# What is the significance of regression analysis in statistics

Publish On: 2019-04-20

Total Post: 475

# Gaurabh Raghav

Total Post: 33

## ANS: What is the significance of regression analysis in statistics

Regression analysis is a branch of statistical theory that is widely used in almost all the scientific disciplines. In economics it is the basic technique for measuring or estimating the relationship among economic variables that constitute the essence of economic theory and economic life. For example, if we know that two variables, price (X) and demand (Y), are closely related we can find out the most probable value of X for a given value of Y or the most probable value of Y for a given value of X. similarly, if we know that the amount of tax and the rise in the price of a commodity are closely related, we can find out the expected price for a certain amount of tax levy. Thus we find that the study of regression is of considerable help to the economists and businessmen. The uses of regression are not confined to economics and business field only. Its applications are extended to almost all the natural, physical and social sciences. The regression analysis attempts to accomplish the following:

1. Regression analysis provides estimates of values of the dependent variable from values of the independent variable. The device used to accomplish this estimation procedure is the regression line. The regression line describes the average relationship existing between X and Y variables, i.e. it displays mean values of X for given values of Y. the equation of this line, known as the regression equation, provides estimates of the dependent variable when values of the independent variables are inserted into the equation.

2. A second goal of regression analysis is to obtain a measure of the error involved in using the regression line as a basis for estimation. For this purpose the standard error of estimate is calculated. This is a measure of the scatter or scatter of the observations around the regression line, good estimates can be made of the Y variable. On the other hand, if there is a great deal of scatter of the observations around the fitted regression line, the line will not produce accurate estimates of the dependent variable?

3. With the help of regression coefficients we can calculate the correlation coefficient. The square of correlation coefficient (r), called coefficient of determination, measures the degree of association of correlation that exists between the two variables. It assesses the proportion of variance in the dependent variable that has been accounted for by the regression equation. In general, the greater the value of r2 the better is the fit and the more useful the regression equations as a predictive device.