08_3_puromycin.Rmd

---
title: "8.3. Multiple regression with interaction: puromycin example"
author: "Lieven Clement & Jeroen Gilis"
date: "statOmics, Ghent University (https://statomics.github.io)"
---

<a rel="license" href="https://creativecommons.org/licenses/by-nc-sa/4.0"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by-nc-sa/4.0/88x31.png" /></a>

```{r, message=FALSE, warning=FALSE}
library(tidyverse)
```

# 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.**

# Import data

```{r}
data(Puromycin)
```

# Data wrangling

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

```{r}

```

## Data Exploration

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

```{r}

```

# 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.

## Assess model assumptions

## Inference

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

1. the association between velocity and the concentration is significant in
the untreated group

2. the association between velocity and the concentration is significant in
the treated group

3. 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`.

## Conclusion