A marine biologist is researching the relationship between the depth of a coral reef, ddd meters, and the number of distinct species, sss, identified at that depth. For a sample of n=12n = 12n=12 sites, the data is transformed using the coded variables u=d−1005u = \frac{d - 100}{5}u=5d−100 and v=s−204v = \frac{s - 20}{4}v=4s−20. The following summary statistics are recorded:
∑u=72Suu=150∑v=120Svv=600∑uv=505 \sum u = 72 \quad S_{uu} = 150 \quad \sum v = 120 \quad S_{vv} = 600 \quad \sum uv = 505 ∑u=72Suu=150∑v=120Svv=600∑uv=505Calculate the product-moment correlation coefficient for the coded variables uuu and vvv. Give your answer to 3 decimal places.
State the value of the product-moment correlation coefficient for the original variables ddd and sss.
The biologist suggests that deeper reef sites are likely to host a higher number of distinct species. Determine, with a reason, whether this suggestion is supported by the data.
