A student uses only the product moment correlation coefficient to interpret the linear correlation f

Question

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. Patient$A$$B$$C$$D$$E$$F$$G$ $t$$42$$74$$48$$35$$56$$26$$60$ $p$$98$$165$$120$$80$$180$$70$$150$ Give a sketch of the scatter diagram for the data, as shown on your calculator.[2] Find the product moment correlation coefficient and comment on its value in the context of the data.[2] 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] Hence interpret the value of $m$ in context of the data.[1] Use your regression line to estimate the systolic blood pressure of a patient of age $58$. Comment on the reliability of this estimate.[2] 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] 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]

Accepted Answer

(ii)r=0.900 (iii)$p=7.03+2.39t$ (v)estimated = 146 mm Hg (vi)$p=0.937+0.318 t$ (vii)(48.7,123)

2204 DHS H1 Q8

2204 DHS H1 Q8