Applying Regression and Correlation: A Guide for Students and Researchers illustrated edition

This book takes a fresh look at applying regression analysis in the behavioural sciences by introducing the reader to regression analysis through a simple model-building approach. <P></P><P>The authors start with the basics and begin by re-visiting the mean, and the standard deviation, with which most readers will already be familiar, and show that they can be thought of a least squares model. The book then shows that this least squares model is actually a special case of a regression analysis and can be extended to deal with first one, and then more than one independent variable.</P><P></P><P>Extending the model from the mean to a regression analysis provides a powerful, but simple, way of thinking about what students believe</P>

This book takes a fresh look at applying regression analysis in the behavioural sciences by introducing the reader to regression analysis through a simple model-building approach.

The authors start with the basics and begin by re-visiting the mean, and the standard deviation, with which most readers will already be familiar, and show that they can be thought of a least squares model. The book then shows that this least squares model is actually a special case of a regression analysis and can be extended to deal with first one, and then more than one independent variable.

Extending the model from the mean to a regression analysis provides a powerful, but simple, way of thinking about what students believe

This book takes a fresh look at applying regression analysis in the behavioural sciences by introducing the reader to regression analysis through a simple model-building approach. The authors start with the basics and begin by re-visiting the mean, and the standard deviation, with which most readers will already be familiar, and show that they can be thought of a least squares model. The book then shows that this least squares model is actually a special case of a regression analysis and can be extended to deal with first one, and then more than one independent variable. Extending the model from the mean to a regression analysis provides a powerful, but simple, way of thinking about what students believe are the more complex aspects of regression analysis. The authors gradually extend the model to include aspects of regression analysis such as non-linear regression, logistic regression, and moderator and mediator analysis. These approaches are often presented in terms that are too mathematical for non-statistically inclined students to deal with. Throughout the book maintains a conceptual, non-mathematical focus.Most equations are placed in an appendix, where a detailed explanation is given, to avoid disrupting the flow of the main text. This book will be indispensable for anyone using regression and correlation from undergraduates doing projects to postgraduate and researchers.

'An excellent book on regression and correlation, which should be on the shopping list of all researchers in psychology and also of many psychology students' - Statistical Methods in Medical Research "This book is a gem. I would certainly recommend it to my students." -- David Clark-Carter

Preface		vii
PART I I NEED TO DO REGRESSION ANALYSIS TOMORROW
Building Models with Regression and Correlation		1	(26)
What are models?
Least squares models
A very simple model
The standard error of the mean
Modelling relationships
The standard error and significance of parameter estimates
Standardised estimates
Looking more at correlations
Correlations and scattergraphs
Correlations and variance
Correlations and size
Notes
Further reading
More than One Independent Variable - Multiple Regression		27	(13)
Introduction: multiple regression in theory
What's multiple regression all about?
Multiple regression in practice
R and R square
Adjusted R square
Analysis of variance (ANOVA) table
Coefficients
Variable entry
Hierarchical variable entry
Methods of variable entry
Note
Further reading
Categorical Independent Variables		40	(18)
Introduction
Categorical data: a special case
The t-test as regression
ANOVA as regression
Coding schemes for categorical data
Notes
Further reading
PART II I NEED TO DO REGRESSION ANALYSIS NEXT WEEK
Assumptions in Regression Analysis		58	(55)
Introduction
Assumptions about measures
Levels of measurement
Conservative interpretation of assumptions
A more liberal approach
Assumptions about data
A bit about normal distributions
Univariate distribution checks
Outliers and the mean
Normal distribution
Detecting and dealing with non-normality
Calculation-based methods
Skew and kurtosis
Outliers
Dealing with outliers, skew and kurtosis
Dealing with outliers
Effects of univariate skew and kurtosis
Multivariate distributions
Assumption 1
Assumption 2
Assumption 3
Assumption 4
Time-series designs
Clustered sampling designs
Notes
Further reading
Issues in Regression Analysis		113	(23)
Causality
Association
Direction of causality
Isolation
The role of theory in determining causation
Sample size
Why should we worry about sample sizes?
Rules of thumb
Power analysis
Collinearity
What is collinearity?
Detecting collinearity
Dealing with collinearity
Measurement error
Notes
Further reading
PART III I NEED TO KNOW MORE OF THE THINGS THAT REGRESSION CAN DO
Non-linear and Logistic Regression		136	(29)
Non-linear regression
Linear and curvilinear relationships
Generating a curve
Carrying out non-linear regression
An example of non-linear regression
Logistic regression
The case of the dichotomous dependent variable
The logit transformation
Using the logit: logistic regression
An annotated example of logistic regression
Hierarchical logistic regression
Polynomial logistic regression
Further reading
Moderator and Mediator Analysis		165	(27)
Introduction
Moderator analysis
Two categorical variables
Categorical and continuous variables
Two continuous predictors
Mediator analysis
Example of mediation
Some concluding points on moderation and mediation
Note
Further reading
Introducing Some Advanced Techniques: Multilevel Modelling and Structural Equation Modelling		192	(24)
Multilevel modelling (MLM)
Algebraic formulation
Hierarchies everywhere
Even more hierarchies
Structural equation modelling
Why use SEM?
Identification
Latent variables
Estimation in SEM
Model testing
Structural models
Programs for MLM and SEM
MLM software
SEM software
Notes
Further reading
Appendix 1 Equations		216	(12)
Appendix 2 Doing regression with SPSS		228	(9)
Appendix 3 Statistical tables		237	(8)
References		245	(4)
Name index		249	(2)
Subject index		251

My research has primarily been in - Evaluation of reliability and validity - Structural equation models - Psychometrics