2021 IBSL P1 Q1
2021 IBSL P1 Q1
Eduardo believes that there is a linear relationship between the age of a male runner and the time it takes them to run \(5000\) metres.
To test this, he recorded the age, \(x\) years, and the time, \(t\) minutes, for eight males in a single \(5000\) m race. His results are presented in the following table and scatter diagram.
| \(x\), years | \(18\) | \(24\) | \(28\) | \(36\) | \(40\) | \(46\) | \(52\) | \(62\) |
|---|---|---|---|---|---|---|---|---|
| \(t\) minutes | \(29.4\) | \(29.2\) | \(31.1\) | \(33.6\) | \(32.2\) | \(33.1\) | \(35.2\) | \(40.4\) |
For this data, find the value of the Pearson's product-moment correlation coefficient, \(r\).
Eduardo looked in a sports science text book. He found that the following information about \(r\) was appropriate for athletic performance.
[2]
| Value of \(|r|\) | Description of the correlation |
|---|---|
| \(0 \leq |r| < 0.4\) | weak |
| \(0.4 \leq |r| < 0.8\) | moderate |
| \(0.8 \leq |r| \leq 1\) | strong |
Comment on your answer to part (a), using the information that Eduardo found.
[1]Write down the equation of the regression line of \(t\) on \(x\), in the form \(t = ax + b\).
[1]
A \(57\)-year-old male also ran in the \(5000\) m race.
Use the equation of the regression line to estimate the time he took to complete the \(5000\) m race.
[2]
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