Tutorial 6.3: Linear regression (continuous) on the fish tank dataset

As an exercise on linear regression, we will analyse the fish tank dataset.

1 Fish tank dataset

In this experiment, 96 fish (dojofish, goldfish and zebrafish) were placed separately in a tank with two litres of water and a certain dose (in mg) of a certain poison EI-43,064. The resistance of the fish a against the poison was measured as the amount of minutes the fish survived upon adding the poison (Surv_time, in minutes). Additionally, the weight of each fish was measured.

2 Goal

The research goal is to study the association between the dose of the poison that was administered to the fish and their survival time by using a linear regression model.

Read the required libraries

library(tidyverse)

3 Import the data

poison <- read_csv("https://raw.githubusercontent.com/GTPB/PSLS20/master/data/poison.csv")

4 Data tidying

We can see a couple of things in the data that can be improved upon:

1. Capitalise the fist column name
2. Set the Species column as a factor
3. Change the species factor levels from 0, 1 and 2 to Dojofish, Goldfish and Zebrafish. Hint: use the fct_recode function.

5 Data Exploration and Descriptive Statistics

Explore the data, there are multiple variables in the dataset.

How many fish do we have per species?

Which variables might influence survival.

Make a suitable visualisation of the association between the dose and the survival time.

6 Modelling the data

In principle we have multiple variables that can affect the survival. We have not seen in the lecture how to model the response based on multiple predictors. In order to get familiar with simple linear regression

1. Check the remaining assumptions

2. Interpret the model parameters of the linear model

3. Interpret the results, both for the intercept as well as for the slope

4. Write a conclusion that answers the research hypothesis.