5.62 ● The paper “Aspects of Food Finding by Wintering Bald Eagles” (The Auk [1983]: 477–484) examined therelationship 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.

x 0 0 0.2 0.5 0.5 1.0 y 28.2 69.0 27.0 38.5 48.4 31.1 x 1.2 1.9 2.6 3.3 4.7 6.5 y 26.9 8.2 4.6 7.4 7.0 6.8

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 Ïx and

Ïy. 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.