The first regression shows the result of regressing LGFDHO, the logarithm of annual household expenditure on food eaten at home, on LGEXP, the logarithm of total annual household expenditure, and LGSIZE, the logarithm of the number of persons in the household, using a sample of 868 households in the 1995 Consumer Expenditure Survey. In the second regression, LGFDHOPC, the logarithm of food expenditure per capita (FDHO/SIZE), is regressed on LGEXPPC, the logarithm of total expenditure per capita (EXP/SIZE). In the third regression LGFDHOPC is regressed on LGEXPPC and LGSIZE.
1. Explain why the second model is a restricted version of the first, stating the restriction.
2. Perform an F test of the restriction.
3. Perform a t test of the restriction.
4. Summarize your conclusions from the analysis of the regression results.