Constrained least squares

lm, r

Solution

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]

Problem

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) + log(pn) + log(pd) + log(ps) + log(years), data=gas) summary(gas_b) ``` I want to include a linear constraint that the beta coefficients of `log(pn)+log(pd)+log(ps)=1` (sum to one). Is there a simple way of implementing this (possibly in the `lm` function) in R without having to use `constrOptim()` function?

Original source