For simple linear regression, with data $x_i,y_i$, $i=1,\ldots,n$, and model $Y_i=\beta_0+\beta_1x_i+\epsilon_i$, the multiple correlation coefficient is define as An identity for simple linear regression is that $R^2$ is the same as square of the sample correlation of the $x$ and $y$ variables.

Part a)
Which of the following is a correct statement used in the proof of the claim.? By choosing the items in a correct order, you will derive the claimed result. Note that an identity for the residual SD (previous homework question) is being used.
Choose all appropriate items:

A. $SS(Total)=(n-1)s_y^2$
B. ${\hat \sigma}^2=(n-1)(1-r_{xy}^2)s_y^2/(n-2)$
C. $SS(Total)=(n-2)s_y^2$
D. $SS(Res)=(n-2){\hat \sigma}^2$
E. $SS(Total)=s_y^2$
F. $SS(Res)=(n-1)(1-r_{xy}^2)s_y^2$
G. $SS(Res)=(n-1){\hat \sigma}^2$
H. $R^2=1-(1-r_{xy}^2)$
I. None of the above

Hint: