Research is being carried out 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.
Calculate the equation of the regression line of \(x\) on \(t\).[2]
Calculate the corresponding estimated value of \(x\) when \(t=300\), and comment on the suitability of the linear model.[2]
The variable \(y\) is defined by \(y=\ln x\). For the variables \(y\) and \(t\),
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]
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