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The scatter plot using excel has been completed as well as the least squares regression model. The part where assistance is needed is in parts b and c of question 2 and question 4.
The Rio-River Railroad, headquartered in Santa Fe, New Mexico, 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 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 effort to deal with this problem, the cost accounting department has randomly sampled 10 trips between the two cities and recorded the data below.
Rail Cars Fuel used (units/mile)
18 55
18 50
35 76
35 80
45 117
40 90
37 80
50 125
40 100
27 75

1. Draw a scatter plot for these two variables and comment on the relationship between fuel consumption and the number of rail cars on the train.
2. (a.) Compute the correlation coefficient between fuel consumption and the number of train cars. (b.) Test Rio-River's preconception of the relation between fuel consumption and the number of train cars using a significance level of 0.025. (c.) Comment on the results of this test. Do these results necessarily indicate that adding more cars will increase fuel usage?
3. Develop the least squares regression model to help explain the variation in fuel consumption.
4. Interpret the regression results by addressing 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 any difference.

See the attached file.

Solution Summary

The solution assists with providing a regression analysis for the Rio River Railroad, including a scatter plot, correlation coefficient, and regression model.

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Posting 17825
The Rio-River Railroad, headquartered in Santa Fe, New Mexico, 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 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 effort to deal with this problem, the cost accounting department has randomly sampled 10 trips between the two cities and recorded the data below.
Rail Cars Fuel used (units/mile)
18 55
18 50
35 76
35 80
45 117
40 90
37 80
50 125
40 100
27 75

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

According to the scatter plot of Rail Cars versus Fuel Used, it appears as though there is an increasing linear relationship between the two variables.
2. (a.) Compute the correlation coefficient between fuel consumption and the number of train cars.
The correlation coefficient is equal to

where is the number of samples, n=10, x is the rail cars and y is the fuel used. Thus

(b.) Test Rio-River's preconception of the ...

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