Question

11.

(5.33) 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:

Temperature(oC)(oC)	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30
Percent heat loss from beak	32	33	37	31	40	47	54	51	40	54	47	50	60	60	62	60

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 is

yˆ=y^= + x

(Use decimal notation. Give your answer to four decimal places.)

Use the equation to predict (±0.01)(±0.01) beak heat loss, as a percent of total body heat loss from all sources, at a temperature of 25 degrees Celsius.

%

What percent (±0.01)(±0.01) of the variation in beak heat loss is explained by the straight-line relationship with temperature?

%

Find the correlation rr (±± 0.001) between beak heat loss and temperature:

r=

Answer 1

from above

a)

y^ =2.0441+2.0147*x

b)

predicted beak heat loss=2.04+25*2.01=

52.41

c)

% of the variation in beak heat loss is explained by the straight-line relationship with temperature =79.88%

d)

correlation coefficient r=

Sxy/(√Sxx*Syy) =

0.894