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# Simple Linear Regression Analysis

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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 attached MegaStat output to identify and interpret the p-value and the confidence interval for the regression coefficient.

p-value for the regression coefficient =

Interpretation of the p-value for the regression coefficient:

A. This is the probability of correctly concluding that there is a relationship between fuel consumption and temperature.

B. This is the probability of being incorrect in concluding that there is a relationship between fuel consumption and temperature.

C. This is the probability of being incorrect in concluding that there is no relationship between fuel consumption and temperature.

D. This is the probability of correctly rejecting the null hypothesis, that there is a relationship between fuel consumption and temperature.

E. This value has no practical interpretation.

95% confidence interval = [ , ]

Interpretation of the 95% confidence interval for the regression coefficient:

A. This says we are 95% confident that, for the given temperature of 44 degrees, 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 an increase of fuel consumption between these values.

C. 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.

D. This says we are 95% confident that over many weeks, the mean fuel consumption will be between these values.

E. This value has no practical interpretation

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