The toco toucan, the largest member of the toucan family,possesses the largest beak relative to body size of all birds. Thisexaggerated feature has received various interpretations, such asbeing a refined adaptation for feeding. However, the large surfacearea may also be an important mechanism for radiating heat (andhence cooling the bird) as outdoor temperature increases. Here aredata for beak heat loss, as a percent of total body heat loss fromall sources, at various temperatures in degrees Celsius. [Note: Thenumerical values in this problem have been modified for testingpurposes.]
Temperature (oC) 15 16 17 18 19 20 21 22 23 24 25 26 27 28 2930
Percent heat loss from beak 34 35 40 29 36 44 60 48 45 56 43 5157 60 58 64
a. The equation of the least-squares regression line forpredicting beak heat loss, as a percent of total body heat lossfrom all sources, from temperature is: (Use decimal notation. Enterthe values of the intercept and slope rounded to two decimalplaces. Use the letter ? to represent the value of thetemperature.) ?? =
b. Use the equation of the least?squares regression line topredict beak heat loss, as a percent of total body heat loss fromall sources, at a temperature of 25 degrees Celsius. Enter youranswer rounded to two decimal places. beak heat as a percent oftotal body heat loss=
c. What percent of the variation in beak heat loss is explainedby the straight-line relationship with temperature? Enter youranswer rounded to two decimal places. percent of variation in beakheat loss explained by the equation= %
d. Find the correlation ? between beak heat loss andtemperature. Enter your answer rounded to three decimal places.?=
