1. Consider the simple regression model, = 0 + 1 + . We can derive the following expression for ^2, by changing the sums of squares to sample variances and then plugging in the definition of the estimated regression line, = 0 + 1. ^2 = SSE/SST Use this expression to show that, in a simple regression, ^2 is the square of the sample correlation coefficient between and . That is, show that ^2 = 2 ,. (Hint: 0 and 1 are estimates here, so they are constants. After bringing 1 out of the variance in the above expression, use one of the expressions for 1.)