3 The table shows the body mass index (BMI), \(x\), and the systolic blood pressure (SBP), \(y \mathrm { mmHg }\), for each of a random sample of 10 men, aged between 35 years and 40 years, from a particular population.
| \(\boldsymbol { x }\) | 13 | 23 | 29 | 35 | 17 | 34 | 25 | 20 | 31 | 27 |
| \(\boldsymbol { y }\) | 103 | 115 | 124 | 126 | 108 | 120 | 113 | 117 | 118 | 119 |
- Calculate the equation of the least squares regression line of \(y\) on \(x\).
- Use your equation to estimate the SBP of a man from this population who is aged 38 years and who has a BMI of 30 .
- State why your equation might not be appropriate for estimating the SBP of a man from this population:
- who is aged 38 years and who has a BMI of 45 ;
- who is aged 50 years and who has a BMI of 25 .
- Find the value of the residual for the point \(( 20,117 )\).
- The mean of the vertical distances of the 10 points from the regression line calculated in part (a) is 2.71, correct to three significant figures.
Comment on the likely accuracy of your estimate in part (b).
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