1. The U.S. Energy Information Administration gathers data on residential consumption and expenditures and publishes its findings in Residential Energy Consumption Survey: Consumption and Expenditures. Independent simple random samples of households in the four U.S. regions yield the data on last year’s energy consumptions shown in the following table.

Northwest Midwest South West

15 17 11 10

10 12 7 12

13 18 9 8

14 13 13 7

13 15 9

12

1. At the 1% significance level, do the data provide sufficient evidence to conclude that a difference exist in last year’s mean energy consumption by households among the four US regions? Conduct a test of hypothesis.
2. Based on the sample data, which region has the highest average? Use the appropriate multiple comparison method.

1. The Rio-River Railroad, headquartered in Santa Fe, NM, is trying to devise a method for allocating fuel costs to individual railroad cars on a particular route between Denver and Santa Fe. The railroad staff thinks that fuel consumption will increase as more cars are added to the train, but it is uncertain how much cost should be assigned to each additional car. In an error to deal with this problem, the cost accounting department has randomly sampled 10 trips between the two cities and recorded the data in the file called Rio-River .

1. Draw a scatter plot for these two variable and comment on the apparent relationship between fuel consumption and the number of rail cars on the train.

B1. Compute the correlation coefficient between fuel consumption and the number

of train cars.

B2. Test Rio-River’s preconception of the relation between fuel consumption and the number of train cars using a significance level of 0.05.

B3. Comment on the results of this test. Do these results necessarily indicate that

adding more cars will increase the fuel usage?

1. Develop the least squares regression model to help explain the variation in fuel
   consumption.
2. Write a (1 page max.) executive summary that interprets the regression results. In the report, address the issue of, on average, how much the addition of another train car will increase fuel consumption. Also, calculate the average fuel consumption, average number of cars per train, and average fuel consumption per car for the data given. Does this average equal the average increase in fuel consumption from adding an additional car using the regression model? Explain differences.

1. A publishing co. in New York is attempting to develop a model that it can use to help predict textbook sales for books it is considering for future publications. The marketing dept. has collected data on several variables from a random sample of 15 books. These data are given in the file Textbook .

The publishing co. recently came up with some additional date for the 15 books in the original sample. Two new variables, production expenditures (X5) and number of prepublication reviewers (X6) have been added. These additional data are as follows:

Book X5 X6 Book X5 X6

1 $38,000 5 9 $51,000 4

2 86,000 8 10 34,000 6

3 59,000 3 11 20,000 2

4 80,000 9 12 80,000 5

5 29,500 3 13 60,000 5

6 31,000 3 14 87,000 8

7 40,000 5 15 29,000 3

8 69,000 4

Incorporating this additional data, calculate the correlation between each of these additional variable and the dependent variable, book sales. Then respond to each of the following questions.

1. Test the significance of the correlation coefficients, using an alpha level of 0.05. Comment on the results.
2. Develop a multiple regression model that includes all six independent variables. Which, if any, variables would you recommend be retained if this model is going to be used to predict book sales for the publishing company? For any statistical tests you might perform, use a significance level of 0.05. Discuss your results.
3. Use the ANOVA approach to test the null hypothesis that all slope coefficients are 0. Test with a significance level of 0.05. What do these results mean? Discuss.
4. Do multicollinearity problems appear to be present in the model? Discuss the potential consequences of multicollinearity with the respect to the regression model.
5. Discuss whether the standard error of the estimate is small enough to make this model useful for predicting the sales of textbooks.
6. Plot the residuals against the predicted value of y, and comment on what this plot means relative to the aptness of the model.
7. Compute the standardized residuals and form these into a frequency histogram. What does this indicate about the normality assumption?
8. Comment on the overall aptness of this model and indicate what might be done to improve the model.

1. The Sunbeam Corp. makes a wide variety of appliances for the home. One product is a digital blood pressure gauge. For obvious reasons, the blood pressure readings made by the monitor need to be accurate. When a new model is being designed, one of the steps is to test it. To do this, a sample of people is selected. Each person has his/her systolic blood pressure taken using the Sunbeam monitor. If the mean blood pressure is the same for the monitor as it is as determined by the physician, the monitor is determined to pass the test.

In a recent test, 15 people were randomly selected to be in the sample. The blood pressure readings for these people using both methods are contained in the file called Sunbeam .

1. Based on the sample data and a significance level equal to 0.05, what conclusion should the Sunbeam engineers reach regarding the latest blood pressure monitor? Discuss your answer in a short written statement.
2. Conduct the test as a paired t-test.
3. Discuss which of the two procedures in parts A and B is more appropriate to analyze the data presented in this problem.

1. Volker Sales and Service sells and installs home security systems in the Detroit area. In order to plan for parts inventory, the company needs an accurate forecast of the number of installations it will do each month. The company’s sales manager has collected data for the past 12 months. The data is a file calle d Volker .

1. Plot the data as a time-series graph. Discuss what the graph implies.
2. Fit a linear trend model to the data. Compute the R-squared value and show the trend line on the time-series graph.
3. Transform the time variable by taking the square root of the month number, and recomputed the linear model using the transformed time variable. Discuss whether this model appears to provide a better fit than the model without the transformation. Compute R-squared values.
4. Compute the MAD and MSE for the 12 data values for the two models in part b and c. Discuss which model is better model to use for forecasting purposes. What are the strengths and weaknesses of the two models?

6) Suppose as part of your job, you are responsible for installing emergency lighting in a series of state office buildings. Bids have been received from 4 manufacturers of battery-operated emergency lights. The costs are about equal, so the decision will be based on the length of time the lights last before failing. A sample of 4 lights from each manufacturer has been tested with the following values (time in hours) recorded for each manufacturer.

1. Using a significance level equal to 001, what conclusion would you reach about the 4 manufacturers' battery-operated emergency lights? Explain
2. If the test conducted in part (a) reveals that the null hypothesis should be rejected, what manufacturer should be used to supply the lights? Are there one or more manufacturers that you can eliminate based on these data? Use the appropriate test for multiple comparisons. Discuss.

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