2026 HCI P2 Q8

A biologist is investigating the relationship between the light intensity level, \(x\) (in arbitrary units), and the growth rate, \(y\) (in mm/month), of a coral species. Samples of this coral species are placed in a controlled environment and exposed to 10 different light intensity levels for a fixed period. The growth rates of the samples are measured. The results are shown in the table below.

The product moment correlation coefficient between \(x\) and \(y\) is 0.960, correct to 3 significant figures.

1. Draw the scatter diagram for these values, labelling the axes clearly. What do the scatter diagram and product moment correlation coefficient suggest about the relationship between the light intensity level and growth rate? Justify your answer.[3]
2. The biologist wishes to find the light intensity level required to achieve a target coral growth rate of 25 mm/month. Suggest, in the context of the question, why the regression line of \(y\) on \(x\) should be used for this purpose.[2]
3. The biologist checks the results and one of the values of \(y\) appears to be an outlier. Indicate the corresponding point on your diagram in part (a) by labelling it \(P\).[1]
   Omit \(P\) for the rest of the question.
4. Use your calculator to find the equation of the least squares regression line suggested in part (b). State the value of the product moment correlation coefficient.[3]
5. Use the equation of the least squares regression line to estimate the growth rate of the coral species when the light intensity level is 12. Explain whether you would expect this estimate to be reliable.[2]