Regression line of x on y for exercise time and resting heart rate, and the point shared with the y on x line
Regression line of x on y for exercise time and resting heart rate, and the point shared with the y on x line
5 marks
Eight adults recorded the average time, \(x\) minutes, that they spend exercising each day and their resting heart rate, \(y\) beats per minute. The results are given in the table.
| Exercise time (\(x\)) | \(10\) | \(25\) | \(30\) | \(45\) | \(50\) | \(60\) | \(75\) | \(80\) |
|---|---|---|---|---|---|---|---|---|
| Heart rate (\(y\)) | \(78\) | \(74\) | \(75\) | \(70\) | \(68\) | \(66\) | \(63\) | \(61\) |
The regression line of \(x\) on \(y\) is \(L_1\), with equation \(x=ay+b\).
- Write down the value of \(a\) and the value of \(b\).[2]
The regression line of \(y\) on \(x\) is \(L_2\). The two lines \(L_1\) and \(L_2\) intersect at the point \((p,q)\).
- Find \(p\) and \(q\).[3]
Solution:
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Answer:(a) \(a=-4.05,\ b=328\) (b) \(p=46.875\approx46.9,\ q=69.375\approx69.4\)
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