*
* HETERO.RPF
* RATS Version 8, User's Guide, Example 2.1
* From Hill, Griffiths, & Lim, Principles of Econometrics, 3rd edition
*
open data food.dat
data(format=free,org=columns) 1 40 food income
*
linreg food
# constant income
*
* The LINES option on SCATTER allows you to add one or more y=a+bx lines
* to a scatter plot. In this case, it takes the 2-vector with the
* intercept and slope from the previous LINREG.
*
scatter(style=dots,lines=%beta,vmin=0.0,$
  hlabel="x = weekly income in $100",vlabel="y = weekly food expenditures in $")
# income food
*
* LINREG with ROBUST does a standard LS estimation, but with a
* heteroscedasticity-robust covariance matrix.
*
linreg(robust) food
# constant income
@regconfidence(conf=.95)
*
* LINREG with the SPREAD option does weighted least squares with a
* variance series proportional to the series given by the SPREAD option.
*
linreg(spread=income) food
# constant income
@regconfidence(conf=.95)
*
linreg food
# constant income
*
* This sequence does feasible GLS. This first runs a regression of
* log(e^2) on the log of income.
*
set esq = log(%resids^2)
set z   = log(income)
*
linreg esq
# constant z
*
* PRJ then computes the fitted values from the above regression, which
* are then "exp"ed to give the estimated variances. That constructed
* series is fed into LINREG with SPREAD to correct for
* heteroscedasticity.
*
prj vhat
linreg(spread=exp(vhat)) food
# constant income