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

Question id: 663. This question is similar to one that appeared on an IB AA Higher paper in 2023. The use of a calculator is allowed.

A programmer recorded the number of web pages she had created since she had begun working for the Corney Content Creation Company. The following table shows the number of days, \(d\), and the cumulative total number of web pages, \(p\).

Number of days \((d)\) | 5 | 9 | 16 | 18 | 23 | 29 | 32 | 40 | 50 |

Number of pages \((p)\) | 14 | 28 | 47 | 54 | 65 | 90 | 95 | 123 | 156 |

The value of Pearson's product moment correlation coefficient, \(r\) for this data is 0.999 to three significant figures.

(a) The regression line of \(p\) on \(d\) for this data can be written in the form \(p=ad + b\). Find the value of a and the value of b.

(b) Use your regression line to estimate the number of web pages created by day 45.

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