Answer each of the following:

a. Suppose that a simple regression has quantities \(N=20, \Sigma y_{i}^{2}=7825.94, \bar{y}=19.21\), and \(S S R=375.47\), find \(R^{2}\).

b. Suppose that a simple regression has quantities \(R^{2}=0.7911, S S T=725.94\), and \(N=20\), find \(\hat{\sigma}^{2}\).

c. Suppose that a simple regression has quantities \(\sum\left(y_{i}-\bar{y}\right)^{2}=631.63\) and \(\sum \hat{e}_{i}^{2}=182.85\), find \(R^{2}\).