Question

Prove that the correlation coefficient is the geometric mean of the two regression coefficient.

Answer 1

Correlation and linear regression are not the same. Correlation quantifies the degree to which two variables are related. ... You simply are computing a correlation coefficient (r) that tells you how much one variable tends to change when the other one does. When r is 0.0, there is no relationship.

Answer 2

Answer:

To show : Correlation coefficient is the geometric mean of two regression coefficients or in other words the sign of the correlation coefficient is the same as of regression coefficients. ... And, if both the regression coefficients have the negative sign then r will be negative.