Chapter 5.4, Problem 45E

The paper “Aspects of Food Finding by Wintering Bald Eagles” (The Auk [1983]: 477–484) examined the relationship between the time that eagles spend aloft 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. Salmon availability is denoted by x and the percentage of eagles in the air is denoted by y.

1. a. Draw a scattcrplot 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 linear pattern involves taking the square root of both the x and y values. Construct a scatterplot using the variables $\sqrt{x}$ and $\sqrt{y.}$ Is a line a more reasonable chioce for describing the pattern in this scatterplot than the pattern in the scatterplot in Part (a)?
3. c. After considering the scatterplot in Part (a), suggest another transformation that might be used to straighten the original plot. Use your suggestion to construct a scatterplot for your x′ and/or y′. Which transformation (the one you suggested or the square root transformation from Part (b)) is preferable? Explain.