Step 1 :Given data is the age and bone density of 5 random women at a hospital. The data is as follows: \n Age: [33, 41, 61, 65, 69] \n Bone Density: [355, 340, 335, 315, 310]
Step 2 :Calculate the means of age and bone density. The mean age is 53.8 and the mean bone density is 331.0
Step 3 :Calculate the terms needed for the formula. The numerator is -1084.0 and the denominator is 1173.27575616306
Step 4 :Calculate the correlation coefficient (r). The correlation coefficient is -0.9239089739184447
Step 5 :Calculate the coefficient of determination (\(r^{2}\)). The coefficient of determination is 0.8536077920870334
Step 6 :Round the coefficient of determination to three decimal places. The final answer is \(\boxed{0.854}\)