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# Regression Model: Natural Gas Consumption vs Temperature

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A very broad consensus has emerged around the proposition that global warming is a reality with likely serious global consequences. 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 geothermal, solar and wind energy forms.

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.

Attached is a portion of the regression output for selected municipalities in Illinois for 10 reporting periods (weeks). The dependent variable is consumption of natural gas in millions of cubic feet (Feulcons) and the independent variable is the temperature (Temp), measured in degrees Fahrenheit.

Determine R-Sq, the Standard Error, and F.

For this problem assume n = 10

For F, round the F value to two decimal places.

https://brainmass.com/statistics/regression-analysis/regression-model-natural-gas-consumption-versus-temperature-418567

#### Solution Preview

Simple Regression Output
A very broad consensus has emerged around the proposition that global warming is a reality with likely serious global consequences. 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 geothermal, ...

#### Solution Summary

The solution provides step by step method for the calculation of R-square value, Standard error of the estimate and F-statistic. Formula for the calculation is also included.

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## Regression Analysis: Fuel Consumption and Temperature

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 (see attachment file). The dependent variable is the consumption of natural gas in millions of cubic feet (Fuelcons) and the independent variable is the temperature (Temp), measured in degrees Fahrenheit.

Using the following MegaStat output, identify the coefficient of determination and the correlation coefficient, and interpret each of them.

Coefficient of determination =

Interpretation of the correlation - Interpretation of the coefficient of determination:

A. This is the proportion of the total variation in temperature (in degrees Fahrenheit) that is explained by the simple linear regression model.

B. This is the point estimate of the change in fuel consumption (in millions of cubic feet) associated with each degree (Fahrenheit) increase in temperature.

C. This is a measure of the variability of the observed values of fuel consumption from their predicted values at particular temperatures.

D. This is the proportion of the total variation in fuel consumption that is explained by the simple linear regression model.

E. This value has no practical interpretation.

Please make the correct selection: A, B, C, D, or E

Correlation coefficient =

Interpretation of the correlation:

A. This tells us that there is a strong negative relationship between fuel consumption and temperature.

B. This is the point estimate of the change in fuel consumption associated with each degree increase in temperature.

C. Because of the negative value, this tells us to drop the temperature variable and look for other ways to explain what drives fuel consumption.

D. This tells us the proportion of the total variation in the 10 fuel consumption values that is explained by the simple linear regression model.

E. This value has no practical interpretation.