An environmental scientist studies the effect of industrial runoff on the growth of certain aquatic plants in a lake. She takes samples from 6 different locations, measuring the concentration of heavy metals, mmm, and the reduction in plant height, rrr. The data are shown in the table below:
m2728221411r2411964\begin{array}{|c|c|c|c|c|c|c|} \hline m & 2 & 7 & 28 & 22 & 14 & 11 \\ \hline r & 2 & 4 & 11 & 9 & 6 & 4 \\ \hline \end{array}mr22742811229146114
[You may use: ∑m=84,∑r=36,∑m2=1638 and ∑mr=666\sum m = 84, \sum r = 36, \sum m^2 = 1638 \text{ and } \sum mr = 666∑m=84,∑r=36,∑m2=1638 and ∑mr=666]
Explain why a linear regression model might be suitable for this data.
Calculate the value of SmrS_{mr}Smr and the value of SmmS_{mm}Smm.
Find the equation of the regression line of rrr on mmm, giving your answer in the form r=a+bmr = a + bmr=a+bm. Give your values to 3 significant figures.
The scientist discovers that a reduction in height greater than the level predicted when metal concentration is 18 mg/L is terminal for the plant species. Estimate this critical reduction in height using your model.
278 exam-style questions on CCEA A Level Maths 2.5 Data presentation and interpretation, covering 2.5.1 Data presentation and interpretation, 2.5.2 Data presentation and interpretation, 2.5.3 Data presentation and interpretation, 2.5.4 Data presentation and interpretation, 2.5.5 Data presentation and interpretation, 2.5.6 Data presentation and interpretation, 2.5.7 Data presentation and interpretation, 2.5.8 Data presentation and interpretation, 2.5.9 Data presentation and interpretation, and 2.5 Data presentation and interpretation. Each one has a worked solution and a mark scheme showing where the marks go.