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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 = 0.384 x + 629

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

Note: Award (A1) for 0.384 x , (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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