- A medical researcher is studying the relationship between age ( \(x\) years) and volume of blood ( \(y \mathrm { ml }\) ) pumped by each contraction of the heart. The researcher obtained the following data from a random sample of 8 patients.
| Age (x) | 20 | 25 | 30 | 45 | 55 | 60 | 65 | 70 |
| Volume (y) | 74 | 76 | 77 | 72 | 68 | 67 | 64 | 62 |
[You may use \(\sum x = 370 , \mathrm {~S} _ { x x } = 2587.5 , \sum y = 560 , \sum y ^ { 2 } = 39418 , \mathrm {~S} _ { x y } = - 710\) ]
- Calculate \(\mathrm { S } _ { y y }\)
- Calculate the product moment correlation coefficient for these data.
- Interpret your value of the correlation coefficient.
The researcher believes that a linear regression model may be appropriate to describe these data.
- State, giving a reason, whether or not your value of the correlation coefficient supports the researcher's belief.
- Find the equation of the regression line of \(y\) on \(x\), giving your answer in the form \(y = a + b x\)
Jack is a 40-year-old patient.
- Use your regression line to estimate the volume of blood pumped by each contraction of Jack's heart.
- Comment, giving a reason, on the reliability of your estimate.