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 (or if they do), they record their consumption of natural gas before the panels are installed. Gas consumption is higher in cold weather, so the relationship between outside temperature and gas consumption is important. Data were collected over 18 consecutive months. Gas consumption was measured in hundreds of cubic feet. To represent the temperature, degree-days are often used.
A month's degree-days are the sum total number of degrees its average temperature falls below 65 degrees F.
Below is the output for the regression of gas used on degree-days collected over the 18 month period.
Regression Analysis: Gas Consumption versus Degree-Days:
The regression equation is: Gas Consumption = 38.40 + 0.25 Degree-Days
Predictor Coef SE Coef T P
Intercept 38.400 0.817229 5.83 0.000
Degree-Days 0.248 0.000007 22.73 0.000
S = 13.02 R-Sq = 97.0% R-Sq(adj) = 96.8%
(a) Give the equation of the least squares line:
(b) According to the regression line, how much more gas should the Sanchez household expect to consume for each additional degree-day that occurs during the month?
(c) According to the regression analysis, what is the correlation between gas consumption and degree-days?
(d) For a month in which there are 102 degree-days, what prediction for gas consumption does the regression line give?