Weight-Length Relationship

Trout Lake Yellow Perch

Fit a weight-length relationsip for Trout Lake Yellow Perch.

Derek H. Ogle


Mar 8, 2019


Feb 13, 2023


This exercise is a continuation of this data wrangling exercise and, thus, depends on data frames constructed there. Please load/run your script from that exercise to access the Yellow Perch captured in the 1990s data frame.


Basic Analysis I

  1. Construct graphs appropriate to answer the following questions.1
    1. Describe the relationship between weight and length (in mm here and throughout).
    2. Describe the relationship between log-transformed weight and length.
  2. From the plots above there is a clear minimum length for which the weights were precisely obtained. What is that length? [Reduce the data frame to fish greater than this minimum length for the questions below. You should also remove all fish for which a weight was not recorded.]2
  3. Compute the weight-length relationship with an appropriate linear regression.
    1. Plot the results (data and the fitted relationship) on both the transformed and raw scales.3 Comment on the fit.
    2. Construct a residual plot.4 Comment.
    3. Express your results as an equation on the transformed scale.
    4. Express your results as an equation on the raw scale.
    5. Carefully interpret the meaning of the slope of the weight-length relationship.
    6. Is there statistical evidence for isometric or allometric growth?

1 If you completed this graphing exercise then you created the necessary graphs there.

2 There are several outliers in this data that should be corrected or removed. For simplicity, leave them in the data for this exercise.

3 This post may be useful.

4 This post may be useful.


Basic Analysis II

  1. Recompute the weight-length relationship using the original length in inches. How do the slope and y-intercept from this model compare to the results from the previous question?


Extended Analysis

  1. Construct a plot that allows you to qualitatively assess if the weight-length (in mm here and throughout) relationship differs between the three gears.
  2. Fit a model that allows you to determine if there is a statistically significant difference in the weight-length relationship between the three gears.
    1. Construct a residual plot for this model.5 Comment.
    2. Is there a statistically significant difference in the weight-length relationship between the three gears? Provide evidence for your findings and be very specific with your conclusions.
    3. Without fitting separate regressions for the three gears express the weight-length relationships on the raw scale for all gears (i.e., write three specific equations).
    4. Construct a plot that illustrates your findings.6

5 This post may be useful.

6 This post may be useful.


Solution Code:

Available upon request to students not in a class. Contact fishR maintainers.