Question

he Federal Tr as compared to lmot all U.S. light-rail systems usc electric cars that run on tracks buit at strest leva.T nsit Acminstration claims light-rail is one o the safest modes cf travel, with an accident rate o 9 accidents per milion passenger miles 2.29 for buses. The ulowing data shon the miles of track and the weekday tidership in theusss of paengers for six light-rail sytums. for six light-rail systeme Miles of Ridership (1 Track 000s) Denver 36 32 76 31 San Dicqa San lu a. Uac theac data to deveop an estimated reqressicn ecuation that could be uaed to predict the ridehip anen the mics of track. Compte y and 2 deima Complete the eatimated rogre saicn equation to 2 dacimab) b. Compute the following (to 1 decimal): SST Does the estimeted regression equation provide good fit? d. Develop a 9re confidence interval forthe mean preekdey ridership for ซิ1 light-rail systems with J0 miles of track (to 1 decimal). e. Suppose that t erlott"'t considerng co struction of 추 íght rs1syster on of e ight-rsil system with 30 mies of treck. Develop, d 95 t predict'on rtervel for th" prediction eekday ndership for tre Char otteeystem to 1 dene m (to 1 deimel Do you think that the aredictian interval you devedlioped wauld he a value to Charlatte plars intipating te amber af woakday ridera for their light-rail system?

Answer 1

data

x	y
14	16
16	36
37	82
20	32
46	76
30	31
33	43

result of regression in excel

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%
Intercept	-4.007500852	14.96770779	-0.267743125	0.799590936	-42.48321862
x	1.755369928	0.497897244	3.525566671	0.01681901	0.475484317

a)

b0 = -4.01

b1 = 1.76

y^ = -4.01 + 1.76* x

b)

SSE	1038.7
SST	3620.9
SSR	2582.1
MSE	207.7

c)

r^2 = 0.713