The coefficient of determination, often denoted as $R^2$, measures the proportion of the variance in the dependent variable that is predictable from the independent variable(s).

It is calculated as the ratio of the Explained Sum of Squares (ESS) to the Total Sum of Squares (TSS).

Given the sums of squares:

• Total Sum of Squares (TSS) = $\sum (Y_i - \bar{Y})^2 = 58$
• Sum of Squared Residuals (SSR) = $\sum (Y_i - \hat{Y})^2 = 10$
• Explained Sum of Squares (ESS) = $\sum (\hat{Y}_i - \bar{Y})^2 = 48$

The formula for the coefficient of determination is: $R^2 = \frac{ESS}{TSS}$

$R^2 = \frac{48}{58} \approx 0.82758$

Rounding to three decimal places gives 0.828. The correct answer is C.