Hal: 176
4.41 Summer-month bus and
subway ridership in Washington, DC, is believed to be tied heavily to the
number of tourists visiting the city. During the past 12 years, the following
data have been obtained:
a)
Plot these data and decide if a linear model is reasonable.
As the number of tourists (x-axis) increases, the ridership
appears to increase: a linear model is reasonable. (1 mark)
b)
Develop a regression relationship.
|
Year
|
Tourists
(x)
|
Ridership
(y)
|
x2
|
y2
|
xy
|
|
1
|
7
|
1.5
|
49
|
2.25
|
10.5
|
|
2
|
2
|
1.0
|
4
|
1.00
|
2.0
|
|
3
|
6
|
1.3
|
36
|
1.69
|
7.8
|
|
4
|
4
|
1.5
|
16
|
2.25
|
6.0
|
|
5
|
14
|
2.5
|
196
|
6.25
|
35.0
|
|
6
|
15
|
2.7
|
225
|
7.29
|
40.5
|
|
7
|
16
|
2.4
|
256
|
5.76
|
38.4
|
|
8
|
12
|
2.0
|
144
|
4.00
|
24.0
|
|
9
|
14
|
2.7
|
196
|
7.29
|
37.8
|
|
10
|
20
|
4.4
|
400
|
19.36
|
88.0
|
|
11
|
15
|
3.4
|
225
|
11.56
|
51.0
|
|
12
|
7
|
1.7
|
49
|
2.89
|
11.9
|
|
|
Sx = 132
|
Sy = 27.1
|
Sx2 = 1796
|
Sy2 = 71.59
|
Sxy = 352.9
|
= Sx / n =
132 / 12 = 11
= Sy / n =
27.1 / 12 = 2.26
\ the
relationship is y = 0.511 + 0.159x (2 marks)
c)
What is expected ridership if 10 million tourists visit the city in a year?
Y = 0.511 + 0.159(10) = 2.101 or 2,101,000 persons. (2 marks)
d)
Explain the predicted ridership if there are no tourists at all.
If there are no tourists at all, the model predicts a
ridership of 0.511 or 511,000 persons. One would not place much confidence in
this forecast, however, because the number of tourists is outside the range of
data used to develop the model. (1 mark)
e)
What is the standard error of the estimate?
(2
marks)
f)
What is the model’s correlation coefficient and coefficient of determination?
r2 = 0.9172 = 0.840
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