Question

Bus and subway ridership for the summer months in London, England, is believed to be tied heavily to the number of tourists visiting the city. During the past 12 years, the data on the next page have been obtained:

Year (Summer Months)		Ridership (In Millions)
1	7	1.5
2	2	1.0
3	6	1.3
4	4	1.5
5	14	2.5
6	15	2.7
7	16	2.4
8	12	2.0
9	14	2.7
10	20	4.4
11	15	3.4
12	7	1.7

Develop a regression relationship.

What is expected ridership if 10 million tourists visit London in a year?

Answer 1

Question: Bus and subway ridership for the summer months in London, England, is believed to be tied heavily to the number of tourists visiting the city. During the past 12 years, the data on the next page have been obtained:

1. Develop a regression relationship.

Answer: Y-hat = 0.5060 + 0.1593(x)

Explanation:

Using Excel:

Year ху X^2 N 12 No of Tourists (x) Ridership (y) 7 1.5 1 10.5 49 Σ 132 2 2 1 2 4 27.1 3 6 1.3 7.8 36 4 4 1.5 6 16 352.9 1796 17424 5 14 2.5 35 Σxy (x^2) ((2x)^2) Slope (b) Intercept (a) 196 6 15 2.7 40.5 225 0.1593 0.5060 7 16 2.4 38.4 256 8 12 2 24 144 9 14 2.7 37.8 196 LO 20 4.4 88 400 11 15 3.4 51 225 12 7 1.7 11.9 49

Formulas for Slope and Intercept are:

Slope (b) = ((N * ∑xy) - (∑x * ∑y)) / ((N * ∑(x^2)) - ((∑x)^2)) = 0.1593

Intercept (a) = (∑y - Slope (b) * (∑x)) / N = 0.5060

Therefore, linear regression equation is:

Y-hat = 0.5060 + 0.1593(x)

2. What is expected ridership if 10 million tourists visit London in a year?

Answer: Y-hat = 2.099

Explanation:

We have the linear regression equation:

Y-hat = 0.5060 + 0.1593(x)

Now, given that x = 10

Therefore:

Y-hat = 0.5060 + 0.1593(10)

Y-hat = 2.099

The expected ridership of there are ten million tourists every year is 2.099