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# Interpret Multiple Regression Output: Description and Point Estimates

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 â??chill indexâ? (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 Minitab output, write the regression equation, and explain the regression coefficients.

Regression equation: y = [ ] + [ ]x1 + [ ]x2

Interpretation of b02:
A. This tells us the average temperature for the selected municipalities in Illinois during the testing period, holding constant the fuel consumption and the chill index.
B. This tells us the average amount of natural gas consumed during the testing period, holding constant the temperature and the chill index.
C. This says we are 95% confident that in the population each additional degree (Fahrenheit) of increase in temperature will result in a decrease of fuel consumption around this value, for a given chill index
D. This value is determined by setting the independent variables = 0, but there is no practical value in this application, since a temperature = 0 is outside the range of values in our data.
E. This value is determined by setting the independent variables = 0, and it has practical usefulness.

Interpretation of b1:
A. This tells us that for each additional degree (Fahrenheit) of increase in temperature, we can expect an increase of .0756 millions of cubic feet of natural gas, holding constant the chill index.
B. This tells us that at a temperature of 1 degree (Fahrenheit) and a chill index of 3, one can expect that there will be 12.2306 millions of cubic feet of natural gas used.
C. This tells us that for each additional unit on the chill index, we can expect an increase of 0.0939 millions of cubic feet of natural gas used, holding constant the temperature.
D. This tells us that for each additional degree (Fahrenheit) of increase in temperature, we can expect a decrease of .0756 millions of cubic feet of natural gas, holding the chill index constant.
E. This value has no practical interpretation.

Interpretation of b2:
A. This tells us that for each additional unit on the chill index, we can expect a decrease of 0.0939 millions of cubic feet of natural gas used, holding constant the temperature.
B. This tells us that at a temperature of 1 degree (Fahrenheit) and a chill index of 3, one can expect that there will be 12.2306 millions of cubic feet of natural gas used.
C. This tells us that for each additional unit on the chill index, we can expect an increase of 0.0939 millions of cubic feet of natural gas used, holding constant the temperature.
D. This tells us that for each additional degree (Fahrenheit) of increase in temperature, we can expect a decrease of .0756 millions of cubic feet of natural gas, holding the chill index constant.
E. This value has no practical interpretation.

#### Solution Preview

Regression equation: y = 12.2306 – 0.0756x1 + 0.0939x2

Interpretation of b02:
D. This value is determined by setting the independent variables = 0, but there is no ...

#### Solution Summary

This solution identifies the multiple regression equation from the given regression output. This solution also provides an interpretation of the regression coefficients and all calculations which are required.

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