Identify and Interpret Confidence and Prediction Intervals
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A very broad consensus has emerged around the proposition that global warming is a reality, with likely serious global consequences. Moreover, while there is still not unanimity that global warming is entirely man-made, there is broad agreement that it is desirable to cut emissions from coal and petroleum. Finally, many energy economists and political leaders are advocating a multipronged approach to providing alternative energy including nuclear, natural gas, clean coal, and renewable sources from solar and wind.
Municipalities and states have been asked by the Department of Energy to assess their energy requirements for each of the alternative fuels. In particular, they have decided to focus initially on natural gas, given the enormity of U.S. reserves and its relative cleanliness.
The regression output for selected municipalities in Illinois for 10 reporting periods (weeks) is attached below. The dependent variable is consumption of natural gas in millions of cubic feet (Fuelcons) and the independent variable is the temperature (Temp), measured in degrees Fahrenheit.
Use the following MegaStat output to identify and interpret the confidence and prediction intervals for a temperature of 44 degrees Fahrenheit.
95% confidence interval = [ , ]
Round your final answers to four decimal places.
Interpretation of the 95% confidence interval:
A. This says we are 95% confident that for the given temperature, in any particular week, the fuel consumption will be between these values.
B. This says we are 95% confident that in the population each additional degree of increase in temperature will result in a decrease of fuel consumption between these values.
C. This says we are 95% confident that for the given temperature, over many weeks, the mean fuel consumption will be between these values.
D. This says that when the temperature is 44 degrees (Fahrenheit), the predicted fuel consumption will be 10.0976 million cubic feet of natural gas.
E. This has no practical interpretation in this problem situation
Please select the correct answer: A, B, C, D, or E
95% prediction interval = [ , ]
Round your final answers to four decimal places.
Interpretation of the 95% prediction interval:
A. This says we are 95% confident that for the given temperature, in any particular week, the fuel consumption will be between these values.
B. This says we are 95% confident that in the population each additional degree of increase in temperature will result in a decrease of fuel consumption between these values.
C. This says we are 95% confident that for the given temperature, over many weeks, the mean fuel consumption will be between these values.
D. This says that when the temperature is 44 degrees (Fahrenheit), the predicted fuel consumption will be 10.0976 million cubic feet of natural gas.
E. This has no practical interpretation in this problem situation
Please select the correct answer: A, B, C, D, or E
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