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Exam-Style Question on CorrelationA mathematics exam-style question with a worked solution that can be revealed gradually |
Question id: 684. This question is similar to one that appeared on an IB AA Higher paper in 2021. The use of a calculator is allowed.
At a large airport, the waiting time between a plane landing and a passenger being able to get off the aircraft is dependent upon the row number of the seat that the passenger has been assigned to.
Betty, a frequent flier, took a flight to the airport on seven consecutive weekends. The following table shows the row number, \( x \), and Betty's waiting time, \( y \) minutes.
| Row number (\( x \)) | Betty’s waiting time (\( y \)) |
|---|---|
| 43 | 18 |
| 50 | 27 |
| 36 | 16 |
| 39 | 20 |
| 58 | 30 |
| 54 | 25 |
| 36 | 19 |
The relationship between \( x \) and \( y \) can be modelled by the regression line of \( y \) on \( x \) with equation \( y = mx + b \).
(a) Find the value of \( m \) and the value of \( b \).
(b) Write down the value of Pearson’s product-moment correlation coefficient, \( r \).
(c) Interpret, in context, the value of \( m \) found in part (a).
On another week, Betty takes the same flight. She has been assigned 42C, a seat in the forty second row.
(d) Use the result from part (a) to estimate Betty’s waiting time to leave the aircraft after it has landed.
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A380 seating plan by S. Solberg J., CC BY 1.0, via Wikimedia Commons
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