A marine biologist investigates the relationship between the depth of water, ddd (in metres), and the concentration of dissolved oxygen, ccc (in mg/L), at 12 specific locations in a deep-sea trench. The following summary statistics were recorded from the collected data:
Sdd=840.5Scc=15.2Sdc=−102.4 S_{dd} = 840.5 \quad S_{cc} = 15.2 \quad S_{dc} = -102.4 Sdd=840.5Scc=15.2Sdc=−102.4Calculate the product moment correlation coefficient (PMCC) for this set of data.
Interpret the calculated PMCC value within the context of the marine biologist's investigation.
The biologist later decides to convert the depth measurements from metres to centimetres by multiplying each ddd value by 100 and then adding a constant sensor offset of 5. Write down the value of the PMCC that would be obtained using these coded depth values and the original concentration values.
