A cross-section data on food expenditure, F, non-food expd. ,N, and total household expd., Y, for a sample of n households. By definition :

Yi = Fi + Ni

The regression
fi = a1 + a2Y
ni = b1 + b2Y

are fitted using OLS regression analysis. show that the regression coefficients will automatically satisy the following equation :

a2 + b2 = 1
a1 + b1 = 0