Question

In: Math

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

eBook 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 17 17
Denver 19 37
Portland 40 83
Sacramento 23 33
San Diego 49 77
San Jose 33 32
St. Louis 36

44

a) 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).

Complete the estimated regression equation (to 2 decimals).

b) Compute the following (to 1 decimal):

SSE
SST
SSR
MSE

c) 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?

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

e) 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?

Solutions

Expert Solution

Sol:

Miles of Track(X) Ridership (1000s)(Y) XY X2^ Y^2
17 17 289 289 289
19 37 703 361 1369
40 83 3320 1600 6889
23 33 759 529 1089
49 77 3773 2401 5929
33 32 1056 1089 1024
36 44 1584 1296 1936
TOTAL 217 323 11484 7565 18525
mean=xbar=31
mean=ybar=46.143

b=slope=7*11484-217*323/7*7565-(217)^2=1.7554

a=intercept=323-1.7554(217)/7=-8.275

Regression equaton is

y=-8.28+1.76*x

b0=y intercept=-8.28

b1=slope=1.76

Solutionb:

get the same outpur in excl by going to

data >data amalysis>Regression

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.844471
R Square 0.713132
Adjusted R Square 0.655758
Standard Error 14.41324
Observations 7
ANOVA
df SS MS F Significance F
Regression 1 2582.149 2582.149 12.42962 0.016819
Residual 5 1038.708 207.7416
Total 6 3620.857
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept -8.27361 16.36798 -0.50548 0.634714 -50.3489 33.80163
Miles of Track(X) 1.75537 0.497897 3.525567 0.016819 0.475484 3.035256
SSE 1038.7
SST 3620.9
SSR 2582.1
MSE 207.7

Solutionc:

rsq=0.713

Does the estimated regression equation provide a good fit?

YES


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