Linear regression: an introduction to statistical models
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Los Angeles ; London ; New Delhi ; Singapore ; Washington DC ; Melbourne
Sage
[2021]
|
| Series: | The Sage quantitative research kit
7th volume |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Enthält Literaturverzeichnis Seite 171-173 und Index |
| Physical Description: | xiii, 178 Seiten Diagramme |
| ISBN: | 9781526424174 |
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CONTENTS List ofFigures, Tables and Boxes About the Author Acknowledgements ix xv xvii Preface xix 1 2 What Is a Statistical Model? 1 Kinds of Models: Visual, Deterministic and Statistical Why Social Scientists Use Models Linear and Non-Linear Relationships: Two Examples First Approach to Models: The t-Test as a Comparison of Two Statistical Models The Sceptic's Model (Null Hypothesis of the t-Test) The Power Pose Model: Alternative Hypothesis of the t-Test Using Data to Compare Two Models The Signal and the Noise 2 3 4 6 8 9 10 14 Simple Linear Regression 17 Origins of Regression: Francis Galton and the Inheritance of Height The Regression Line Regression Coefficients: Intercept and Slope Errors of Prediction and Random Variation The True and the Estimated Regression Line Residuals How to Estimate a Regression Line How Well Does Our Model Explain the Data? The R2 Statistic Sums of Squares: Total, Regression and Residual R2 as a Measure of the Proportion of Variance Explained R2 as a Measure of the Proportional Reduction of Error Interpreting R2 Final Remarks on the R2 Statistic Residual Standard Error Interpreting Galton's Data and the Origin of 'Regression' Inference: Confidence Intervals and Hypothesis Tests 18 21 23 24 25 26 27 29 29 31 31 32 32 , 33 33 35
vi 3 I LINEAR REGRESSION: AN INTRODUCTION TO STATISTICAL MODELS Confidence Range for a Regression Line 39 Prediction and Prediction Intervals 42 Regression in Practice: Things That Can Go Wrong Influential Observations 44 45 Selecting the Right Group 46 The Dangers ofExtrapolation 47 Assumptions and Transformations 51 The Assumptions of Linear Regression 52 Investigating Assumptions: Regression Diagnostics Errors and Residuals 54 54 Standardised Residuals Regression Diagnostics: Application With Examples 55 56 Normality 56 Homoscedasticity and Linearity: The Spread-Level Plot 61 Outliers and Influential Observations Independence ofErrors 64 70 What if Assumptions Do Not Hold? An Example 71 A Non-Linear Relationship 71 Model Diagnostics for the Linear Regression of Life Expectancy on GDP 73 Transforming a Variable: Logarithmic Transformation of GDP 73 Regression Diagnostics for the Linear Regression With Predictor Transformation 79 Types of Transformations, and When to Use Them 79 Common Transformations Techniques for Choosing an Appropriate Transformation 4 Multiple Linear Regression: A Model for Multivariate Relationships Confounders and Suppressors 80 * 83 87 88 Spurious Relationships and Confounding Variables 88 Masked Relationships and Suppressor Variables 91 Multivariate Relationships: A Simple Example With Two Predictors Multiple Regression: General Definition Simple Examples of Multiple Regression Models Example 1: One Numeric Predictor, One Dichotomous Predictor 93 96 97 98 Example 2: Multiple Regression With Two Numeric Predictors 107 Research Example:
Neighbourhood Cohesion and Mental Wellbeing 113
CONTENTS Dummy Variables for Representing Categorical Predictors What Are Dummy Variables? Research Example: Highest Qualification Coded Into Dummy Variables Choice ofReference Category for Dummy Variables 5 117 118 118 122 Multiple Linear Regression: Inference, Assumptions and Standardisation 125 Inference About Coefficients 126 Standard Errors of Coefficient Estimates 126 Confidence Interval for a Coefficient Hypothesis Test for a Single Coefficient 128 128 Example Application of the t-Test for a Single Coefficient 129 Do We Need to Conduct a Hypothesis Test for Every Coefficient? 130 The Analysis of Variance Table and the F-Test of Model Fit F-Test ofModel Fit Model Building and Model Comparison 131 132 135 Nested and Non-Nested Models Comparing Nested Models: F-Test of Difference in Fit 135 137 Adjusted R2 Statistic 139 Application ofAdjusted R2 140 Assumptions and Estimation Problems 141 Collinearity and Multicollinearity 141 Diagnosing Collinearity 142 Regression Diagnostics 144 Standardisation Standardisation and Dummy Predictors 6 vìi 148 151 Standardisation and Interactions Comparing Coefficients of Different Predictors 151 152 Some Final Comments on Standardisation 152 Where to Go From Here 155 Regression Models for Non-Normal Error Distributions 156 Factorial Design Experiments: Analysis of Variance 157 Beyond Modelling the Mean: Quantile Regression 158 Identifying an Appropriate Transformation: Fractional Polynomials 158 Extreme Non-Linearity: Generalised Additive Models 159 Dependency in Data: Multilevel Models (Mixed Effects Models, Hierarchical Models) 159
LINEAR REGRESSION: AN INTRODUCTION TO STATISTICAL MODELS viii Missing Values: Multiple Imputation and Other Methods Bayesian Statistical Models Causality Measurement Models: Factor Analysis and Structural Equations Glossary References Index 159 160 160 161 163 171 175 |
| adam_txt |
CONTENTS List ofFigures, Tables and Boxes About the Author Acknowledgements ix xv xvii Preface xix 1 2 What Is a Statistical Model? 1 Kinds of Models: Visual, Deterministic and Statistical Why Social Scientists Use Models Linear and Non-Linear Relationships: Two Examples First Approach to Models: The t-Test as a Comparison of Two Statistical Models The Sceptic's Model (Null Hypothesis of the t-Test) The Power Pose Model: Alternative Hypothesis of the t-Test Using Data to Compare Two Models The Signal and the Noise 2 3 4 6 8 9 10 14 Simple Linear Regression 17 Origins of Regression: Francis Galton and the Inheritance of Height The Regression Line Regression Coefficients: Intercept and Slope Errors of Prediction and Random Variation The True and the Estimated Regression Line Residuals How to Estimate a Regression Line How Well Does Our Model Explain the Data? The R2 Statistic Sums of Squares: Total, Regression and Residual R2 as a Measure of the Proportion of Variance Explained R2 as a Measure of the Proportional Reduction of Error Interpreting R2 Final Remarks on the R2 Statistic Residual Standard Error Interpreting Galton's Data and the Origin of 'Regression' Inference: Confidence Intervals and Hypothesis Tests 18 21 23 24 25 26 27 29 29 31 31 32 32 , 33 33 35
vi 3 I LINEAR REGRESSION: AN INTRODUCTION TO STATISTICAL MODELS Confidence Range for a Regression Line 39 Prediction and Prediction Intervals 42 Regression in Practice: Things That Can Go Wrong Influential Observations 44 45 Selecting the Right Group 46 The Dangers ofExtrapolation 47 Assumptions and Transformations 51 The Assumptions of Linear Regression 52 Investigating Assumptions: Regression Diagnostics Errors and Residuals 54 54 Standardised Residuals Regression Diagnostics: Application With Examples 55 56 Normality 56 Homoscedasticity and Linearity: The Spread-Level Plot 61 Outliers and Influential Observations Independence ofErrors 64 70 What if Assumptions Do Not Hold? An Example 71 A Non-Linear Relationship 71 Model Diagnostics for the Linear Regression of Life Expectancy on GDP 73 Transforming a Variable: Logarithmic Transformation of GDP 73 Regression Diagnostics for the Linear Regression With Predictor Transformation 79 Types of Transformations, and When to Use Them 79 Common Transformations Techniques for Choosing an Appropriate Transformation 4 Multiple Linear Regression: A Model for Multivariate Relationships Confounders and Suppressors 80 * 83 87 88 Spurious Relationships and Confounding Variables 88 Masked Relationships and Suppressor Variables 91 Multivariate Relationships: A Simple Example With Two Predictors Multiple Regression: General Definition Simple Examples of Multiple Regression Models Example 1: One Numeric Predictor, One Dichotomous Predictor 93 96 97 98 Example 2: Multiple Regression With Two Numeric Predictors 107 Research Example:
Neighbourhood Cohesion and Mental Wellbeing 113
CONTENTS Dummy Variables for Representing Categorical Predictors What Are Dummy Variables? Research Example: Highest Qualification Coded Into Dummy Variables Choice ofReference Category for Dummy Variables 5 117 118 118 122 Multiple Linear Regression: Inference, Assumptions and Standardisation 125 Inference About Coefficients 126 Standard Errors of Coefficient Estimates 126 Confidence Interval for a Coefficient Hypothesis Test for a Single Coefficient 128 128 Example Application of the t-Test for a Single Coefficient 129 Do We Need to Conduct a Hypothesis Test for Every Coefficient? 130 The Analysis of Variance Table and the F-Test of Model Fit F-Test ofModel Fit Model Building and Model Comparison 131 132 135 Nested and Non-Nested Models Comparing Nested Models: F-Test of Difference in Fit 135 137 Adjusted R2 Statistic 139 Application ofAdjusted R2 140 Assumptions and Estimation Problems 141 Collinearity and Multicollinearity 141 Diagnosing Collinearity 142 Regression Diagnostics 144 Standardisation Standardisation and Dummy Predictors 6 vìi 148 151 Standardisation and Interactions Comparing Coefficients of Different Predictors 151 152 Some Final Comments on Standardisation 152 Where to Go From Here 155 Regression Models for Non-Normal Error Distributions 156 Factorial Design Experiments: Analysis of Variance 157 Beyond Modelling the Mean: Quantile Regression 158 Identifying an Appropriate Transformation: Fractional Polynomials 158 Extreme Non-Linearity: Generalised Additive Models 159 Dependency in Data: Multilevel Models (Mixed Effects Models, Hierarchical Models) 159
LINEAR REGRESSION: AN INTRODUCTION TO STATISTICAL MODELS viii Missing Values: Multiple Imputation and Other Methods Bayesian Statistical Models Causality Measurement Models: Factor Analysis and Structural Equations Glossary References Index 159 160 160 161 163 171 175 |
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| isbn | 9781526424174 |
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| spelling | Martin, Peter Verfasser (DE-588)1046973851 aut Linear regression an introduction to statistical models Peter Martin Los Angeles ; London ; New Delhi ; Singapore ; Washington DC ; Melbourne Sage [2021] xiii, 178 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier The Sage quantitative research kit 7th volume Enthält Literaturverzeichnis Seite 171-173 und Index Statistisches Modell (DE-588)4121722-6 gnd rswk-swf Lineare Regression (DE-588)4167709-2 gnd rswk-swf Lineare Regression (DE-588)4167709-2 s Statistisches Modell (DE-588)4121722-6 s DE-604 The Sage quantitative research kit 7th volume (DE-604)BV047607953 7 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032994725&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| title | Linear regression an introduction to statistical models |
| title_auth | Linear regression an introduction to statistical models |
| title_exact_search | Linear regression an introduction to statistical models |
| title_exact_search_txtP | Linear regression an introduction to statistical models |
| title_full | Linear regression an introduction to statistical models Peter Martin |
| title_fullStr | Linear regression an introduction to statistical models Peter Martin |
| title_full_unstemmed | Linear regression an introduction to statistical models Peter Martin |
| title_short | Linear regression |
| title_sort | linear regression an introduction to statistical models |
| title_sub | an introduction to statistical models |
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| topic_facet | Statistisches Modell Lineare Regression |
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