{Exercise 14.39} Almost all U.S. light-rail systems use electric cars that run o

ID: 3158937 • Letter: #

Question

{Exercise 14.39} 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 (USA Today, January 7, 2003). 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 3 decimals if necessary). b1 1.7554 b0 -6.7629 Complete the estimated regression equation (to 3 decimals if necessary). = -6.7629 + 1.7554 x Compute the following (to 3 decimals if necessary). SSE : SST : SSR : MSE : What is the coefficient of determination (to 1 decimal)? Note: report r2 between 0 and 1. 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 if necessary). ( , )

Miles of Track 15 17 38 21 47 31 34 Ridership (1000s) 15 35 81 31 75 30 42 City Cleveland Denver Portland i tla.is| Sacramento San Diego San Jose St. Louis

Explanation / Answer

The regression Analysis is given as below:

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.844471444

R Square

0.713132019

Adjusted R Square

0.655758423

Standard Error

14.41324376

Observations

ANOVA

Significance F

Regression

2582.149165

2582.149

12.42962

0.01681901

Residual

1038.707978

207.7416

Total

3620.857143

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

-6.762870781

15.43251993

-0.43822

0.679511

-46.43342618

32.90768462

Miles of track

1.755369928

0.497897244

3.525567

0.016819

0.475484318

3.035255539

The regression equation is given as below:

Readership = -6.7629 + 1.7554*Miles of track

Compute the following (to 3 decimals if necessary).

SSE: 1038.708

SST: 3620.857

SSR: 2582.149

MSE: 207.742

What is the coefficient of determination (to 1 decimal)?

The coefficient of determination or the value of R square is given as 0.713 which means about 71.3% of the variation in the dependent variable readership is explained by the independent variable miles of track.

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 if necessary). ( , )

Confidence Interval Estimate

Data

X Value

Confidence Level

95%

Intermediate Calculations

Sample Size

Degrees of Freedom

t Value

2.570582

XBar, Sample Mean of X

Sum of Squared Differences from XBar

838

Standard Error of the Estimate

14.41324

h Statistic

0.14405

Predicted Y (YHat)

45.89823

For Average Y

Interval Half Width

14.0621

Confidence Interval Lower Limit

31.8361

Confidence Interval Upper Limit

59.96034

For Individual Response Y