Question

Almost all U.S. light-rail systems use electric cars that run on tracks built at street level. The Federal Transit Administration claims light-rail is one of the safest modes of travel, with an accident rate of .99 accidents per million passenger miles as compared to 2.29 for buses. The following data show the miles of track and the weekday ridership in thousands of passengers for six light-rail systems.

City	Miles of Track	Ridership (1000s)
Cleveland	13	16
Denver	15	36
Portland	36	82
Sacramento	19	32
San Diego	45	76
San Jose	29	31
St. Louis	32	43

1. Use these data to develop an estimated regression equation that could be used to predict the ridership given the miles of track.
   
   Compute b₀ and b₁ (to 2 decimals).
   b₁  
   b₀  
   
   Complete the estimated regression equation (to 2 decimals).
   y =  +  x
   
2. Compute the following (to 1 decimal):

   SSE
   SST
   SSR
   MSE

   
   
3. What is the coefficient of determination (to 3 decimals)? Note: report r² between 0 and 1.
   
   
   Does the estimated regression equation provide a good fit?
   SelectYes, it even provides an excellent fitYes, it provides a good fitNo, it does not provide a good fitItem 10
   
4. Develop a 95% confidence interval for the mean weekday ridership for all light-rail systems with 30 miles of track (to 1 decimal).
   (  ,  )
   
5. Suppose that Charlotte is considering construction of a light-rail system with 30 miles of track. Develop a 95% prediction interval for the weekday ridership for the Charlotte system (to 1 decimal).
   (  ,  )
   
   Do you think that the prediction interval you developed would be of value to Charlotte planners in anticipating the number of weekday riders for their new light-rail system?

Answer 1

a)

b1 =1.76

bo =-2.25

y^ =-2.25+1.76x

b)

SSE =Syy-(Sxy)2/Sxx=

1,038.7

SST=Syy=

3,620.9

SSR =(Sxy)2/Sxx =

2,582.1

MSE = 207.7

c)

Coeffficient of determination R^2 =SSR/SST=

0.713

Yes, it provides a good fit

d)

95% confidence interval =35.9 , 64.9

e)

95% prediction interval =10.6 , 90.2