2. Bus and Subway ridership for the summer months in London, England, is believe
ID: 428881 • Letter: 2
Question
2. Bus and Subway ridership for the summer months in London, England, is believed to be tied heavily to the number of tourist visiting the city. During the past 10 years, the following data was obtained: Ridership Year Number of Tourists (in millions) Summer Months (in millions) 6 4 14 15 17 13 14 20 1.0 1.3 1.5 2.5 2.7 2.4 2.0 2.7 4 6 10 a) Develop a regression relationship. b) What is the expected ridership if 10 million tourists visit London in a year? c) Explain the predicted ridership if there are no tourists at all.Explanation / Answer
Solution:
Regression line can be found as
Ridership=alpha(intercept)+(slope)*No.of tourists
slope can be calculated as
summation(Xi-Xbar)(Yi-Ybar)/summation(Xi-Xbar)^2
X
Y
Xi-Xbar
Yi-Ybar
(Xi-Xbar)(Yi-Ybar)
(Xi-Xbar)^2
7
1.5
-4.2
-0.7
2.94
17.64
2
1
-9.2
-1.2
11.04
84.64
6
1.3
-5.2
-0.9
4.68
27.04
4
1.5
-7.2
-0.7
5.04
51.84
14
2.5
2.8
0.3
0.84
7.84
15
2.7
3.8
0.5
1.9
14.44
17
2.4
5.8
0.2
1.16
33.64
13
2
1.8
-0.2
-0.36
3.24
14
2.7
2.8
0.5
1.4
7.84
20
4.4
8.8
2.2
19.36
77.44
11.2
2.2
48
325.6
Slope = 48/325.6 = 0.1474
Intercept can be calculated as above and we found that it is 0.5488
So regression line is Y = 0.5488 + 0.1474*X
Solution(b)
Given that X=10 than Y = 0.5488+0.1474*10 = 0.5488+1.474 = 2.0228 million
Solution(c)
If there is no tourist than Ridership = 0.5488+0.1474*0 = 0.5488 million
X
Y
Xi-Xbar
Yi-Ybar
(Xi-Xbar)(Yi-Ybar)
(Xi-Xbar)^2
7
1.5
-4.2
-0.7
2.94
17.64
2
1
-9.2
-1.2
11.04
84.64
6
1.3
-5.2
-0.9
4.68
27.04
4
1.5
-7.2
-0.7
5.04
51.84
14
2.5
2.8
0.3
0.84
7.84
15
2.7
3.8
0.5
1.9
14.44
17
2.4
5.8
0.2
1.16
33.64
13
2
1.8
-0.2
-0.36
3.24
14
2.7
2.8
0.5
1.4
7.84
20
4.4
8.8
2.2
19.36
77.44
11.2
2.2
48
325.6
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