13.29 Mercury Concentration in Dolphins Because dolphins (and other large marine mammals) are considered to be the top predators in the marine food chain, the heavy metal concentrations in striped dolphins were measured as part of a marine pollution study. The concentration of mercury, the heavy metal reported in this study, is expected to differ in males and females because the mercury in a female is apparently transferred to her offspring during gestation and nursing. This study involved 28 males between the ages of 0.21 and 39.5 years, and 17 females between the ages of 0.80 and 34.5 years. For the data in the table,

a. Write a second-order model relating Y to x and x2. Allow for curvature in the relationship between age and mercury concentration, and allow for an interaction between gender and age. Use a computer software package to perform the multiple regression analysis. Refer to the printout to answer these questions.

b. Comment on the fit of the model, using relevant statistics from the printout.

c. What is the prediction equation for predicting the mercury concentration in a female dolphin as a function of her age?

d. What is the prediction equation for predicting the mercury concentration in a male dolphin as a func- tion of his age?

e. Does the quadratic term in the prediction equation for females contribute significantly to the prediction of the mercury concentration in a female dolphin?

f. Are there any other important conclusions that you feel were not considered regarding the fitted predic- tion equation?

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x Age of the dolphin (in years). Jo if female x2= 1 if male = Y Mercury concentration (in micrograms/gram) in the liver y X1 x y X X2 1.70 0.21 1 481.00 22.50 1 1.72 0.33 1 485.00 24.50 1 8.80 2.00 1 221.00 24.50 1 5.90 2.20 1 406.00 25.50 1 101.00 8.50 1 252.00 26.50 1 85.40 11.50 1 329.00 26.50 1 118.00 11.50 1 316.00 26.50 1 183.00 13.50 1 445.00 26.50 1 168.00 16.50 1 278,00 27.50 1 218.00 16.50 1 286.00 28.50 1 180.00 17.50 1 315.00 29.50 1 264.00 20.50 1 y X2 y X X2 241.00 31.50 1 142.00 17.50 0 397.00 31.50 1 180.00 17.50 0 209.00 36.50 1 174.00 18.50 0 314.00 37.50 1 247.00 19.50 0 318.00 39.50 1 223.00 21.50 0 2.50 0.80 0 167.00 21.50 0 9.35 1.58 0 157.00 25.50 0 4.01 1.75 29.80 5.50 45.30 7.50 101.00 8.05 135.00 11.50 DOOOO 0 177.00 25.50 0 0 475.00 32.50 0 0 342.00 34.50 0 0 0