The dissolved oxygen concentration, DDD (mg/L), and the water temperature, TTT (∘^{\circ}∘C), were measured at n=12n = 12n=12 distinct sampling stations in a hydro-thermal basin.
Some of the summary statistics for these measurements are given below:
∑T=108∑T2=1119SDD=75.0STD=−78.5 \sum T = 108 \quad \sum T^2 = 1119 \quad S_{DD} = 75.0 \quad S_{TD} = -78.5 ∑T=108∑T2=1119SDD=75.0STD=−78.5(i) Calculate the mean of the 12 recorded values of TTT.
(ii) Show that the standard deviation of the 12 values of TTT is 3.503.503.50 to 3 significant figures.
Calculate the product moment correlation coefficient (PMCC) between TTT and DDD.
To standardize the data for an international report, the temperature values were converted using the linear transformation W=1.5T+12W = 1.5T + 12W=1.5T+12.
Use your results from part (a) to calculate the mean and the standard deviation of the transformed values, WWW.
Given that VVV is the equivalent transformed value of DDD using the same linear coding V=1.5D+12V = 1.5D + 12V=1.5D+12, state the value of the product moment correlation coefficient between WWW and VVV. Give a reason for your answer.