Linear regression : an introduction to statistical models /
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| Main Author: | |
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| Corporate Author: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
London :
SAGE Publications,
2021.
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| Series: | The Sage quantitative research kit
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| Subjects: | |
| Online Access: | Connect to this title online (unlimited simultaneous users allowed; 325 uses per year) |
Table of Contents:
- Machine generated contents note: 1. What Is a Statistical Model?
- 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
- Sceptic's Model (Null Hypothesis of the t-Test)
- Power Pose Model: Alternative Hypothesis of the t-Test
- Using Data to Compare Two Models
- Signal and the Noise
- 2. Simple Linear Regression
- Origins of Regression: Francis Galton and the Inheritance of Height
- Regression Line
- Regression Coefficients: Intercept and Slope
- Errors of Prediction and Random Variation
- 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
- Confidence Range for a Regression Line
- Prediction and Prediction Intervals
- Regression in Practice: Things That Can Go Wrong
- Influential Observations
- Selecting the Right Group
- Dangers of Extrapolation
- 3. Assumptions and Transformations
- Assumptions of Linear Regression
- Investigating Assumptions: Regression Diagnostics
- Errors and Residuals
- Standardised Residuals
- Regression Diagnostics: Application With Examples
- Normality
- Homoscedasticity and Linearity: The Spread-Level Plot
- Outliers and Influential Observations
- Independence of Errors
- What if Assumptions Do Not Hold? An Example
- Non-Linear Relationship
- Model Diagnostics for the Linear Regression of Life Expectancy on GDP
- Transforming a Variable: Logarithmic Transformation of GDP
- Regression Diagnostics for the Linear Regression With Predictor Transformation
- Types of Transformations, and When to Use Them
- Common Transformations
- Techniques for Choosing an Appropriate Transformation
- 4. Multiple Linear Regression: A Model for Multivariate Relationships
- Confounders and Suppressors
- Spurious Relationships and Confounding Variables
- Masked Relationships and Suppressor Variables
- 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
- Example 2 Multiple Regression With Two Numeric Predictors
- Research Example: Neighbourhood Cohesion and Mental Wellbeing
- Dummy Variables for Representing Categorical Predictors
- What Are Dummy Variables?
- Research Example: Highest Qualification Coded Into Dummy Variables
- Choice of Reference Category for Dummy Variables
- 5. Multiple Linear Regression: Inference, Assumptions and Standardisation
- Inference About Coefficients
- Standard Errors of Coefficient Estimates
- Confidence Interval for a Coefficient
- Hypothesis Test for a Single Coefficient
- Example Application of the t-Test for a Single Coefficient
- Do We Need to Conduct a Hypothesis Test for Every Coefficient?
- Analysis of Variance Table and the F-Test of Model Fit
- F-Test of Model Fit
- Model Building and Model Comparison
- Nested and Non-Nested Models
- Comparing Nested Models: F-Test of Difference in Fit
- Adjusted R2 Statistic
- Application of Adjusted R2
- Assumptions and Estimation Problems
- Collinearity and Multicollinearity
- Diagnosing Collinearity
- Regression Diagnostics
- Standardisation
- Standardisation and Dummy Predictors
- Standardisation and Interactions
- Comparing Coefficients of Different Predictors
- Some Final Comments on Standardisation
- 6. Where to Go From Here
- Regression Models for Non-Normal Error Distributions
- Factorial Design Experiments: Analysis of Variance
- Beyond Modelling the Mean: Quantile Regression
- Identifying an Appropriate Transformation: Fractional Polynomials
- Extreme Non-Linearity: Generalised Additive Models
- Dependency in Data: Multilevel Models (Mixed Effects Models, Hierarchical Models)
- Missing Values: Multiple Imputation and Other Methods
- Bayesian Statistical Models
- Causality
- Measurement Models: Factor Analysis and Structural Equations.