Question

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 y (in cubic feet) to heat the home and outside temperature x (in degree days, where a day's degree-days are the number of degrees its average temperature falls below 65 degrees F) over a 23-month period. The software used to compute the least-squares regression line (ŷ = 85 + 16x) says that . This suggests that:

a. although degree-days and gas used are correlated, degree-days does not predict gas used very accurately.

b. gas used increases by √0.98 = 0.99 cubic feet for each additional degree-day.

c. prediction of gas used from degree-days will be quite accurate.

Answer 1

Rsquare is the coefficient of determination and tells us how much of the variability in the y is explained by the model. Its values lie between 1 and 0. Higher the value better is the model. In this case, the R2 is about 0.98, which indicates the model is very good and hence the predictions of the model would be very good.

Correct option : c. prediction of gas used from degree days will be quite accurate.