1) a) A linear regression yields β1=0. show that R^2=0
b) A linear regression yields R^2=0. Does this imply that β1=0?
2) a) show that the regression R^2 in the regression of Y on X is the squared value of the sample correlation between X and Y. That is, show that R^2=r^2xy
b) show that the R^2 from the regression of Y on X is the same as the R^2 from the regression of X on Y.