2024 DHS H1 Q8

A student uses only the product moment correlation coefficient to interpret the linear correlation for a sample taken from a two-variable distribution. Give a reason why he should also draw a scatter diagram to support his conclusion.[1]

The systolic blood pressures, \(p\) mmHg, and the ages, \(t\) years, of \(7\) hospital patients are shown in the table below.

1. Give a sketch of the scatter diagram for the data, as shown on your calculator.[2]
2. Find the product moment correlation coefficient and comment on its value in the context of the data.[2]
3. Find the equation of the regression line of \(p\) on \(t\), giving your answer in the form \(p = mt + c\), with the values of \(m\) and \(c\) correct to \(3\) significant figures. Sketch this line on your scatter diagram.[2]
4. Hence interpret the value of \(m\) in context of the data.[1]
5. Use your regression line to estimate the systolic blood pressure of a patient of age \(58\). Comment on the reliability of this estimate.[2]
6. It is given that \(1\) mmHg is approximately equal to \(0.133322\) kPa. Re-write your equation so that it can be used when the systolic blood pressures, \(p\), is measured in kPa.[1]
7. It is found that the inclusion of a \(8^{\mathrm{th}}\) point \((t_8, p_8)\) will not affect the equations of the regression line \(p\) on \(t\) and \(t\) on \(p\). Find the point \((t_8, p_8)\).[1]