: help lsq2
Macro: variable number of arguments (3 <= narg <= 6)
# do a least squares fit to a set of vectors, errors in x and y
# syntax: lsq2 x y lambda [ x2 y2 [rms] ]
# Fit line y2=$a*x2+$b to x y, assuming that the errors
# in x and y are uncorrelated and sigma_y^2/sigma_x^2 = lambda.
# Optionally, calculate rms residual as $rms
# See lsq for the case where all the errors are in x or y,
# rxy to find product moment correlation coeff,
# and spear for Spearman's corr. coeff. and significance
SET _n = DIMEN($1)              # number of points
SET _mx = SUM($1)/_n            # x bar
SET _my = SUM($2)/_n            # y bar
SET $0$1 = $1 - _mx             # relative to mean
SET $0$2 = $2 - _my
SET _sxx = SUM($0$1*$0$1)       # sigma xx
SET _sxy = SUM($0$1*$0$2)       # sigma xy
SET _syy = SUM($0$2*$0$2)       # sigma yy
DEFINE a ( (_syy - $3*_sxx + \
    sqrt((_syy - $3*_sxx)**2 + 4*$3*_sxy**2))/(2*_sxy) )
DEFINE b ( _my - $a*_mx )
IF($?4 && $?5) {
   SET $5=$a*$4+$b
   IF($?6) {
      DEFINE $6 ( sqrt(sum(($a*$1 + $b - $2)**2)/dimen($2)) )
   }
}
FOREACH v ( _n _mx _my _sxx _sxy _syy ) { DELETE $v }