Almost all U.S. light-rail systems use electric cars that run on tracks built at

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.

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).
=   +  x

Compute the following (to 1 decimal):

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  

Develop a 95% confidence interval for the mean weekday ridership for all light-rail systems with 30 miles of track (to 1 decimal).
(  ,   )

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).
(  ,   )

City Miles of Track Ridership (1000s) Cleveland 13 17 Denver 15 37 Portland 36 83 Sacramento 19 33 San Diego 45 77 San Jose 29 32 St. Louis 32 44

Explanation / Answer

a) b1    1.76 b0   -1.25 b) y =  -1.25 + 1.76*x c) SSE 1038.707978 SST 3620.857143 SSR 2582.149165 MSE 207.7415956 d) R^2= 0.713 e) Yes, it provides a good fit SUMMARY OUTPUT Regression Statistics Multiple R 0.844471444 R Square 0.713132019 Adjusted R Square 0.655758423 Standard Error 14.41324376 Observations 7 ANOVA df SS MS F Significance F Regression 1 2582.149165 2582.149 12.42962 0.016819 Residual 5 1038.707978 207.7416 Total 6 3620.857143 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -1.252130924 14.50509169 -0.08632 0.93456 -38.5387 36.0343943 -38.5387 36.03439 Miles of Track 1.755369928 0.497897244 3.525567 0.016819 0.475484 3.035255539 0.475484 3.035256

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