Coefficient of determination and correlation coefficient

[DylsexicChciken]

For the topic of linear regression, my book says that the (coefficient of determination) = (correlation coefficient squared). But it doesn't explain why. So why is on equal to the square of the other when their formulas look completely different?

Edited December 18, 2014 by DylsexicChciken

[studiot]

If you substitute the equation of the linear regression line into the defining formula for the coefficient of determination and play with the algebra for about a page you arrive at the definition formula for the coefficient of correlation.