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Date November 2019 Marks available 2 Reference code 19N.1.SL.TZ0.T_6
Level Standard Level Paper Paper 1 Time zone Time zone 0
Command term Estimate and Use Question number T_6 Adapted from N/A

Question

Galois Airways has flights from Hong Kong International Airport to different destinations. The following table shows the distance, x kilometres, between Hong Kong and the different destinations and the corresponding airfare, y, in Hong Kong dollars (HKD).

The Pearson’s product–moment correlation coefficient for this data is 0.948, correct to three significant figures.

The distance from Hong Kong to Tokyo is 2900 km.

Use your graphic display calculator to find the equation of the regression line y on x.

[2]
a.

Use your regression equation to estimate the cost of a flight from Hong Kong to Tokyo with Galois Airways.

[2]
b.

Explain why it is valid to use the regression equation to estimate the airfare between Hong Kong and Tokyo.

[2]
c.

Markscheme

y=0.384x+629

y=(0.384221)x+(629.421)         (A1)(A1)  (C2)

Note: Award (A1) for 0.384x, (A1) for 629. If the answer is not given as an equation, award a maximum of (A1)(A0).

[2 marks]

a.

y=0.384221×2900+629.421         (M1)

Note: Award (M1) for substitution into their regression equation.

1740   (1744, 1743.66) (HKD)         (A1)(ft)  (C2)

Note: Follow through from part (a).

[2 marks]

b.

the correlation is (very) strong        (R1)

2900 (km) is within the given data range (interpolation)         (R1) (C2)

Note: Two correct reasons are required for the awarding of (C2).

[2 marks]

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

Topic 4—Statistics and probability » SL 4.4—Pearsons, scatter diagrams, eqn of y on x
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Topic 4—Statistics and probability

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