Estimation and comparison of ratio and regression estimates of true mean food expenditure data

Abstract

Data about family income and food expenditures is distributed into six income strata. Mean per unit, Ratio type and Linear Regression estimation methods are used to estimate true mean food expenditures of families in each income strata. It is statistically decided that Ratio method is appropriate for estimating mean food expenditures of families in 1st, 4th and 5th income strata and linear regression estimation is appropriate for 2nd and 3rd income strata. In comparison of Mean per unit, ratio type and linear regression methods, it can be concluded that linear regression is more efficient as compared to ratio and mean per unit and Ratio estimation is more efficient than mean per unit estimation methods. On the basis of satisfied conditions of regression analysis on these methods, It is concluded that estimates of true mean monthly food expenditures using ratio types estimation for 1st, 4th and 5th income groups’ families are 4987Rs, 18412Rs and 27470Rs with corresponding standard errors (precisions of estimates) 9.79Rs, 31.62Rs and 17.60Rs respectively and estimates based on linear regression for 2nd and 3rd strata are 10844Rs and 15192Rs with their measures of precisions 15.85Rs and 27.24Rs respectively. Estimate of true mean in last income stratum is found theoretically quite strange and estimate obtained from mean per unit is more precise. In analysis of food consumed, income elasticity varies from 0.12 to 0.63, which means as income increases, expenditure on food also increases but at the lesser rate. Also average food purchased/adult and average food consumed/adult among strata vary from 1881Rs to 7176Rs and from 1841Rs to 7068Rs respectively. Stability exists in expenditures on cereals origin among income strata and a steady sharp uprising trend on vegetable origin and on animal origin exists. Variation in monthly food expenditures exists from 2111Rs to 11890Rs in vegetable origin and from 2980Rs to 19296Rs in animal origin. In analysis of calories intake from specific food origins, per capita/day calories intake increases in cereals, vegetables and in animal origins and vary from 1416 to1741, from 62 to 239 and from 100 to 839 respectively.