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 y (in cubic feet) to heat the home and outside temperature x x (in degree-days, where a day's degree-days are the number of degrees its average temperature falls below 65 oF o F) 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 + 13x. How much, on average, does gas used increase for each additional degree-day?

Question

Mathematics

Lilyana Eaton

30 August, 08:12

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 y (in cubic feet) to heat the home and outside temperature x x (in degree-days, where a day's degree-days are the number of degrees its average temperature falls below 65 oF o F) 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 + 13x. How much, on average, does gas used increase for each additional degree-day?

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Answers (1)

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Kaelyn Bush · Answer 1

13

Step-by-step explanation:

The slope of the regression shows the average increase in response variable due to unit increase in explanatory variable. The regression equation of structure y=a+bx has slope=b.

The given regression equation y^=85+13x shows that the slope in the given equation is b=13. The response variable is amount of natural gas is used and explanatory variable is outside temperature in this case.

So, we can say that on increase of every unit of degree day the amount of gas used increase by 13 cubic feet.