5.45 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.

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 plot as linear or curved?

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 Ïx and Ïy. Is the pattern in this scatterplot more linear than the scatterplot in Part (a)?

c. After considering your 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 x9 and/or y9.

Which transformation (the one from this part or the square root transformation from Part (b)) do you prefer? Explain.