Applied Regression Analysis and Experimental Design

✍ Scribed by Brook, Richard J

• Publisher: Routledge;CRC
• Year: 2018
• Tongue: English
• Leaves: 252
• Series: Statistics textbooks and monographs
• Category: Library

✦ Synopsis

For a solid foundation of important statistical methods, the concise, single-source text unites linear regression with analysis of experiments and provides students with the practical understanding needed to apply theory in real data analysis problems. Stressing principles while keeping computational and theoretical details at a manageable level, Applied Regression Analysis and Experimental Design features an emphasis on vector geometry and least squares to unify and provide an intuitive basis for most topics covered ... abundant examples and exercises using real-life data sets clearly illustrating practical of data analysis ... essential exposure to MINITAB and GENSTAT computer packages, including computer printouts ... and important background material such as vector and matrix properties and the distributional properties of quadratic forms. Designed to make theory work for students, this clearly written, easy-to-understand work serves as the ideal texts for courses Regression, Experimental Design, and Linear Models in a broad range of disciplines. Moreover, applied statisticians will find the book a useful reference for the general application of the linear model.  Read more...

Abstract: For a solid foundation of important statistical methods, the concise, single-source text unites linear regression with analysis of experiments and provides students with the practical understanding needed to apply theory in real data analysis problems. Stressing principles while keeping computational and theoretical details at a manageable level, Applied Regression Analysis and Experimental Design features an emphasis on vector geometry and least squares to unify and provide an intuitive basis for most topics covered ... abundant examples and exercises using real-life data sets clearly illustrating practical of data analysis ... essential exposure to MINITAB and GENSTAT computer packages, including computer printouts ... and important background material such as vector and matrix properties and the distributional properties of quadratic forms. Designed to make theory work for students, this clearly written, easy-to-understand work serves as the ideal texts for courses Regression, Experimental Design, and Linear Models in a broad range of disciplines. Moreover, applied statisticians will find the book a useful reference for the general application of the linear model

✦ Table of Contents

Content: Cover
Half Title
Title Page
Copyright Page
Preface
Table of Contents
1: Fitting a Model to Data
1.1 Introduction
1.2 How to Fit a Line
1.3 Residuals
1.4 Transformations to Obtain Linearity
1.5 Fitting a Model Using Vectors and Matrices
1.6 Deviations from Means
1.7 An Example --
Value of a Postage Stamp over Time
Problems
2: Goodness of Fit of the Model
2.1 Introduction
2.2 Coefficient Estimates for Univariate Regression
2.3 Coefficient Estimates for Multivariate Regression
2.4 ANOVA Tables
2.5 The F-Test
2.6 The Coefficient of Determination 2.7 Predicted Values of Y and Confidence Intervals2.8 Residuals
2.9 Reduced Models
2.10 Pure Error and Lack of Fit
2.11 Example --
Lactation Curve
Problems
3: Which Variables Should Be Included in the Model
3.1 Introduction
3.2 Orthogonal Predictor Variables
3.3 Linear Transformations of the Predictor Variables
3.4 Adding Nonorthogonal Variables Sequentially
3.5 Correlation Form
3.6 Variable Selection --
All Possible Regressions
3.7 Variable Selection --
Sequential Methods
3.8 Qualitative (Dummy) Variables
3.9 Aggregation of Data
Problems
4: Peculiarities of Observations 4.1 Introduction4.2 Sensitive, or High Leverage, Points
4.3 Outliers
4.4 Weighted Least Squares
4.5 More on Transformations
4.6 Eigenvalues and Principal Components
4.7 Ridge Regression
4.8 Prior Information
4.9 Cleaning up Data
Problems
5: The Experimental Design Model
5.1 Introduction
5.2 What Makes an Experiment
5.3 The Linear Model
5.4 Tests of Hypothesis
5.5 Testing the Assumptions
Problems
6: Assessing the Treatment Means
6.1 Introduction
6.2 Specific Hypothesis
6.3 Contrasts
6.4 Factorial Analysis
6.5 Unpredicted Effects
6.6 Conclusion
Problems
7: Blocking 7.1 Introduction7.2 Structure of Experimental Units
7.3 Balanced Incomplete Block Designs
7.4 Confounding
7.5 Miscellaneous Tricks
Problems
8: Extensions to the Model
8.1 Introduction
8.2 Hierarchic Designs
8.3 Repeated Measures
8.4 Covariance Analysis
8.5 Unequal Replication
8.6 Modelling the Data
Problems
Appendix A: Review of Vectors and Matrices
A.1 Some Properties of Vectors
A.2 Some Properties of Vector Spaces
A.3 Some Properties of Matrices
Appendix B: Expectation, Linear and Quadratic Forms
B.1 Expectation
B.2 Linear Forms
B.3 Quadratic Forms
B.4 The F-Statistic Appendix C: Data SetsC. 1 Ultra-Sound Measurements of Horses' Hearts
C.2 Ph Measurement of Leaf Protein
C.3 Lactation Records of Cows
C.4 Sports Cars
C.5 House Price Data
C.6 Computer Teaching Data
C.7 Weedicide Data
References
Index

✦ Subjects

Regression analysis;Experimental design;Analyse de régression;Plan d'expérience