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° F) over a 23-month period. He then computed the least-squares regression line for predicting y from x and found it to be ŷ = 84 + 18x. How much, on average, does gas used increase for each additional degree-day?

Answer 1

18

Explanation:

In the linear regression equation y=a+bx, slope coefficient b represents average unit increases in y variable due to unit increase in x variable.

In the given equation ŷ = 84 + 18x, b=18 represents average unit increases in gas used due to unit increase in degree day.

Hence,on average, gas used increase by 18 for each additional degree-day.