Use these data to develop an estimated regression equation that could be used to

Question

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

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).
(  ,  )

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?

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 14 14 Denver 16 34 Portland 37 80 Sacramento 20 30 San Diego 46 74 San Jose 30 29 St. Louis 33 41

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): SSE SST SSR MSE

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).
(  ,  )

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?

Explanation / Answer

Using excel:

Compute b0 and b1 (to 2 decimals).
b1 =1.75
b0 =-6.00

Complete the estimated regression equation

Y=-6.00+1.75X

Compute the following (to 1 decimal):

Compute the following (to 1 decimal):

What is the coefficient of determination (to 3 decimals)?

   R2=SSR/SST

        =2582.1/3620.8

        =0.713

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 2582.149165 12.42962035 0.01681901 Residual 5 1038.707978 207.7415956 Total 6 3620.857143 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -6.007500852 14.96770779 -0.401364119 0.70473114 -44.48321861 32.4682169 -44.48321861 32.4682169 X Variable 1 1.755369928 0.497897244 3.525566671 0.01681901 0.475484318 3.035255539 0.475484318 3.035255539

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