QUESTION 1:

An owner of a home in the Midwest installed solar panels toreduce heating costs. After installing the solar panels, hemeasured the amount of natural gas used yy (in cubic feet) to heatthe home and outside temperature xx ( in degree-days, where a day'sdegree-days are the number of degrees its average temperature fallsbelow 65 oFoF) over a 23-month period. He then computed theleast-squares regression line for predicting y fromx and found it to be:

yˆ=y^=85 + 14x

The predicted amount of gas used when the outside temperature is15 degree-days

is about:  cubic feet. (Answer to the nearest cubicfoot.)

QUESTION 2:

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, atvarious 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	36	36	32	36	33	44	52	51	40	54	44	51	63	56	65	66

The equation of the least-squares regression line for predictingbeak heat loss, as a percent of total body heat loss from allsources, from temperature is

yˆ=y^= + x

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

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

%

What percent (±0.01)(±0.01) of the variation in beak heat lossis explained by the straight-line relationship withtemperature?

%

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

r=