Understanding Regression Analysis

✍ Scribed by Michael Patrick Allen (auth.)

• Publisher: Springer US
• Year: 1997
• Tongue: English
• Leaves: 226
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-x
The origins and uses of regression analysis....Pages 1-5
Basic matrix algebra: Manipulating vectors....Pages 6-10
The mean and variance of a variable....Pages 11-15
Regression models and linear functions....Pages 16-20
Errors of prediction and least-squares estimation....Pages 21-25
Least-squares regression and covariance....Pages 26-30
Covariance and linear independence....Pages 31-35
Separating explained and error variance....Pages 36-40
Transforming variables to standard form....Pages 41-45
Regression analysis with standardized variables....Pages 46-50
Populations, samples, and sampling distributions....Pages 51-55
Sampling distributions and test statistics....Pages 56-60
Testing hypotheses using the t test....Pages 61-65
The t test for the simple regression coefficient....Pages 66-70
More matrix algebra: Manipulating matrices....Pages 71-75
The multiple regression model....Pages 76-80
Normal equations and partial regression coefficients....Pages 81-85
Partial regression and residualized variables....Pages 86-90
The coefficient of determination in multiple regression....Pages 91-95
Standard errors of partial regression coefficients....Pages 96-100
The incremental contributions of variables....Pages 101-105
Testing simple hypotheses using the F test....Pages 106-108
Testing compound hypotheses using the F test....Pages 109-112
Testing hypotheses in nested regression models....Pages 113-117
Testing for interaction in multiple regression....Pages 118-122
Nonlinear relationships and variable transformations....Pages 123-127
Regression analysis with dummy variables....Pages 128-132
One-way analysis of variance using the regression model....Pages 133-137
Two-way analysis of variance using the regression model....Pages 138-142
Testing for interaction in analysis of variance....Pages 143-146
Analysis of covariance using the regression model....Pages 147-151
Interpreting interaction in analysis of covariance....Pages 152-155
Structural equation models and path analysis....Pages 156-160
Computing direct and total effects of variables....Pages 161-165
Model specification in regression analysis....Pages 166-170
Influential cases in regression analysis....Pages 171-175
The problem of multicollinearity....Pages 176-180
Assumptions of ordinary least-squares estimation....Pages 181-185
Beyond ordinary regression analysis....Pages 186-190
Back Matter....Pages 191-216

✦ Subjects

Social Sciences, general; Public Health/Gesundheitswesen