19N.1.SL.TZ0.T_6

pestleMathematicsAISLPaper 119N· sl-4-4-pearsons-scatter-diagrams-eqn-of-y-on-xsource ↗

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]

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

[2]

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

[2]

Markscheme / solution

$y = 0.384x + 629$

$y = \left( {0.384221 \ldots } \right)x + \left( {629.421 \ldots } \right)$ (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]

$y = 0.384221 \ldots \times 2900 + 629.421 \ldots$ (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]

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]

Examiners’ report

[N/A]