# how many stations and how many vehicles will be needed for a 100-mile system? Justify your answers.

Relatively few business travelers use mass transit systems when visiting large cities. The payoff could be substantial—in both time and money—if they learned how to use the systems, as noted in the December 28, 2004, USA Today article “Mass transit could save business travelers big bucks.” USA Today gathered the following information on the busiest U.S. rail systems.,Suppose a mass transit system is being proposed for a city and you have been put in charge of preparing statistical information (both graphic and numerical) about the relationship between the following three variables: the number of stations, the number of vehicles, and the number of miles of rail. You were provided with the preceding data.,a. Start by inspecting the data given. Do you notice anything unusual about the data? Are there any values that seem quite different from the rest? Explain.,b. Your supervisor suggests that you remove the data for New York. Make a case for that being acceptable. Include some preliminary graphs and calculated statistics to justify removing these values. Using the data from the other 10 cities:,c. Construct a scatter diagram using miles of track as the independent variable, x, and the number of stations as the dependent variable, y.,d. Is there evidence of a linear relationship between these two variables? Justify your answer.,e. Find the equation of the line of best fit for part c.,f. Interpret the meaning of the equation for the line of best fit.What does it tell you?,g. Construct a scatter diagram using miles of track as the independent variable, x, and the number of vehicles as the dependent variable, y. ,h. Is there evidence of a linear relationship between these two variables? Justify your answer. ,i. Find the equation of the line of best fit for part g ,j. Interpret the meaning of the equation for the line of best fit.What does it tell you? ,k. Construct a scatter diagram using number of stations as the independent variable, x, and the number of vehicles as the dependent variable, y. ,l. Is there evidence of a linear relationship between these two variables? Justify your answer. ,m. Find the equation of the line of best fit for part k. ,n. Interpret the meaning of the equation for the line of best fit. What does it tell you? ,o. The city is entertaining initial proposals for a mass transit system of 50 miles of track. Based on the answers found in parts c through n, how many stations and how many vehicles will be needed for the system? Justify your answers. ,p. If someone wants an estimate for the number of stations and vehicles needed for a 100-mile system, he or she should not just double the results found in part o. Explain why not. ,q. Based on the answers found in parts c through n, how many stations and how many vehicles will be needed for a 100-mile system? Justify your answers.