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.