A travel agent sells flights to different destinations from Beerow airport - Edexcel - A-Level Maths Statistics - Question 6 - 2010 - Paper 2

A linear regression model is appropriate since the plotted data points appear to have a linear trend, indicating a proportional relationship between distance and fare. Therefore, a straight line can effectively model this relationship.

$S_{uu}$ is calculated as follows:

S_{uu} = rac{ extstyle extstyle extstyle extstyle extstyle d^2}{n} - rac{ extstyle extstyle d}{n}^2 = rac{152.09}{6} - rac{27.7^2}{6} = 24.2 \

For S_{ar{u}}:

S_{ar{u}} = rac{d imes f}{n} - rac{d}{n} imes rac{f}{n} = rac{723.1}{6} - rac{27.7 imes 146}{6} = 49.1

Using the calculated values:

b = rac{S_{uu}}{S_{ar{u}}} = rac{24.2}{146} = 0.206

To find $a$, substitute back:

a = rac{f}{n} - b imes rac{d}{n} = rac{146}{6} - 0.206 imes 27.7

Thus,

$f = 15.0 + 2.03 d$

The value of $b = 2.03$ indicates that for each additional 100 km of distance from Beerow airport, the fare increases by approximately £2.03.

The rival travel agent charges 5p per km, making the cost $5t$ for $t$ km. Setting the fare of the first agent less than the rival:

$15.0 + 2.03t < 5t$

Solving this gives:

$15.0 < (5 - 2.03)t \Rightarrow 15.0 < 2.97t \Rightarrow t > 5.05$

Thus, for $t > 5.05$, the first travel agent is cheaper.