Why would you not feel comfortable computing a Pearson correlation on the data in Exercise 9.10?

Exercise 9.10

Down syndrome is another problem that psychologists deal with. It has been proposed that mothers who give birth at older ages are more likely to have a child with Down syndrome. Plot the data below relating age to incidence. The data were taken from Geyer (1991).

Plot a scatter diagram for the percentage of Down⁸ syndrome cases (Down / Births) as a function of age.

Age 17.5 18.5 19.5 20.5 21.5 22.5 23.5 24.5 25.5 Births 13555 13675 18752 22005 23796 24667 24807 23986 22860 Down 16 15 16 22 16 12 17 22 15 Age 26.5 27.5 28.5 29.5 30.5 31.5 32.5 33.5 34.5 Births 21450 19202 17450 15685 13954 11987 10983 9825 8483 Down 15 27 14 9 12 12 18 13 "I Age 35.5 36.5 37.5 38.5 39.5 40.5 41.5 42.5 43.5 Births 7448 6628 5780 4834 3961 2952 2276 1589 1018 Downs 23 13 17 15 30 31 33 20 16 Age 44.5 45.5 46.5 Births 596 327 249 Downs 22 7