Heating a home. The Sanchez household is about to install solar panels to reduce the cost of heating their house. In order to know how much the solar panels help, they record their consumption of natural gas before the solar panels are installed. Gas consumption is higher in cold weather, so the relationship between outside temperature and gas consumption is important. Here are the data for 16 consecutive months:
Outside temperature is recorded in degree-days, a common measure of demand for heating. A day's degree-days are the number of degrees its average temperature falls below 65oF. Gas used is recorded in hundreds of cubic feet.
(a) Create an indicator variable, say INDwinter, which is 1 for the months of November, December, January, and February. Make a plot of all the data using a different symbol for winter months.
(b) Fit the model with two regression lines, one for winter months and one for other months, and identify the estimated regression lines.
(c) Do you think that two regression lines were needed to explain the relationship between gas used and degree-days? Explain.