The Hitchhiker's Guide to Linear Models
Free!
With Membership
$10.00
Suggested price
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
Reader Testimonials
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
University of Toronto
Grounded book. I like the UofT-related examples.
Badi H. Baltagi
Syracuse University
This is a lot of work.
Table of Contents
Contents
Preface
i
1 R Setup
1
1.1 R and Rstudio
1
1.2 Installing R
1
1.2.1 Windows and Mac
1
1.2.2 Linux
1
1.3 Installing RStudio
2
1.3.1 Windows and Mac
2
1.3.2 Linux
2
1.4 Installing R Packages.
2
1.5 Changing RStudio colors and font
4
1.6 Installing Quarto
4
1.6.1 Windows and Mac
4
1.6.2 Linux1
4
2 Linear algebra review
5
2.1 Using R as a calculator
5
2.2 System of linear equations
5
2.3 Matrix
5
2.4 Transpose matrix
6
2.5 Matrix multiplication
6
2.6 Matrix representation of a system of linear equations
6
2.7 Identity matrix
7
2.8 Inverse matrix
7
2.9 Solving systems of linear equations
7
3 Statistics review
3.1 Using R as a calculator
11
3.2 Data and dataset
11
3.3 Summation
11
3.4 Probability
11
3.5 Descriptive statistics
13
3.5.1 Mean
13
3.5.2 Variance
13
3.5.3 Standard deviation
14
3.5.4 Covariance
15
3.5.5 Correlation
16
3.6 Distributions
20
3.6.1 Normal distribution
20
3.6.2 Poisson distribution
22
3.6.3 Student’s t-distribution
23
3.6.4 Computing probabilities with the normal distribution
24
3.6.5 Computing probabilities with the Poisson distribution
27
3.6.6 Computing probabilities with the t-distribution
28
3.7 Sample size
29
4 Recommended workflow
30
4.1 Creating projects
30
4.2 Creating scripts
30
4.3 Creating notebooks
32
4.4 Organizing code sections
33
4.5 Customizing notebooks’ output
34
5 Read, Manipulate, and Plot Data
35
5.1 The datasauRus dataset in R format.
35
5.2 The Quality of Government dataset in CSV format.
40
5.3 The Quality of Government dataset in SAV (SPSS) format
44
5.4 The Quality of Government dataset in DTA (Stata) format
48
5.5 The Freedom House dataset in XLSX (Excel) format
50
6 Linear Model with One Explanatory Variable
60
6.1 Model specification
60
6.2 The Galton dataset
64
6.3 A word of caution about Galton’s work
64
6.4 Loading the Galton dataset
65
6.5 Estimating linear models’ coefficients
66
6.5.1 Linear model as correlation
66
6.5.2 Linear model as matrix multiplication
67
6.5.3 Relation between correlation and matrix multiplication
71
6.5.4 Computational note
75
6.6 Logarithmic transformations
75
6.7 Plotting model results
76
6.8 Linear model does not equal straight line
81
6.9 Transforming variables
85
6.10 Regression with weights
89
7 Linear Model with Multiple Explanatory Variables
91
7.1 Model specification
91
7.2 Life expectancy, GDP and well-being in the Quality of Government dataset
94
7.3 Estimating linear models’ coefficients
96
7.4 Model accuracy
103
7.4.1 Root Mean Squared Error and Mean Absolute Error
103
7.4.2 RMSE and MAE interpretation
104
7.5 Model summary
107
7.5.1 Coefficient’s standard error
107
7.5.2 Coefficient’s t-statistic
108
7.5.3 Coefficient’s p-value
108
7.5.4 Residual standard error
109
7.5.5 Model’s multiple R-squared (or unadjusted R-squared)
109
7.5.6 Model’s adjusted R-squared
110
7.5.7 Model’s F-statistic
111
7.6 Error’s assumptions
111
7.6.1 Error’s normality
112
7.6.2 Error’s homoscedasticity (homogeneous variance)
113
8 Linear Model with Binary and Categorical Explanatory Variables
114
8.1 Model specification with binary variables
114
8.1.1 ANOVA is a particular case of a linear model with binary variables
114
8.1.2 Corruption and popular vote in the Quality of Government dataset
114
8.1.3 Estimating a linear model and ANOVA with one predictor and two categories
116
8.1.4 Corruption and regime type in the Quality of Government dataset
118
8.1.5 Estimating a linear model and ANOVA with one predictor and multiple categories
120
8.1.6 Estimating a linear model with continuous and categorical predictors
126
8.2 Model specification with binary interactions
128
8.2.1 Corruption and interaction variables in the Quality of Government dataset
128
8.2.2 Estimating a linear model with binary interactions
131
8.2.3 Confidence intervals with binary interactions
133
8.3 Model specification with categorical interactions
136
8.3.1 Estimating a linear model with categorical interactions
136
8.3.2 Confidence intervals with categorical interactions
137
9 Linear Model with Fixed Effects
140
9.1 Year fixed effects
140
9.1.1 Model specification
140
9.1.2 Corruption and popular vote in the Quality of Government dataset
140
9.1.3 Estimating year fixed effects’ coefficients
142
9.2 Country fixed effects
145
9.2.1 Model specification
145
9.2.2 Corruption and popular vote in the Quality of Government dataset
145
9.2.3 Estimating country-time fixed effects’ coefficients
145
9.3 Country-year fixed effects
148
9.3.1 Model specification
148
9.3.2 Corruption and popular vote in the Quality of Government dataset
149
9.3.3 Estimating country-time fixed effects’ coefficients
149
10 Generalized Linear Model with One Explanatory Variable
152
10.1 Model specification
152
10.2 Model families.
152
10.2.1 Gaussian model
153
10.2.2 Poisson model
153
10.2.3 Quasi-Poisson model
154
10.2.4 Binomial model (or logit model)
157
11 Generalized Linear Model with Multiple Explanatory Variables
165
11.1 Obtaining the original codes and data
165
11.2 Loading the original data
165
11.3 Ordinary Least Squares
166
11.4 Poisson Pseudo Maximum Likelihood
167
11.5 Tobit
169
11.6 Reporting multiple models
170
References
172
Other books by this author
The Leanpub 60-day 100% Happiness Guarantee
Within 60 days of purchase you can get a 100% refund on any Leanpub purchase, in two clicks.
See full terms
80% Royalties. Earn $16 on a $20 book.
We pay 80% royalties. That's not a typo: you earn $16 on a $20 sale. If we sell 5000 non-refunded copies of your book or course for $20, you'll earn $80,000.
(Yes, some authors have already earned much more than that on Leanpub.)
In fact, authors have earnedover $12 millionwriting, publishing and selling on Leanpub.
Learn more about writing on Leanpub
Free Updates. DRM Free.
If you buy a Leanpub book, you get free updates for as long as the author updates the book! Many authors use Leanpub to publish their books in-progress, while they are writing them. All readers get free updates, regardless of when they bought the book or how much they paid (including free).
Most Leanpub books are available in PDF (for computers) and EPUB (for phones, tablets and Kindle). The formats that a book includes are shown at the top right corner of this page.
Finally, Leanpub books don't have any DRM copy-protection nonsense, so you can easily read them on any supported device.
Learn more about Leanpub's ebook formats and where to read them
