The Hitchhiker's Guide to Linear Models
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The Hitchhiker's Guide to Linear Models

Based on the famous R programming language

About the Book

This book aims to get straight to the point, and the only thing I assume here is that you have used spreadsheets at some point and that you are motivated to estimate linear models in R. Here I do not assume that you know how to install R or the basics of the R programming language.

About the Author

Mauricio 'Pacha' Vargas Sepúlveda
Mauricio 'Pacha' Vargas Sepúlveda

I am a PhD student in Political Science at the University of Toronto. My research interests include International Relations, Canadian Politics and Public Policy, with a focus on the politics of trade agreements and sanctions. I have a Master of Arts in Political Science from the University of Toronto, a Master of Science in Statistics from the Catholic University of Chile, and an Engineering degree from the University of Chile. I can provide my CV (academic/professional) upon request. You can reach me at m.sepulveda+removethis@mail.utoronto.ca (please remove the +removethis).

See my website (pacha.dev) and my blog (pacha.dev/blog).

Reader Testimonials

Claudia Negri-Ribalta
Claudia Negri-Ribalta

Université Paris 1 Panthéon-Sorbonne

I think it's great that you are teaching them how to write in R. My big problem was always that, the syntax.

Catherine Moez
Catherine Moez

University of Toronto

Grounded book. I like the UofT-related examples.

Badi H. Baltagi
Badi H. Baltagi

Syracuse University

This is a lot of work.

Table of Contents

  • I. Preface
  • II. R Setup
    • 1. R and RStudio
      • 1.1. Windows and Mac
      • 1.2. Linux
    • 2. Installing R
      • 2.1. Windows and Mac
      • 2.2. Linux
    • 3. Installing RStudio
      • 3.1. Windows and Mac
      • 3.2. Linux
    • 4. Installing R Packages
      • 4.1. Windows and Mac
      • 4.2. Linux
    • 5. Changing RStudio colors and font
      • 5.1. Windows and Mac
      • 5.2. Linux
    • 6. Installing Quarto
      • 6.1. Windows and Mac
      • 6.2. Linux
  • III. Linear algebra review
    • 1. Using R as a calculator
    • 2. System of linear equations
    • 3. Matrix
    • 4. Transpose matrix
    • 5. Matrix multiplication
    • 6. Matrix representation of a system of linear equations
    • 7. Identity matrix
    • 8. Inverse matrix
    • 9. Solving systems of linear equations
  • IV. Statistics review
    • 1. Using R as a calculator
      • 1.1. Mean
      • 1.2. Variance
      • 1.3. Standard deviation
      • 1.4. Covariance
      • 1.5. Correlation
      • 1.6. Normal distribution
      • 1.7. Poisson distribution
      • 1.8. Student's t-distribution
      • 1.9. Computing probabilities with the normal distribution
      • 1.10. Computing probabilities with the Poisson distribution
      • 1.11. Computing probabilities with the t-distribution
    • 2. Data and dataset
      • 2.1. Mean
      • 2.2. Variance
      • 2.3. Standard deviation
      • 2.4. Covariance
      • 2.5. Correlation
      • 2.6. Normal distribution
      • 2.7. Poisson distribution
      • 2.8. Student's t-distribution
      • 2.9. Computing probabilities with the normal distribution
      • 2.10. Computing probabilities with the Poisson distribution
      • 2.11. Computing probabilities with the t-distribution
    • 3. Summation
      • 3.1. Mean
      • 3.2. Variance
      • 3.3. Standard deviation
      • 3.4. Covariance
      • 3.5. Correlation
      • 3.6. Normal distribution
      • 3.7. Poisson distribution
      • 3.8. Student's t-distribution
      • 3.9. Computing probabilities with the normal distribution
      • 3.10. Computing probabilities with the Poisson distribution
      • 3.11. Computing probabilities with the t-distribution
    • 4. Probability
      • 4.1. Mean
      • 4.2. Variance
      • 4.3. Standard deviation
      • 4.4. Covariance
      • 4.5. Correlation
      • 4.6. Normal distribution
      • 4.7. Poisson distribution
      • 4.8. Student's t-distribution
      • 4.9. Computing probabilities with the normal distribution
      • 4.10. Computing probabilities with the Poisson distribution
      • 4.11. Computing probabilities with the t-distribution
    • 5. Descriptive statistics
      • 5.1. Mean
      • 5.2. Variance
      • 5.3. Standard deviation
      • 5.4. Covariance
      • 5.5. Correlation
      • 5.6. Normal distribution
      • 5.7. Poisson distribution
      • 5.8. Student's t-distribution
      • 5.9. Computing probabilities with the normal distribution
      • 5.10. Computing probabilities with the Poisson distribution
      • 5.11. Computing probabilities with the t-distribution
    • 6. Distributions
      • 6.1. Mean
      • 6.2. Variance
      • 6.3. Standard deviation
      • 6.4. Covariance
      • 6.5. Correlation
      • 6.6. Normal distribution
      • 6.7. Poisson distribution
      • 6.8. Student's t-distribution
      • 6.9. Computing probabilities with the normal distribution
      • 6.10. Computing probabilities with the Poisson distribution
      • 6.11. Computing probabilities with the t-distribution
    • 7. Sample size
      • 7.1. Mean
      • 7.2. Variance
      • 7.3. Standard deviation
      • 7.4. Covariance
      • 7.5. Correlation
      • 7.6. Normal distribution
      • 7.7. Poisson distribution
      • 7.8. Student's t-distribution
      • 7.9. Computing probabilities with the normal distribution
      • 7.10. Computing probabilities with the Poisson distribution
      • 7.11. Computing probabilities with the t-distribution
  • V. Recommended workflow
    • 1. Creating projects
    • 2. Creating scripts
    • 3. Creating notebooks
    • 4. Organizing code sections
    • 5. Customizing notebooks' output
  • VI. Read, Manipulate, and Plot Data
    • 1. The datasauRus dataset in R format
    • 2. The Quality of Government dataset in CSV format
    • 3. The Quality of Government dataset in SAV (SPSS) format
    • 4. The Quality of Government dataset in DTA (Stata) format
    • 5. The Freedom House dataset in XLSX (Excel) format
  • VII. Linear Model with One Explanatory Variable
    • 1. Model specification
      • 1.1. Linear model as correlation
      • 1.2. Linear model as matrix multiplication
      • 1.3. Relation between correlation and matrix multiplication
      • 1.4. Computational note
    • 2. The Galton dataset
      • 2.1. Linear model as correlation
      • 2.2. Linear model as matrix multiplication
      • 2.3. Relation between correlation and matrix multiplication
      • 2.4. Computational note
    • 3. A word of caution about Galton's work
      • 3.1. Linear model as correlation
      • 3.2. Linear model as matrix multiplication
      • 3.3. Relation between correlation and matrix multiplication
      • 3.4. Computational note
    • 4. Loading the Galton dataset
      • 4.1. Linear model as correlation
      • 4.2. Linear model as matrix multiplication
      • 4.3. Relation between correlation and matrix multiplication
      • 4.4. Computational note
    • 5. Estimating linear models' coefficients
      • 5.1. Linear model as correlation
      • 5.2. Linear model as matrix multiplication
      • 5.3. Relation between correlation and matrix multiplication
      • 5.4. Computational note
    • 6. Logarithmic transformations
      • 6.1. Linear model as correlation
      • 6.2. Linear model as matrix multiplication
      • 6.3. Relation between correlation and matrix multiplication
      • 6.4. Computational note
    • 7. Plotting model results
      • 7.1. Linear model as correlation
      • 7.2. Linear model as matrix multiplication
      • 7.3. Relation between correlation and matrix multiplication
      • 7.4. Computational note
    • 8. Linear model does not equal straight line
      • 8.1. Linear model as correlation
      • 8.2. Linear model as matrix multiplication
      • 8.3. Relation between correlation and matrix multiplication
      • 8.4. Computational note
    • 9. Transforming variables
      • 9.1. Linear model as correlation
      • 9.2. Linear model as matrix multiplication
      • 9.3. Relation between correlation and matrix multiplication
      • 9.4. Computational note
    • 10. Regression with weights
      • 10.1. Linear model as correlation
      • 10.2. Linear model as matrix multiplication
      • 10.3. Relation between correlation and matrix multiplication
      • 10.4. Computational note
  • VIII. Linear Model with Multiple Explanatory Variables
    • 1. Model specification
      • 1.1. Root Mean Squared Error and Mean Absolute Error
      • 1.2. RMSE and MAE interpretation
      • 1.3. Coefficient's standard error
      • 1.4. Coefficient's t-statistic
      • 1.5. Coefficient's p-value
      • 1.6. Residual standard error
      • 1.7. Model's multiple R-squared (or unadjusted R-squared)
      • 1.8. Model's adjusted R-squared
      • 1.9. Model's F-statistic
      • 1.10. Error's normality
      • 1.11. Error's homoscedasticity (homogeneous variance)
    • 2. Life expectancy, GDP and well-being in the Quality of Government dataset
      • 2.1. Root Mean Squared Error and Mean Absolute Error
      • 2.2. RMSE and MAE interpretation
      • 2.3. Coefficient's standard error
      • 2.4. Coefficient's t-statistic
      • 2.5. Coefficient's p-value
      • 2.6. Residual standard error
      • 2.7. Model's multiple R-squared (or unadjusted R-squared)
      • 2.8. Model's adjusted R-squared
      • 2.9. Model's F-statistic
      • 2.10. Error's normality
      • 2.11. Error's homoscedasticity (homogeneous variance)
    • 3. Estimating linear models' coefficients
      • 3.1. Root Mean Squared Error and Mean Absolute Error
      • 3.2. RMSE and MAE interpretation
      • 3.3. Coefficient's standard error
      • 3.4. Coefficient's t-statistic
      • 3.5. Coefficient's p-value
      • 3.6. Residual standard error
      • 3.7. Model's multiple R-squared (or unadjusted R-squared)
      • 3.8. Model's adjusted R-squared
      • 3.9. Model's F-statistic
      • 3.10. Error's normality
      • 3.11. Error's homoscedasticity (homogeneous variance)
    • 4. Model accuracy
      • 4.1. Root Mean Squared Error and Mean Absolute Error
      • 4.2. RMSE and MAE interpretation
      • 4.3. Coefficient's standard error
      • 4.4. Coefficient's t-statistic
      • 4.5. Coefficient's p-value
      • 4.6. Residual standard error
      • 4.7. Model's multiple R-squared (or unadjusted R-squared)
      • 4.8. Model's adjusted R-squared
      • 4.9. Model's F-statistic
      • 4.10. Error's normality
      • 4.11. Error's homoscedasticity (homogeneous variance)
    • 5. Model summary
      • 5.1. Root Mean Squared Error and Mean Absolute Error
      • 5.2. RMSE and MAE interpretation
      • 5.3. Coefficient's standard error
      • 5.4. Coefficient's t-statistic
      • 5.5. Coefficient's p-value
      • 5.6. Residual standard error
      • 5.7. Model's multiple R-squared (or unadjusted R-squared)
      • 5.8. Model's adjusted R-squared
      • 5.9. Model's F-statistic
      • 5.10. Error's normality
      • 5.11. Error's homoscedasticity (homogeneous variance)
    • 6. Error's assumptions
      • 6.1. Root Mean Squared Error and Mean Absolute Error
      • 6.2. RMSE and MAE interpretation
      • 6.3. Coefficient's standard error
      • 6.4. Coefficient's t-statistic
      • 6.5. Coefficient's p-value
      • 6.6. Residual standard error
      • 6.7. Model's multiple R-squared (or unadjusted R-squared)
      • 6.8. Model's adjusted R-squared
      • 6.9. Model's F-statistic
      • 6.10. Error's normality
      • 6.11. Error's homoscedasticity (homogeneous variance)
  • IX. Linear Model with Binary and Categorical Explanatory Variables
    • 1. Model specification with binary variables
      • 1.1. ANOVA is a particular case of a linear model with binary variables
      • 1.2. Corruption and popular vote in the Quality of Government dataset
      • 1.3. Estimating a linear model and ANOVA with one predictor and two categories
      • 1.4. Corruption and regime type in the Quality of Government dataset
      • 1.5. Estimating a linear model and ANOVA with one predictor and multiple categories
      • 1.6. Estimating a linear model with continuous and categorical predictors
      • 1.7. Corruption and interaction variables in the Quality of Government dataset
      • 1.8. Estimating a linear model with binary interactions
      • 1.9. Confidence intervals with binary interactions
      • 1.10. Estimating a linear model with categorical interactions
      • 1.11. Confidence intervals with categorical interactions
    • 2. Model specification with binary interactions
      • 2.1. ANOVA is a particular case of a linear model with binary variables
      • 2.2. Corruption and popular vote in the Quality of Government dataset
      • 2.3. Estimating a linear model and ANOVA with one predictor and two categories
      • 2.4. Corruption and regime type in the Quality of Government dataset
      • 2.5. Estimating a linear model and ANOVA with one predictor and multiple categories
      • 2.6. Estimating a linear model with continuous and categorical predictors
      • 2.7. Corruption and interaction variables in the Quality of Government dataset
      • 2.8. Estimating a linear model with binary interactions
      • 2.9. Confidence intervals with binary interactions
      • 2.10. Estimating a linear model with categorical interactions
      • 2.11. Confidence intervals with categorical interactions
    • 3. Model specification with categorical interactions
      • 3.1. ANOVA is a particular case of a linear model with binary variables
      • 3.2. Corruption and popular vote in the Quality of Government dataset
      • 3.3. Estimating a linear model and ANOVA with one predictor and two categories
      • 3.4. Corruption and regime type in the Quality of Government dataset
      • 3.5. Estimating a linear model and ANOVA with one predictor and multiple categories
      • 3.6. Estimating a linear model with continuous and categorical predictors
      • 3.7. Corruption and interaction variables in the Quality of Government dataset
      • 3.8. Estimating a linear model with binary interactions
      • 3.9. Confidence intervals with binary interactions
      • 3.10. Estimating a linear model with categorical interactions
      • 3.11. Confidence intervals with categorical interactions
  • X. Linear Model with Fixed Effects
    • 1. Year fixed effects
      • 1.1. Model specification
      • 1.2. Corruption and popular vote in the Quality of Government dataset
      • 1.3. Estimating year fixed effects' coefficients
      • 1.4. Estimating country-time fixed effects' coefficients
    • 2. Country fixed effects
      • 2.1. Model specification
      • 2.2. Corruption and popular vote in the Quality of Government dataset
      • 2.3. Estimating year fixed effects' coefficients
      • 2.4. Estimating country-time fixed effects' coefficients
    • 3. Country-year fixed effects
      • 3.1. Model specification
      • 3.2. Corruption and popular vote in the Quality of Government dataset
      • 3.3. Estimating year fixed effects' coefficients
      • 3.4. Estimating country-time fixed effects' coefficients
  • XI. Generalized Linear Model with One Explanatory Variable
    • 1. Model specification
      • 1.1. Gaussian model
      • 1.2. Poisson model
      • 1.3. Quasi-Poisson model
      • 1.4. Binomial model (or logit model)
    • 2. Model families
      • 2.1. Gaussian model
      • 2.2. Poisson model
      • 2.3. Quasi-Poisson model
      • 2.4. Binomial model (or logit model)
  • XII. Generalized Linear Model with Multiple Explanatory Variables
    • 1. Obtaining the original codes and data
    • 2. Loading the original data
    • 3. Ordinary Least Squares
    • 4. Poisson Pseudo Maximum Likelihood
    • 5. Tobit
    • 6. Reporting multiple models

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