The toco toucan, the largest member of the toucan family, possesses the largest beak relative to body size of all birds. this exaggerated feature has received various interpretations, such as being a refined adaptation for feeding. however, the large surface area may also be an important mechanism for radiating heat (and hence cooling the bird) as outdoor temperature increases. here are data for beak heat loss, as a percent of total body heat loss, at various temperatures in degrees celsius:

col1 temperature the toco toucan, the largest member of the toucan 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
col2 percent heat loss from beak 33 34 33 36 36 47 52 51 41 50 49 50 55 60 60 62

the equation of the least-squares regression line for predicting beak heat loss, as a percent of total body heat loss from all sources, from temperature
what percent the toco toucan, the largest member of the toucan of the variation in beak heat loss is explained by the straight-line relationship with temperature?