Uses of regression analysis

The Regression analysis is a branch of statistical theory that is widely used in almost all the scientific streams. In economics it is the basic method for measuring or estimating the relationship among economic variables that constitute the essence of economic theory and economic life. For e.g., 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. Thus we find that the study of regression is of considerable help to the economists and businessmen. The uses of regression are not restricted to economics and business field only. Its applications are widen to almost all the physical, natural and social sciences. The regression analysis attempts to accomplish the following:

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

The 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 aim 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.

By the help of regression coefficients we can calculate the correlation coefficient. The square of correlation coefficient (r), known as the coefficient of determination, measures the degree of association of correlation which 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 normal, the greater the value of r2 the better is the fit and the more useful the regression equations as a predictive device.