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 from all sources, at various temperatures in degrees Celsius. [Note: The numerical values in this problem have been modified for testing purposes.]

Temperature (oC)(oC)	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30
Percent heat loss from beak	33	32	33	32	39	43	56	48	44	49	44	56	58	60	60	63

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: (Use decimal notation. Enter the values of the intercept and slope rounded to two decimal places. Use the letter ?x to represent the value of the temperature.)

?̂=y^=

3.77+1.91x

Use the equation of the least‑squares regression line to predict beak heat loss, as a percent of total body heat loss from all sources, at a temperature of 2525 degrees Celsius. Enter your answer rounded to two decimal places.

beak heat as a percent of total body heat loss=beak heat as a percent of total body heat loss=

%

What percent of the variation in beak heat loss is explained by the straight-line relationship with temperature? Enter your answer rounded to two decimal places.

percent of variation in beak heat loss explained by the equation=percent of variation in beak heat loss explained by the equation=

%

Find the correlation ?r between beak heat loss and temperature. Enter your answer rounded to three decimal places.

?=r=

Answer 1

Using TI 84 calculator

press 2nd then catalog, then click on Diagnostic On

press stat then edit and enter the data sets in L1 and L2

press stat again, then calc and select LinReg(ax+b)

select L1 is X list and L2 as Y list

press calculate we get

y = 2.12x - 0.90

r = 0.917 (correlation coefficient)

and r^2 = 0.8416

so, explained variation = 0.8416*100 = 84.16%

Settting x = 25 in the regression equation, we get

predicted beak heat loss = 2.12*25 - 0.90

= 52.10