4  Interaction

Linear regression where the effect of one variable depends on another.

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4.1 Summary

Slope × groups

Mathematical formula:

\[\begin{align} \eta &= \beta_0 + \beta_1 \cdot x_1 + \beta_2 \cdot x_2 + \beta_3 \cdot x_1 \cdot x_2 \\ \tag{1}\label{interactionslope}\\ x_2 &= \begin{cases}1 \quad \text{if B}\\ 0 \quad \text{otherwise} \end{cases} \end{align}\]

Code:

R

model <- lm(y ~ x * group, data)

Python

import statsmodels.formula.api as smf
model = smf.ols("y ~ x * group", data).fit()

Symbols & definitions

To do.

Explanation

To do.

Example

To do.

Groups × groups

Mathematical formula:

\[\begin{align} \eta &= \beta_0 + \beta_1 \cdot x_1 + \beta_2 \cdot x_2 + \beta_3 \cdot x_1 \cdot x_2 \\ \tag{2}\label{interactiondummy}\\ x_1 &= \begin{cases}1 \quad \text{if B}\\ 0 \quad \text{otherwise} \end{cases}, \quad x_2 = \begin{cases}1 \quad \text{if treated}\\ 0 \quad \text{otherwise} \end{cases} \end{align}\]

Code:

R

model <- lm(y ~ group * treatment, data)

Python

import statsmodels.formula.api as smf
model = smf.ols("y ~ group * treatment", data).fit()

Symbols & definitions

To do.

Explanation

To do.

Example

To do.

Slope × slope

To do.

\[\begin{align} \eta &= \beta_0 + \beta_1 \cdot x_1 + \beta_2 \cdot x_2 + \beta_3 \cdot x_1 \cdot x_2 \tag{3}\label{interactionslopeslope} \end{align}\]

R

model <- lm(y ~ x1 * x2, data)

Python

import statsmodels.formula.api as smf
model = smf.ols("y ~ x1 * x2", data).fit()

4.2 Quiz

Question 1

To do.

Hint

To do.

Answer

To do.

Learn why

To do.

Question 2

To do.

Hint

To do.

Answer

To do.

Learn why

To do.

Interactive app

Practice the concepts covered in this chapter:

Regression tables

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4.3 Apply your knowledge

Now analyze a dataset yourself. Start with the worked examples, then do the exercise:

• Tutorial — linear model (qmd , data )
• Tutorial — binomial GLM (qmd , data )
• Exercise (qmd , data )

How to read data in R

1. Save the data and qmd file in the same location on your computer.
2. Open the qmd file in RStudio.
3. Set working directory to source file location.
   (Session > Set Working Directory > To Source File Location)
4. R will now read from the folder the qmd file is located, so you can just use read.csv("name-of-data.csv").