*
* Example 11.7, page 416
* Weighted least squares
*
*  The only lines in Table 11.1 that we need are the 11th, 13th and 12th,
*  which give the average compensation and average productivity, and
*  the sample standard deviations. Note, however, a typo in y(5) in the CD text
*  file, which is corrected below.
*
data(unit=input,format=free) 1 9 y x sigma
3396.00 3787.00 4013.00 4104.00 4146.00 4241.00 4387.00  4538.00  4843.00
9355.00 8584.00 7962.00 8275.00 8389.00 9418.00 9795.00 10281.00 11750.00
 743.70  851.40  727.80  805.06  929.90 1080.60 1243.20  1307.70  1112.50
*
* Doing weighted least squares "by hand"
*
set wy = y/sigma
set wc = 1/sigma
set wx = x/sigma
linreg wy
# wc wx
*
* OLS
*
linreg y
# constant x
*
* Using weighted least squares through linreg. For WLS, RATS has you specify the
* the variances (or at least a series proportional to them). This is related to
* the weights by weight = 1/sqrt(spread)
*
linreg(spread=sigma**2) y
# constant x