# Basic Analysis I

- Construct graphs appropriate to answer the following questions.
^{1}- Describe the relationship between weight and length (in mm here and throughout).
- Describe the relationship between log-transformed weight and length.

- 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} - Compute the weight-length relationship with an appropriate linear regression.
- Plot the results (data and the fitted relationship) on both the transformed and raw scales.
^{3}Comment on the fit. - Construct a residual plot.
^{4}Comment. - Express your results as an equation on the transformed scale.
- Express your results as an equation on the raw scale.
- Carefully interpret the meaning of the slope of the weight-length relationship.
- Is there statistical evidence for isometric or allometric growth?

- Plot the results (data and the fitted relationship) on both the transformed and raw scales.

^{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

- 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

- Construct a plot that allows you to qualitatively assess if the weight-length (
*in mm here and throughout*) relationship differs between the three gears. - Fit a model that allows you to determine if there is a statistically significant difference in the weight-length relationship between the three gears.
- Construct a residual plot for this model.
^{5}Comment. - 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.
- 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).
- Construct a plot that illustrates your findings.
^{6}

- Construct a residual plot for this model.