2007 H2 Mathematics

Paper 2 Question 11

Research is being carried our into how the concentration of a drug in the bloodstream varies with time, measured from when the drug is given. Observations at successive times give the data shown in the following table.

Time $(t minutes)$	15	30	60	90	120	150	180	240	300
Concentration $(x micrograms$ $per litre)$	82	65	43	37	22	19	12	6	2

It is given that the value of the product moment correlation coefficient for this data is $- 0.912,$ correct to $3$ decimal places. The scatter diagram for the data is shown below.

scatter diagram

(a)

Calculate the equation of the regression line of $x$ on $t .$

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(b)

Calculate the corresponding estimated value of $x$ when $t = 300,$ and comment on the suitability of the linear mode.

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(c)

The variable $y$ is defined by $y = \ln x .$ For the variables $y$ and $t,$

(i)

calculate the product moment correlation coefficient and comment on its value,

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(ii)

calculate the equation of the appropriate regression line.

[2]

(d)

Use a regression line to give the best estimate that you can of the time when the drug concentration is $15$ micrograms per litre.

[2]