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