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a) Yes a linear model would be appropriate in this context. As we can see from the scatterplot that the points are close to each other and are positively correlated. From the residuals fitted value we see that they are almost i…View the full answer
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Transcribed image text: Problem #4 The Great Plains Railroad is interested in studying how fuel consumption is related to the number of railcars for its trains on a certain route between Oklahoma City and Omaha. A random sample of 10 trains on this route has yielded the following data: Number of Railcars 2 0 20 37 31 47 43 39 50 40 29 Fuel Consumption (units/mile) 58 5291 801149887 122 100 70 A scatterplot, a residual plot, and the output from the regression analysis for these data are shown below: RESIDUALS VERSUS THE FITTED VALUES st. Fucl Consumption 0 ----- Resida 10 50 60 70 40 Number of Railcars 80 90 100 110 120 Fitted Value The regression equation is Fuel Consumption = 10.7+ 2.15 Railcars Predictor Constant Railcar Coef 10.677 2.1495 S 4.361 R-Sq=96.7% a) Is a linear model appropriate for these data? Clearly explain your reasoning. b) Suppose the fuel consumption cost is $48 per unit. Give a point estimate (single value) for the change in the average cost of fuel per mile for each additional railcar attached to a train Show your work. c) Interpret the value of R in the context of this problem. d) Would it be reasonable to use the fitted regression equation to predict the fuel consumption for a train on this route if the train had 65 railcars? Explain. c) What is the value of the correlation coefficient? Interpret this value in context. 1) What is the residual for the train with 40 cars? Interpret this value in context g) Suppose the fuel consumption cost is $48 per unit. If the trip from Victoria to Edmonton is 775 miles, estimate the operating cost for a train with 33 cars to make the trip. h) Suppose a train with 34 rail cars and a fuel consumption of 130 units/mile was added to these data. Describe the effect this would have on the correlation coefficient and describe the effect this would have on the slope of the LSRL Note that no calculations are necessary.