components
673
11
Autoregressive Error Structures
684
10
Remedies for Non-Normality
694
3
Using SAS
697
32
Exercises
701
28
One-Factor Analysis
729
71
Basic Concepts of Experimental Design
730
1
The Completely Randomized Experimental Design
731
1
An Introduction to One-Factor Analysis
732
3
The ANOVA Approach
735
25
The Regression Approach
760
16
Fixed and Random Models
776
3
Hartley's Test and Bartlett's Test for Variance Equality
779
1
Using SAS
780
20
Exercises
783
17
Two-Factor Analysis: I
800
54
Introductory Concepts
800
3
The ANOVA Approach to the Analysis of a Balanced Complete Factorial Experiment
803
24
The Regression Approach to the Analysis of a Complete Factorial Experimental
827
14
Using SAS
841
13
Exercises
843
11
Two-Factor Analysis: II
854
69
The Regression Approach to the Analysis of an Incomplete Factorial Experiment
855
30
Fixed, Random, and Mixed Models
885
5
Nested Factors
890
12
Using SAS
902
21
Exercises
909
14
The Randomized Block and Latin Square Designs
923
52
Introductory Concepts
923
4
The ANOVA Approach to Randomized Blocks
927
9
The Regression Approach to Randomized Blocks
936
19
Latin Squares
955
7
Using SAS
962
13
Exercises
964
11
Appendix A Derivations of the Mean and Variance of y
975
3
Appendix B Derivation of the Least Squares Point Estimates
978
3
Appendix C Derivation of the Computational Formula for SSE
981
3
Appendix D Derivations of the Means and Variances of bj, yo, and y0 -- yo
984
8
Appendix E Statistical Tables
992
15
Appendix F Descriptions of Data Bases
1007
4
References
1011
2
Index
1013