Question

QUESTION 1:

An owner of a home in the Midwest installed solar panels to reduce heating costs. After installing the solar panels, he measured the amount of natural gas used yy (in cubic feet) to heat the home and outside temperature xx ( in degree-days, where a day's degree-days are the number of degrees its average temperature falls below 65 oFoF) over a 23-month period. He then computed the least-squares regression line for predicting y from x and found it to be:

yˆ=y^=85 + 14x

The predicted amount of gas used when the outside temperature is 15 degree-days

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

QUESTION 2:

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	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 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

The answers are obtained using R- software. Codes and output are attached below.