Natural gas is used in many households to heat water, provide cooking fuel, and heat the home. January is typically a month in which many homes have their highest usage of natural gas. A utility company reviewed data from their customers in a certain city for a period of 15 years. For each year, the company recorded the average daily high temperature in the month of January (in degrees Fahrenheit), as well as the average household usage of natural gas (measured in therms, a unit of heat energy). The company displayed the data on a scatterplot, with the average daily high temperature on the x-axis and the average household usage of natural gas on the y-axis. The company noticed a negative, strong, linear association between the variables.
a. In the context of this situation, describe the meaning of the words “negative,” “strong,” and “linear.”
b. A least-squares regression line created from the company’s data is shown below.
Interpret the meaning of the slope of this regression line in the context of this problem.
c. In one of the years in the data set (2015), the average daily high temperature for the month of January was 20 degrees Fahrenheit, and the average household natural gas usage was 45 therms. Calculate and interpret the residual for the year 2015.