An owner of a home in the Midwest installed solar panels to reduce heating costs

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 ( = 85 + 16x) says that r^2=0.98 . This suggests

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

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

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

Explanation / Answer

r^2 = 0.98 is a high value This means about 98% of the variation in y is explained by the variation in x.

The model is a good fit to the data.

Prediction of gas used from degree-days will be quite accurate

Option A.

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