How do I calculate the coefficient of determination, $R^2$, using the following data?

Question

Supposing that a simple linear regression has quantities $N=20$, $\sum_{i=1}^{N}y_{i}^{2}=5930.94$, $\bar{y}=16.035$ and $SSR=666.72$.

Answer 1

Assuming hat $SSR$ is Sum of Squares of the regression, then recall that $$ R^ 2= \frac{SSReg}{SST} = \frac{666.72}{\sum y_i ^2 - N \bar{y}} = \frac{666.72}{5930.94 - 20 \times 16.035}. $$ If by $SSR$ you meant the Sum of Squares of the residuals, then just apply the fact that $SST = SSReg + SSRes$.