An environmental scientist monitors the annual growth rate of a specific lichen, LLL mm/year, and the atmospheric concentration of a pollutant, CCC parts per million (ppm), across 18 distinct sites. The collected data is summarised as follows:
SCC=12.8S_{CC} = 12.8SCC=12.8 ∑L2=142.5\sum L^2 = 142.5∑L2=142.5 ∑CL=105.0\sum CL = 105.0∑CL=105.0 ∑L=48.6\sum L = 48.6∑L=48.6 ∑C=43.2\sum C = 43.2∑C=43.2
Calculate the value of SCLS_{CL}SCL and the value of SLLS_{LL}SLL.
Calculate the value of the product moment correlation coefficient (PMCC) between CCC and LLL.
Show that the equation of the regression line of LLL on CCC can be written as
L=4.88−0.909C L = 4.88 - 0.909C L=4.88−0.909C(Rounding constants to 3 significant figures).
Give an interpretation of the gradient of the regression line.
Explain why it would not be appropriate to use this regression line to estimate the growth rate of lichen at a site with a pollutant concentration of 10 ppm.
The scientist decides to code the data using u=C−1.5u = C - 1.5u=C−1.5 and v=5L+2.5v = 5L + 2.5v=5L+2.5.
Write down the value of the PMCC between uuu and vvv.
Write down an equation of the regression line of vvv on uuu. You do not need to simplify your equation.
