Understanding Regression Analysis

1. Front Matter

   Pages i-x

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2. The origins and uses of regression analysis

   Pages 1-5

3. Basic matrix algebra: Manipulating vectors

   Pages 6-10

4. The mean and variance of a variable

   Pages 11-15

5. Regression models and linear functions

   Pages 16-20

6. Errors of prediction and least-squares estimation

   Pages 21-25

7. Least-squares regression and covariance

   Pages 26-30

8. Covariance and linear independence

   Pages 31-35

9. Separating explained and error variance

   Pages 36-40

10. Transforming variables to standard form

    Pages 41-45

11. Regression analysis with standardized variables

    Pages 46-50

12. Populations, samples, and sampling distributions

    Pages 51-55

13. Sampling distributions and test statistics

    Pages 56-60

14. Testing hypotheses using the t test

    Pages 61-65

15. The t test for the simple regression coefficient

    Pages 66-70

16. More matrix algebra: Manipulating matrices

    Pages 71-75

17. The multiple regression model

    Pages 76-80

18. Normal equations and partial regression coefficients

    Pages 81-85

19. Partial regression and residualized variables

    Pages 86-90

20. The coefficient of determination in multiple regression

    Pages 91-95

By assuming it is possible to understand regression analysis without fully comprehending all its underlying proofs and theories, this introduction to the widely used statistical technique is accessible to readers who may have only a rudimentary knowledge of mathematics. Chapters discuss:

-descriptive statistics using vector notation and the components of a simple regression model;
-the logic of sampling distributions and simple hypothesis testing;
-the basic operations of matrix algebra and the properties of the multiple regression model; -testing compound hypotheses and the application of the regression model to the analyses of variance and covariance, and
-structural equation models and influence statistics.

• Nation
• Regression analysis
• Transformation
• Variance
• descriptive statistics
• interaction
• knowledge
• statistics

"Allen's book will, no doubt, earn the praises of statistics instructors and students alike...Provides the reader a thorough, yet lucid, journey through a variety of statistical concepts...This gem should be made a part of every prospective statistician's collection. Undergraduates through professional."
(Choice, March 1998)

• Washington State University, Pullman

  Michael Patrick Allen