Analysis and Approaches for IBDP Maths Ebook 1 | Page 302

Your Practice Set – Analysis and Approaches for IBDP Mathematics
98
Paper 2 Section A – Coefficients of a regression line
Example
The following table shows the amount of fuel ( y litres) used by a vehicle to travel certain
distances ( x km) .
Travel distance ( x km) 5 8 11 16
Amount of fuel ( y litres) 0.5 0.7 1.2 1.3
This data can be modelled by the regression line with equation y �ax � b .
(a) (i) Write down the value of a and of b .
(b)
(ii)
Explain what the gradient a represents.
Use the model to estimate the amount of fuel the vehicle would use if its
travelling distance is 13 km.
[3]
[2]
Solution
(a) (i) a � 0.0772727273
a � 0.0773
A1 N1
b � 0.1522727273
b � 0.152
A1 N1
(b)
(ii)
a represents the average amount of fuel
required to travel 1 km A1 N1
The estimated amount of fuel
�0.0772727273(13) � 0.1522727273
(A1) for substitution
� 1.156818182
� 1.16 litres A1 N2
[3]
[2]
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