#read in data set
   data logdata
   read {lnamp 1 lnmass 2}

#define macro
MACRO lsfit 4 {
# Calculate least squares fit of a data set (x,y)
# to y = m*x + b
#
# Arguments:
#      $1      x data
#      $2      y data
# Output:
#      $3      the slope
#      $4      the  y-intercept
   set sumx   = sum($1)
   set sumy   = sum($2)
   set sumxy  = sum($1*$2)
   set sumxsq = sum($1**2)
   set n      = dimen($1)
   set m      = (n*sumxy - sumy*sumx)/(n*sumxsq - sumx**2)
   set b      = (sumy - m*sumx)/n
   set $3 = m
   set $4 = b
   set x      = $1 
   set y      = m*x + b
}
#Call fit macro
lsfit lnamp lnmass m b 

#output slope and intercept
print {m}
print {b}

MACRO drawparab 5 {
#Draw a parabola with extremum point ($1,$2) from $3 to $4
#with "slope" $5
# pick a point at top of parabola
   set x_p = $1
   set y_p = $2
   set xt  = $3, $4, ($4-$3)/100
   set a   = $5
   set b   = -2*a*x_p
   set c   = y_p - a*x_p**2 - b*x_p
   set yt  = a*xt**2 + b*xt + c
   connect xt yt
#
}
MACRO drawarc 5 {
# draw an arc, centre ($1,$2) radius $3,
# between centered around angle $4, of length $5
SET _ang local set _x local set _y local
SET _ang = $4-$5,$4+$5,PI/30
SET _x = $1 + $3*COS(_ang)
SET _y = $2 + $3*SIN(_ang)
CONNECT _x _y
#
}

MACRO makebox 4 {
#draw lines from ($1,$2)->($1,$4)->($3,$4)->($3,$2)->($1,$2)
relocate $1 $2
draw $1 $4
draw $3 $4
draw $3 $2
draw $1 $2
#
}

MACRO makebox2 5 {
#draw lines from ($1,$2)->($1,$4)->($3,$4)->($3,$2)->($1,$2)
relocate $1 $2
draw $1 $4
draw $3 $4
draw $3 $2
draw $1 $2
#set p  = { $1 $1 $3 $3 $1 }
#set p' = { $2 $4 $4 $2 $2 }
set p  = $1 concat $1 concat $3 concat $3 concat $1
set p' = $2 concat $4 concat $4 concat $2 concat $2
shade $5 p p'
#
}