# Key Data Regarding Multiple Regression Analysis

See attached file for full output.

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 and interpret the confidence and prediction intervals for given values of the independent variables

When the temperature = 44 degrees (Fahrenheit) and the chill index = 12

Round all entries to four decimal places.

predicted value =

Interpretation of the predicted value:

A. This is the point prediction of fuel consumption when the temperature = 44 degrees (Fahrenheit) and the chill index = 12

B. This is the fuel consumption we predict will occur 95% of the time when the temperature = 44 degrees (Fahrenheit) and the chill index = 12.

C. This is the fuel consumption amount we use to predict when the temperature will = 44 degrees (Fahrenheit) and the chill index will = 12.

D. This is our prediction of the standard error associated with a temperature = 44 degrees (Fahrenheit) and a chill index = 12.

E. This value has no practical interpretation, because global warming makes any predictions uncertain.

Please make your selection: A, B, C, D, or E

95% confidence interval = [ , ]

Interpretation of the 95% confidence interval:

A. This says we are 95% confident that the mean fuel consumption for all weeks will be between these values.

B. This says we are 95% confident that the mean fuel consumption in a single week having a temperature = 44 degrees (Fahrenheit) and a chill index = 12 will be between these values.

C. This says 95% of the fuel consumption values will be between these values.

D. This says we are 95% confident that the mean fuel consumption for all weeks having a temperature = 44 degrees (Fahrenheit) and a chill index = 12 will be between these values.

E. This confidence interval has no practical interpretation because of the uncertainty of global warming.

Please make your selection: A, B, C, D, or E

95% prediction interval = [ , ]

Interpretation of the 95% prediction interval:

A. This says we are 95% confident that the mean fuel consumption for all weeks will be between these values.

B. This says we are 95% confident that the mean fuel consumption in any single week having a temperature = 44 degrees (Fahrenheit) and a chill index = 12 will be between these values.

C. This says 95% of the fuel consumption values will be between these values.

D. This says we are 95% confident that the mean fuel consumption for all weeks having a temperature = 44 degrees (Fahrenheit) and a chill index = 12 will be between these values.

E. This confidence interval has no practical interpretation because of the uncertainty of global warming.

Please make this selection: A, B, C, D, or E

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#### Solution Preview

When the temperature = 44 degrees (Fahrenheit) and the chill index = 12

Round all entries to four decimal places.

Predicted value = 10.0316

Interpretation of the predicted value:

A. This is the point prediction of fuel consumption when the temperature = 44 degrees (Fahrenheit) and the chill index = 12

B. This is the fuel consumption we predict will occur 95% of the time when the temperature = 44 degrees (Fahrenheit) and the chill index = 12.

C. This is the fuel consumption amount we use to predict when the temperature will = 44 degrees (Fahrenheit) and the chill index will = 12.

D. This is our ...

#### Solution Summary

The solution provides step by step method for the calculation of multiple regression model. Formula for the calculation and Interpretations of the results are also included.