As explained earlier, the slope of regression line is called the regression coefficient. It tells the effect on dependent variable if there is a unit change in the independent variable. Since for a paired data on *X *and *Y *variables, there are two regression lines: regression line of *Y *on *X *and regression line of *X *on *Y*, so we have two regression coefficients:

*Y*on*X*, denoted by*b*[_{yx}*b*in*(5.1)*]- Regression coefficient of
*X*on*Y*, denoted by*b*[_{xy}*b*’ in*(5.13)*]

**Properties of Regression Coefficients**

The following are the important properties of regression coefficients that are helpful in data analysis

- The value of both the regression coefficients cannot be greater than 1. However, value of both the coefficients can be below 1 or at least one of them must be below 1, so that the square root of the product of two regression coefficients must lie in the limit ±1.
- Coefficient of correlation is the geometric mean of the regression coefficients,
*e*.

The signs of both the regression coefficients are the same, and so the value of *r *will also have the same sign.