8.3. Multiple regression with interaction: puromycin example

statOmics, Ghent University (https://statomics.github.io)

Author

Lieven Clement & Jeroen Gilis

Code

library(tidyverse)

1 Puromycin data

Data on the velocity of an enzymatic reaction were obtained by Treloar (1974). The number of counts per minute of radioactive product from the reaction was measured as a function of substrate concentration in parts per million (ppm) and from these counts the initial rate (or velocity) of the reaction was calculated (counts/min/min). The experiment was conducted once with the enzyme treated with Puromycin, and once with the enzyme untreated.

Assess if there is an association between the substrate concentration and rate for both the treated and untreated enzymes.

2 Import data

Code

data(Puromycin)

3 Data wrangling

For a clearer interpretation of the model parameters later on, we will make the untreated state enzymes the reference category.

3.1 Data Exploration

First, we visualize the association between the concentration and the enzyme rate, for both of the enzyme states.

4 Linear regression

We will model the data that explains enzyme rates in function of a main effect for concentration, a main effect for enzyme state and an interaction term between these two variables.

4.1 Assess model assumptions

4.2 Inference

Use the model to test the parameters of interest. We are now interested in assessing if

the association between velocity and the concentration is significant in the untreated group
the association between velocity and the concentration is significant in the treated group
the association between velocity and the concentration is different between treated and untreated group

Step 1: translate these research questions into parameters (cobinations of parameters) of the linear model. Step 2: test the relevant parameters. This can be done for the three hypotheses at once using the package multcomp.