Chapter 5, Problem 73CR

The paper “Aspects of Food Finding by Wintering Bald Eagles” (The Auk [1983]: 477–484) examined the relationship between the lime that eagles spend aerially searching for food (indicated by the percentage of eagles soaring) and relative food availability. The accompanying data were taken from a scatterplot that appeared in this paper. Use x to denote salmon availability and y to denote the percentage of eagles in the air.

1. a. Draw a scatterplot for this data set. Would you describe the pattern in the plot as linear or curved?
2. b. One possible transformation that might lead to a more nearly linear plot involves taking the square root of both the x and y values. Explain why this might be a reasonable transformation.
3. c. Construct a scatterplot using the variables $\sqrt{x}$ and $\sqrt{y}.$ Is this scatterplot more nearly linear than the scatterplot in Part (a)?
4. d. Suggest another transformation that might be used to straighten the original plot.