Properties of Regression Coefficient

Statistics refers to the study of the analysis, interpretation, collection, presentation, and organization of data. Statistics find applications in different fields such as psychology, geology, sociology, weather forecasting, probability, and much more. Regression coefficients are an important topic in statistics. They are a statistical measure that is used to measure the average functional relationship between variables. In regression analysis, one variable is dependent and the other is independent. It also measures the degree of dependence of one variable on the other variables. In this article, we come across the important properties of regression coefficient.

Regression coefficients determine the slope of the line which is the change in the independent variable for the unit change in the independent variable. So they are also known as the slope coefficient. They are classified into three. They are simple partial and multiple, positive and negative, and linear and non-linear.

In the linear regression line, the equation is given by Y = b0 + b1X. Here b0 is a constant and b1 is the regression coefficient.

The formula for the regression coefficient is given below.

b1 = ∑[(xi-x)(yi-y)]/∑[(xi-x)2]

The observed data sets are given by xi and yi. x and y are the mean value.

Important Properties of Regression Coefficient

1. The regression coefficient is denoted by b.

2. We express it in the form of an original unit of data.

3. The regression coefficient of y on x is denoted by byx. The regression coefficient of x on y is denoted by bxy.

4. If one regression coefficient is greater than 1, then the other will be less than 1.

5. They are not independent of the change of scale. There will change if the regression coefficient if x and y are multiplied by any constant.

6. AM of both regression coefficients is greater than or equal to the coefficient of correlation.

7. GM between the two regression coefficients is equal to the correlation coefficient.

8. If bxy is positive, then byx is also positive and vice versa.