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# Multiple Regression and Model Building

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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.

Following are the data and output for selected municipalities in Illinois for 10 reporting periods (weeks). The dependent variable is consumption of natural gas in millions of cubic feet (Fuelcons) and the independent variables are the temperature (Temp), measured in degrees Fahrenheit, and a 'chill index' (Chill), which takes values from 0 to 30, and which includes other fuel consumption determinants besides temperature, such as wind speed and direction, and cloud cover.
Using the attached MegaStat output, identify the adjusted multiple coefficient of determination and interpret it.

Adjusted multiple coefficient of determination =

A. This is the proportion of the total variation in temperature (in degrees Fahrenheit) that is explained by the multiple 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, holding the chill index constant.

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

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

E. This value has no practical interpretation