## Exam-Style Question on Correlation## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 336. This question is similar to one that appeared on an IB Standard paper in 2015. The use of a calculator is allowed.

The following table shows the average number of hours per night sleeping by seven men and their youngest child.

Hours sleep per night of father (x) | 6.7 | 7.1 | 7.2 | 7.9 | 8.1 | 8.2 | 8.2 |

Hours sleep per night of youngest child (y) | 7.9 | 8.0 | 8.5 | 8.7 | 9.1 | 9.2 | 9.5 |

The relationship can be modelled by a regression line with equation \(y = mx + c\).

(a) Find the correlation coefficient.

(b) Write down the value of \(m\) and of \(c\).

(c) Young Ramin sleeps for an average of 8.6 hours per day. Use your regression line to predict the average number of hours his father sleeps. Give your answer in hours and minutes correct to the nearest minute.

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