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Lecture notes. Written from the material of GTPB Psls20, licensed CC BY 4.0. These are notes, not a transcript: the material has been reorganised and rewritten. This adaptation carries the same licence, and the original is linked above.

34. Linear Regression on Fish Survival

What this covers

This chapter walks through a tutorial exercise: fitting a simple linear regression to see whether the dose of a poison predicts how long a fish survives it. It assumes you already have simple linear regression from the lecture — fitting a line by least squares, and reading its intercept and slope — and adds the practice of applying that model to a real, slightly untidy dataset in R, checking its assumptions, and writing a conclusion tied to the research question, rather than any new theory.

The fish tank experiment

96 fish — dojofish, goldfish and zebrafish — were each placed alone in a tank holding two litres of water and a measured dose (in mg) of poison EI-43,064. Two things were then recorded for every fish:

  • Surv_time — how many minutes the fish survived after the poison was added, and
  • its weight.

The species each fish belonged to was also noted. The raw data is a single CSV (poison.csv), read directly from the course's GitHub repository with read_csv().

The research goal is to describe the relationship between poison dose and survival time with a linear regression model.

Why simple regression, and not the full model

Dose is not the only thing in the data that plausibly affects how long a fish survives — its species and its weight are recorded for exactly this reason, since a heavier fish or a hardier species might tolerate the same dose differently. A model that accounted for all of them at once would be a multiple regression, but multiple regression had not yet been covered in the lecture at this point in the course. So the tutorial deliberately restricts itself to a single predictor — dose alone — to get comfortable with the mechanics of simple linear regression: fitting it, checking it, and reading its two parameters, before multiple regression is introduced later to bring the other variables back in.

Getting the data into usable shape

Before any modelling, the raw table needs the same kind of tidying that shows up throughout this course: Species is stored as a bare number (0, 1, 2) rather than a proper label, and the first column name needs capitalising to match the convention used elsewhere. Converting Species to a factor and relabelling its three levels as Dojofish, Goldfish and Zebrafish — the tutorial's own hint points at fct_recode for the relabelling — turns the column from a number a model would happily average into the three-way grouping variable it actually is.

The workflow the tutorial follows

  1. Import the data from the CSV and inspect it.
  2. Tidy it: fix the column name and turn Species into a properly labelled factor.
  3. Explore it: count how many fish there are of each species, think about which of the recorded variables could plausibly affect survival, and plot survival time against dose.
  4. Fit a simple linear regression of survival time on dose alone, restricting to a single predictor for the reason above.
  5. Check the model's remaining assumptions before trusting it.
  6. Interpret the two fitted parameters — intercept and slope — and translate the fit back into an answer to the research question.

Exercises

Working from the fish tank dataset described above (96 fish; Surv_time in minutes; poison dose in mg; Species coded 0/1/2 for dojofish/goldfish/zebrafish; weight also recorded):

  1. Tidy the imported data: capitalise the first column's name, convert Species to a factor, and recode its levels from 0, 1, 2 to Dojofish, Goldfish and Zebrafish.
  2. How many fish are there of each species?
  3. Which of the recorded variables might plausibly influence survival time? Produce a suitable plot showing the association between dose and survival time.
  4. Fit a simple linear regression of survival time on dose, and check whatever assumptions of the model still need verifying.
  5. Interpret the fitted model's parameters — both the intercept and the slope.
  6. Write a conclusion, in terms of the original research question, that states what the fitted model says about the relationship between poison dose and fish survival.

Sources

  • Tutorial notes: tutorialScripts/excercises/06_linearRegression/Linreg_continuous_fish_poison_half.Rmd (GTPB PSLS20 course, Tutorial 6.3, "Linear regression (continuous) on the fish tank dataset") — the experimental description, the stated research goal, the data-import URL, and all the exercise steps (data tidying, data exploration, model fitting, assumption checking, parameter interpretation, conclusion) come from this file.
  • The file's own R code chunks — for loading libraries, importing the data, tidying it, exploring it, and modelling it — are left blank in the source; they are the student's task to complete, not material the course supplied, so no R code is reproduced here.
  • No slide deck or lecture transcript was supplied for this tutorial. The simple linear regression theory it applies (least-squares fitting, the interpretation of an intercept and a slope, and the model's assumptions) is referred to as already covered "in the lecture" but is not contained in this file; neither is the fct_recode function the tutorial names as a hint for relabelling Species.

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