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Exam-Style Question on CorrelationA mathematics exam-style question with a worked solution that can be revealed gradually |
Question id: 729. This question is similar to one that appeared on an IB AA Higher paper in 2023. The use of a calculator is allowed.
A community leader is monitoring the state of flood water levels in a local area.
The depth of the flood water is recorded on seven different days.
The following table shows the number of days, \( d \), since the monitoring began and the average depth, \( h \) cm, of the flood water on each of those days.
The value of Pearson’s product-moment correlation coefficient, \( r \), for this data is -0.991, correct to three significant figures.
$$ \begin{array}{|c|c|} \hline \text{Number of days } (d) & \text{Average height } (h) \\ \hline 1 & 24.5 \\ 3 & 18.1 \\ 4 & 15.3 \\ 6 & 11.7 \\ 7 & 10.3 \\ 9 & 5.9 \\ 11 & 2.9 \\ \hline \end{array} $$(a) The regression line of \( h \) on \( d \) for this data can be written in the form \( h = ad + b \).
Find the value of \( a \) and the value of \( b \).
(b) Use your regression line to estimate the average height of the plants when the experiment has been running for 8 days.
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