The following table shows the weight ($w$) of a foetus, in grams, taken at various weeks ($t$).

Question

The following table shows the weight ($w$) of a foetus, in grams, taken at various weeks ($t$). $t$ $12$ $16$ $20$ $24$ $28$ $32$ $36$ $w$ $15$ $100$ $300$ $600$ $1005$ $1700$ $2622$ Draw a scatter diagram to illustrate the data, labelling the axes clearly. [2] It is thought that the weight of the foetus at week $t$ can be modelled by one of the formulae $w=a+b\ln t$ or $w=c{{t}^{\text{}\hspace{0.5em}d}}$, where $a$, $b$, $c$ and $d$ are positive constants. Using your scatter diagram, explain which of $w=a+b\ln t$ or $w=c{{t}^{\text{}\hspace{0.5em}d}}$ is the better model. [1] It is required to estimate the value of $w$ for which $t=30$. Find the equation of a suitable regression line, and use it to find the required estimate, giving your answer to the nearest grams. [3] It is also required to estimate the value of $t$ for which $w=2000$. Explain whether the regression line of $t$ on $w$ or $\ln t$ on $\ln w$ could be used to find this estimate. [1]

Accepted Answer

(ii) $w=ct^d$ (iii) $\ln w=-8.218166+4.546146\ln t$, giving $w=1400\text{ g}$ at $t=30$ (iv) use the regression of $\ln t$ on $\ln w$

2015 RI P2 Q7

2015 RI P2 Q7

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