A study of bone density on 5 random women at a hospital produced the following results.
\begin{tabular}{|c|c|c|c|c|c|}
\hline Age & 33 & 41 & 61 & 65 & 69 \\
\hline Bone Density & 355 & 340 & 335 & 315 & 310 \\
\hline
\end{tabular}

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Step 3 of 3 : Calculate the coefficient of determination, $r^{2}$. Round your answer to three decimal places.

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 \(\boxed{0.854}\)