Show first that the regression $R ^ { 2 }$ is the square of the sample correlation coefficient. Next, show that the slope of a simple regression of Y on X is only identical to the inverse of the regression slope of X on Y if the regression $R ^ { 2 }$ equals one.

Question

Show first that the regression $R ^ { 2 }$  is the square of the sample correlation coefficient. Next, show that the slope of a simple regression of  Y  on  X  is only identical to the inverse of the regression slope of  X  on  Y  if the regression  $R ^ { 2 }$ equals one.

Quizplus · Accepted Answer

The Answer of Show first that the regression $R ^ { 2 }$  is the square of the sample correlation coefficient. Next, show that the slope of a simple regression of  Y  on  X  is only identical to the inverse of the regression slope of  X  on  Y  if the regression  $R ^ { 2 }$ equals one.

Show First That the Regression R2R ^ { 2 }R2 Is the Square of the Sample Correlation Coefficient

Show First That the Regression $R ^ { 2 }$ Is the Square of the Sample Correlation Coefficient