A construction science class project was to compare the daily gas consumption of 20 homes with a new form of insulation to that of 20 similar homes with standard insulation. The students set up instruments to record the temperature both inside and outside of the homes over a 6- month period of time (October€“ March). The average differences in these values are given below. The students also obtained the average daily gas consumption (in kilowatt hours). All the homes were heated with gas. The data are given here:
Data for Homes with Standard Form of Insulation:

Data for Homes with New Form of Insulation:

a. Obtain the estimated regression lines for the two types of insulation.
b. Compare the fits of the two lines.
c. Is the rate of increase in gas consumption as temperature difference increases less for the new type of insulation? Justify your answer by using 95% confidence intervals.
d. If the rates are comparable, describe how the two lines differ.

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TempDiff F) 20.3 20.7 20.9 22.8 23.1 248 25.9 26.1 270 27.2 GasConsumptin kWh) 70.3 70.7 72.9 77.6 79.3 86.5 90.6 919 945 92.7 298 302 306 318 332 33.4 34.2 35.1 362 36.5 GasConsumption (kWh) 104.8 1032 912 896 116.2 1169 105.1 106.1 1178 120.3 TempDiff GasConsumption (kWh) 65.3 665 67.8 73.2 75.3 811 822 85.7 909 874 TempDiff OF) GasConsumption (kWh) 94.9 93.9 87.1 84.2 106.6 1113 100.9 1019 1101 119.1 20.1 211 219 22.6 23.4 24.2 24.9 251 26.0 27.2 28.8 29.2 30.6 308 32.6 324 348 35.9 36.0 36.5