AMU 2026 — Mathematics PYQ

In simple linear regression, we have two regression coefficients:

1. $b_{yx}$ (the regression coefficient of $Y$ on $X$)

2. $b_{xy}$ (the regression coefficient of $X$ on $Y$)

The property states that the product of these two coefficients is equal to the square of the correlation coefficient ($r$):

$$b_{yx}\cdot b_{xy}=r^2$$

Explanation:

• The value $r^2$ is formally known as the coefficient of determination.

• It measures the proportion of the variance in the dependent variable that is predictable from the independent variable(s).

• While the square root of this product gives the correlation coefficient ($r=\pm \sqrt{b_{yx}\cdot b_{xy}}$), the product itself is the coefficient of determination.