Question

prove that the coefficient of correlation is Geometric mean of the coefficients of regression

Answer 1

Answer:

The prove is discussed below :

Step-by-step explanation:

The sample correlation coefficient :  

$r = \pm\sqrt(b_{xy}\times b_{yx})$

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.

Here in this expression we  have given both the signs: +sign and the –sign. The  question arises: whether r will be positive or whether r will  be negative?

Once we take the square root of the product  of both the regression coefficients. Now, the sign of correlation coefficient will  depend on the sign of the regression coefficients. If the  regression coefficients have the positive sign then r will be  positive. And, if both the regression coefficients have the  negative sign then r will be negative.

That is in another  words, both the regression coefficients will  always have the same sign. Because the sign of the  regression coefficients depends on the value of r. And r  can be either positive or it can be negative.

So,the coefficient of correlation is Geometric mean of the coefficients of regression

Hence Proved.

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. ... Once we take the square root of the product of both the regression coefficients.

hope this helps you