1. The problem asks to find the coefficient of determination and the coefficient of nondetermination given the correlation coefficient $r=0.57$. 2. The coefficient of determination, denoted as $R^2$, is calculated by squaring the correlation coefficient: $$R^2 = r^2$$ 3. Calculate $R^2$: $$R^2 = (0.57)^2 = 0.3249$$ This means that approximately 32.49% of the variation in $y$ can be explained by the variation in $x$. 4. The coefficient of nondetermination is the proportion of variation in $y$ that is not explained by $x$. It is calculated as: $$1 - R^2$$ 5. Calculate the coefficient of nondetermination: $$1 - 0.3249 = 0.6751$$ This means that approximately 67.51% of the variation in $y$ is not explained by the variation in $x$. 6. Summary: - Coefficient of determination: $0.3249$ - $32.49\%$ of the variation of $y$ is explained by the variation of $x$. - Coefficient of nondetermination: $0.6751$ - $67.51\%$ of the variation of $y$ is not explained by the variation of $x$. These coefficients help us understand how well $x$ predicts $y$. A higher coefficient of determination means a better fit of the model.