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^=89 + 19x. How much, on average, does gas used increase for each additional degree-day?

Question

Mathematics

Esther Garrett

1 June, 06:53

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^=89 + 19x. How much, on average, does gas used increase for each additional degree-day?

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Martha Lucero · Answer 1

19

Step-by-step explanation:

The estimated least square regression line is

y^=89+19x

Here, dependent variable y is the amount of gas and independent variable is temperature.

The intercept and slope of the estimated regression line are 89 and 19 respectively.

The slope of the regression line shows that how the dependent variable varies when independent variable increased by 1 unit.

We can say that for additional degree day on average gas used increased by 19 units.

So, on average, gas used increased by 19 for each additional degree-day.