# Properties of Regression Coefficient

**Definition:** The constant ‘b’ in the regression equation (Y_{e }= a + bX) is called as the **Regression Coefficient**. It determines the slope of the line, i.e. the change in the value of Y corresponding to the unit change in X and therefore, it is also called as a **“Slope Coefficient.”**

## Properties of Regression Coefficient

- The correlation coefficient is the
**geometric mean**of two regression coefficients. Symbolically, it can be expressed as: - The value of the coefficient of correlation
**cannot exceed unity i.e. 1.**Therefore, if one of the regression coefficients is greater than unity, the other must be less than unity. - The
**sign of both the regression coefficients will be same**, i.e. they will be either positive or negative. Thus, it is not possible that one regression coefficient is negative while the other is positive. - The
**coefficient of correlation will have the same sign**as that of the regression coefficients, such as if the regression coefficients have a positive sign, then “r” will be positive and vice-versa. - The
**average value of the two regression coefficients will be greater than the value of the correlation**. Symbolically, it can be represented as - The regression coefficients are
**independent of the change of origin, but not of the scale**. By origin, we mean that there will be no effect on the regression coefficients if any constant is subtracted from the value of X and Y. By scale, we mean that if the value of X and Y is either multiplied or divided by some constant, then the regression coefficients will also change.

Thus, all these properties should be kept in mind while solving for the regression coefficients.

## 1 Comment

Clearly defined