The toco toucan, the largest member of the toucan family, possesses the largest
ID: 3064127 • Letter: T
Question
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:
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= ------+-------- 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=
Temperature (oC)(oC) 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Percent heat loss from beak 34 35 37 32 40 49 55 52 41 53 46 51 60 62 63 62Explanation / Answer
Solution:
The least square regression equation is Y = 3.3824 + 1.9941X
When x = 25, the percent of total body heat loss from all sources is
Y = 3.3824 + 1.9941 (25)
Y = 53
78.65% of the variation in beak heat loss is explained by the straight-line relationship with temperature.
The correlation, r = 0.887
SUMMARY OUTPUT Regression Statistics Multiple R 0.886854 R Square 0.786511 Adjusted R Square 0.771261 Standard Error 5.119907 Observations 16 ANOVA df SS MS F Significance F Regression 1 1352.012 1352.012 51.57703 4.7E-06 Residual 14 366.9882 26.21345 Total 15 1719 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 3.382353 6.377256 0.530378 0.604162 -10.2955 17.06021 X Variable 1 1.994118 0.277666 7.181715 4.7E-06 1.398583 2.589652Related Questions
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