Constrained least squares

Question

I am fitting a simple regression in R on gas usage per capita. The regression formulas looks like:

gas_b <- lm(log(gasq_pop) ~ log(gasp) + log(pcincome) +         


        

Answer 1

Modify your regression as follows:

gas_b <- lm(log(gasq_pop) - log(ps) ~ log(gasp) + log(pcincome) +
  I(log(pn)-log(ps)) + I(log(pd)-log(ps)) + log(years), data=gas) 
summary(gas_b)

If b=coef(gas_b), then the relevant coefficients are

log(pn): b[4]
log(pd): b[5]
log(ps): 1 - b[4] - b[5]