# Exam-Style Question on Correlation

## A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 72. This question is similar to one that appeared on an IB Standard paper in 2014. The use of a calculator is allowed.

The following table shows the amount of diesel required by a train to travel certain distances.

 Distance ($$x$$ km) Diesel used ($$y$$ litres) 90 150 230 310 390 19.2 33.9 49 79.5 89.9

This data can be modelled by the regression line with equation $$y=ax+b$$.

(a) Find the values of $$a$$ and of $$b$$.

(b) Explain what the gradient $$a$$ represents.

(c) Use the model to estimate the amount of diesel the train would use if it is driven 270 km.

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