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:

• Regression coefficient of Y on X, denoted by byx [b in (5.1)]
• Regression coefficient of X on Y, denoted by bxy [b’ in (5.13)]

## Properties of Regression Coefficients

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

1. 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.
2. 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.

1. The mean of both the regression coefficients is either equal to or greater than the coefficient of correlation, i.e,  