# gnuplot script
# Biochem 721.3 Foster 05/05
# for problem 7.8
# data are time (s), conc (mM)
set title "Problem 7.8"
unset label
set fit errorvariables
set autoscale
a=1; b=1
set ylabel 'Conc (mM)'
set xlabel 'Time (s)'
set xrange [0:22]
f(x) = a*exp(-x*b)
plot 'p7_8.txt' ps 3 pt 4
fit f(x) 'p7_8.txt' via a,b
set label "conc. = A * exp( -time*rate)" at graph 0.1,0.8
set label "A = %.2f", a, "+/- %.2g", a_err at graph 0.6,0.2
set label "rate = %.2f b", b, "+/- %.2g", b_err at graph 0.6,0.25
replot f(x)
print 'Check plot for fitting accuracy
print ""
pause -1 'Now calculate the residuals; press return'
set ylabel 'Conc. (mM); residuals'
plot 'p7_8.txt' using 1:($2-f($1)) wi boxes, 0
pause -1 'If instead we fit to 2nd order (1/c) ... (return)'
plot 'p7_8.txt' ps 3 pt 4
y(x) = 1/(b*x + 1/a)
#fit y(x) 'p7_8.txt' using 1:(1/$2) via a,b
fit y(x) 'p7_8.txt' via a,b
unset label
set label "conc. = 1/(rate*time + 1/A)" at graph 0.1,0.8
set label "A = %.2f", a, "+/- %.2g", a_err at graph 0.6,0.2
set label "rate = %.2f", b, "+/- %.2g", b_err at graph 0.6,0.25
replot y(x)
pause -1 'Inspect plot, then check residuals (rtrn)'
plot 'p7_8.txt' using 1:($2-y($1)) w boxes, 0
print 'Now residuals are RANDOM!'