Regression Method of Estimation

Abstract

Analogous to the ratio and product estimators, the linear regression estimator is also designed to increase the efficiency of estimation by using information on the auxiliary variable x which is correlated with the study variable y. As stated before, the ratio method of estimation is at its best when the correlation between y and x is positive and high, and also the regression of y on x is linear through the origin. In practice, however, it is observed that even when the regression of y on x is linear, the regression line passes through a point away from the origin. The efficiency of the ratio estimator in such cases is very low, as it decreases with the increase in length of the intercept cut on y-axis by the regression line. Regression estimator is the appropriate estimator for such situations. Although this estimator requires little more calculations than the ratio estimator, it is always at least as efficient as the ratio estimator for estimating population mean or total. Similarly, the product estimator of population mean or total is never more efficient than the corresponding linear regression estimator.