On the Ratio and Regression Estimation in Finite Population Sampling

In this department The American Statistician publishes articles, reviews, and notes of interest to teachers of the first mathematical statistics course and of applied statistics courses.The department includes the Accent on Teaching Materials section; suitable contents for the section are described under the section heading.Articles and notes for the department, but not intended specifically for the section, should be useful to a substantial number of teachers of the indicated types of courses or should have the potential for fundamentally affecting the way in which a course is taught.A simple and more intuitive explanation of the bias of the ratio and the regression estimators of finite population is provided.The finite population is represented by certain regression fits, and the leading term of bias is described in terms of familiar concepts.We show that the asymptotic bias of the ratio estimator is due to intercept of a linear regression fit, whereas for the regression estimator, it is due to the coefficient of the quadratic term of a quadratic regression fit.We also give some variance formulas written in terms of easily interpretable quantities of the linear regression fit.