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# Key Data Regarding Multiple Regression Analysis

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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 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.

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.

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

https://brainmass.com/statistics/regression-analysis/key-data-regarding-multiple-regression-analysis-376807

#### 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.

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## Multiple Regression Analysis

The task is to provide evidence, for or against, common perceptions about property crime. Are crime rates higher in urban than rural areas? Does unemployment or education level contribute to property crime rates? How about public assistance? What other factors relate to property crimes? The file named Data File may help answer some of these questions. This data should be used to prepare a 4-5 page report on the characteristics of and determinants of property crimes in the United States.

The statistical analysis of the data involves multiple regression analysis.

1. What are the primary determinants of property crimes in the United States?
2. What would you like to know about property crime rates that cannot be answered by this data set?
3. How does population density affect property crime rates? Is this expected?

You will find and explain the regression model using a non-technical discussion to explain the important factors effect on the property crime rate. Please include statistical analysis output in excel data spreadsheet attached (i.e. descriptive stats, multiple regression, etc).

Findings Outline (4 -5 pages)

I. The executive summary
A. Most important facts and conclusions.
B. One paragraph, no more!

II. The introduction
A. Several paragraphs.
B. Contents
1. Background on the problem.
2. Questions of interest, problem statement, and/or hypotheses.
3. The nature of the data set - describe the sample.

III. Analysis and methods section
A. Interpret the statistical summaries
1. Tell the reader what you found in the data (results, facts only).
2. Explain what those findings mean with regard to the problem (interpret results).

IV. Conclusions and summary section.
A. What has the analysis revealed?
B. Why was the analysis done? (Refers back to case background.)
C. What of value was discovered? (Any unexpected results.)
D. How have your questions been answered? (Refers back to questions of interest, problem statement, and/or hypotheses

V. References

VI. Appendix

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