(a) Monthly natural gas consumption for 6 inches of insulation and 46 degrees F is 30.3 cubic feet.
(b) A decrease of 1.06 cubic feet monthly natural gas consumption, down to 29.24 cubic feet.
(c) The regression coefficients b1 and b2 are negative because there is a negative relationship between the amount of insulation and outdoor temperature, on the one hand, and natural gas consumption, on the other hand.
(a) Monthly natural gas consumption for 6 inches of insulation and 46 degrees F
To calculate the monthly natural gas consumption for 6 inches of insulation and 46 degrees F, we can plug these values into the regression equation:
Y = 100.75 - 1.06(6) - 1.39(46) = 30.3 cubic feet
Therefore, homeowners can expect to use 30.3 cubic feet of natural gas per month if they install 6 inches of insulation and the outdoor temperature is 46 degrees F.
(b) Effect of increasing insulation thickness from 6 to 7 inches
To calculate the effect of increasing insulation thickness from 6 to 7 inches on monthly natural gas consumption, we can plug in these values into the regression equation:
Y = 100.75 - 1.06(7) - 1.39(46) = 29.24 cubic feet
Therefore, increasing insulation thickness from 6 to 7 inches would reduce monthly natural gas consumption by 1.06 cubic feet.
(c) Why are the regression coefficients b1 and b2 negative? Is this logical?
The regression coefficients b1 and b2 are negative because there is a negative relationship between the amount of insulation and outdoor temperature, on the one hand, and natural gas consumption, on the other hand. This means that as the amount of insulation and outdoor temperature increase, natural gas consumption decreases. This is logical because better insulation and warmer temperatures reduce the need for heating, which leads to lower natural gas consumption.