If the regression equation as $\displaystyle \hat{y}=1-0.30x$ and $r^2=0.64$. Then the correlation coefficient is
Here is what I've tried: We have given $r^2=0.64$. Then we have $r=0.8$. So our correlation coefficient is $0.8$.
But it is unclear to me what is the use of the regression equation in the above problem.
The regression equation is there to tell you the direction of the correlation. If you know $r^2 = 0.64$, then $r = \pm 0.8$. To decide on whether the correlation is positive or negative you should look at the slope of the regression line. Since the slope is negative, $r = -0.8$.