Linear regression in R

Cheatsheet

License

This work was developed using resources that are available under a Creative Commons Attribution 4.0 International License, made available on the SOLES Open Educational Resources repository by the School of Life and Environmental Sciences, The University of Sydney.

Assumed knowledge

• You know how to install and load packages in R.
• You know how to import data into R.
• You recognise data frames and vectors.

Data structure

The data should be in a long format (also known as tidy data), where each row is an observation and each column is a variable (Figure 1). If your data is not already structured this way, reshape it manually in a spreadsheet program or in R using the pivot_longer() function from the tidyr package.

Sex	BW
F	2.15
M	2.55
F	2.95
F	2.70
M	2.20
F	1.85
M	2.55
M	2.60

 

F	M
2.15	2.55
2.95	2.20
2.70	2.55
1.85	2.60

Figure 1: Data should be in long format (left) where each row is an observation and each column is a variable. This is the preferred format for most statistical software. Wide format (right) is also common, but may require additional steps to analyse or visualise in some instances.

Data

For this cheatsheet we will use data from the penguins dataset from the palmerpenguins package. You may need to install this package:

install.packages("palmerpenguins")
data(penguins)

About

Regression analysis is the most commonly used statistical technique for modelling the relationship between variables that can be continuous, categorical or a mix of both. In fact, other techniques such as the t-test, ANOVA, ANCOVA and even non-parametric tests can be considered as special cases of regression analysis. In this cheatsheet, we will focus on linear regression.

R packages used

Implementing linear models

Simple linear regression

fit01 <- lm(body_mass_g ~ flipper_length_mm, data = penguins)

Multiple linear regression

fit02 <- lm(body_mass_g ~ flipper_length_mm + bill_length_mm,
    data = penguins
)

Interactions

fit03 <- lm(body_mass_g ~ flipper_length_mm * bill_length_mm,
    data = penguins
)

Regression involving categorical variables

fit04 <- lm(body_mass_g ~ species + sex, data = penguins)

Regression involving a mix of continuous and categorical variables

fit04 <- lm(body_mass_g ~ species + flipper_length_mm,
    data = penguins
)

Assumptions

Use the plot() function on the linear mode object to check the assumptions of the linear regression model.

par(mfrow = c(2, 2)) # Set up a 2x2 grid of plots
plot(fit01)

par(mfrow = c(1, 1)) # Reset the plot layout

Viewing interactions

Use the emmeans() function to interpret interactions in a linear model. For continuous variables, you need to specify the range of the covariate with the cov.reduce argument – set to range to avoid the default of using the mean.

emmip(fit03, flipper_length_mm ~ bill_length_mm, cov.reduce = range)

emmip(fit03, bill_length_mm ~ flipper_length_mm, cov.reduce = range)

Other resources

• It might be worthwhile to use the performance package to assess model fit (including assumptions using check_model()).
• I use this a lot: the interactions package for visualising interactions in GLM models. However it is very technical and not for beginners – use if you are comfortable with R.
• The gtsummary package is great for summarising regression models using tbl_regression(), but you may need to tweak it further to get the output you want. Another package that can do something similar is the sjPlot package, using tab_model(). Alternatively, you can manually create the table (sometimes it can be easier to copy numbers depending on your level of expertise).