Weight-Length Relationship

Inch Lake

Fit a weight-length relationsip for Inch Lake Bluegill.

Derek H. Ogle


Mar 8, 2019


Dec 27, 2022


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 Bluegill only data frames.


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.]
  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.2 Comment on the fit.
    2. Construct a residual plot.3 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 This post may be useful.

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

4 This post may be useful.

5 This post may be useful.


Solution Code:

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