The paper "Aspects of Food Finding by Wintering Bald Eagles" (The Auk [1983]: 477-484) examined the relationship between the time 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.
a. Draw a scatterplot for this data set. Would you describe the pattern in the plot as linear or curved?
b. One possible transformation that might lead to a straighter plot involves taking the square root of both the x and y values. Explain why this might be a reasonable transformation.
c. Construct a scatterplot using the variables x and y. Is this scatterplot more nearly linear than the scatterplot in Part (a)?
d. Suggest another transformation that might be used to straighten the original plot.