Question

State the following statement is true or false

The arithmetic mean of regression coefficients is less than coefficient of correlation.

• A. True
• B. False

Answer 1

The correct option is B False

Coeff. of correlation $=$ Geometric Mean of Regression coeff.

$=\sqrt{r_x.r_y}$

Acc. to A.M-G.M inequality,

$A.M\ge G.M$

$\frac{x+y}{2}\ge xy$

$\therefore$ Arithmetic mean of Regression coeff. $\ge$ G.M of Regression coeff.

$\therefore$ A.M of Regression coeff. $\ge$ coeff. of correlation.

$\therefore$ Given statement is FALSE.