A medical officer wishes to investigate a patient’s walking $s$ speed km/h and his heart-beat rate

Question

A medical officer wishes to investigate a patient’s walking $s$ speed km/h and his heart-beat rate $h$ beats per minute (bpm). The data is shown below: $s$ (km/h) $1$ $1.5$ $2$ $2.5$ $3$ $3.5$ $4$ $4.5$ $5$ $h$ (bpm) $60$ $63$ $66$ $75$ $86$ $99$ $150$ $110$ $130$ Sketch a scatter plot of the above data. [1] One of the values of $h$ appears to be incorrect. Indicate the corresponding point on your diagram by labelling it $P$.[1] Omit $P$ for the remainder of this question. Calculate the product moment correlation coefficient for this set of data. Use the equation of an appropriate regression line to predict the value of $s$ when $h=100$, justifying your choice of regression line. [4] It is suggested to use one of the following two models instead: Model (I): $h=a+b{{s}^{2}}$, Model (II): $h=a+b{{e}^{s}}$, where $a$ and $b$ are real constants. Determine which of the two models is a better choice, giving a reason for your answer. [2] Suppose a new data pair $\left( \overline{s},\overline{h} \right)$ is added to the table above, where $\overline{s}$ and $\overline{h}$ are the patient’s sample mean walking speed (in km/h) and his sample mean heart-beat rate (in bpm) respectively, based on the data above. Without any calculations, explain whether the equation of the regression line you have obtained in part (iii) would change.[2]

Accepted Answer

(iii) $r$-value $=0.9812$, $~s=3.67$($3$ s.f.) (iv) For model (I), $r$-value $=0.9898$; For model (I), $r$-value $=0.9380$; Model (I) is more suitable since the correlation coefficient is nearer to $1$, which suggests a stronger linear relationship between $h$ 	ext{ and } ${{s}^{2}}$ as compared to that between $h$ 	ext{ and } ${{e}^{s}}$. (v) Since the data point $\left( \bar{s},\bar{h} ight)$ lies on the regression line, the answer in part (iii) will not change as the equation of the regression line is not affected.

2015 NJC P2 Q12

2015 NJC P2 Q12