On the next page we give the average hourly outdoor temperature (x) in a city during a week and the city’s natural gas consumption (y) during the week for each of eight weeks (the temperature readings are expressed in degrees Fahrenheit and the natural gas consumptions are expressed in millions of cubic feet of natural gas— denoted MMcf). The output to the right of the data is obtained when MINITAB is used to fit a least squares line to the natural gas consumption data.
a. Find the least squares point estimates b0 and b1 on the computer output and report their values. Interpret b0 and b1. Is an average hourly temperature of 0ºF in the experimental region? What does this say about the interpretation of b0?
b. Use the facts that SSxy = – 179.6475; SSxx = 1,404.355; y-bar = 10.2125; and x-bar = 43.98 to hand calculate (within rounding) b0 and b1.
c. Use the least squares line to compute a point estimate of the mean natural gas consumption for all weeks having an average hourly temperature of 40° F and a point prediction of the natural gas consumption for an individual week having an average hourly temperature of 40° F.