Exercise 6.1: Linear regression on puromycin data

1 Puromycin dataset

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.

2 Goal

Assess if there is an association between the substrate concentration and rate for the treated enzyme.

Import libraries

3 Import data

In contrast to the other datasets we have worked with so far, this dataset is not available through a URL link. In stead, the data is directly available from an R package that was pre-installed in your R working environment. As such, we can simply do

data(Puromycin)

and an object called Puromycin is immediately available in your working environment.

4 Data wrangling

For this exercise, we only want to assess if there is an association between the substrate concentration and rate for the treated enzyme. As such, we should filter the data so that we are left with only the treated enzymes.

5 Data exploration

Make a visualization that allows for exploring if there is a linear relationship between the substrate concentration and enzyme’s rate.

Puromycin %>%
  ggplot(...) + # select which elements of the dataset we need to visualize
  ... # use a relevant plotting geometry
  stat_smooth(...) + # draw a smooth line through the data cloud
  stat_smooth(...) # draw a straight (linear regression) line through the data cloud
  ... # you can add some extra elements like axis labels, title, ...

Does the relationship look linear? Can you think of any other steps that we might take to assess this relationship?

Now may we assume a linear relationship between the substrate concentration and the enzyme’s rate?

6 Linear regression

6.1 Formulate the research question

6.2 Check the assumptions

6.3 Interpret the model parameters of the linear model

6.4 Interpret the results, both for the intercept as well as for the slope

6.5 Write a conclusion that answers the research hypothesis.

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