$\%$ Initialize data and parameters

xdata $=[1$; $2$; $3$; $4$; $5]$;

ydata $=[0\mathrm{.}5$; $2$; $2\mathrm{.}9$; $3\mathrm{.}5$; $4]$;

N $=$ length$($xdata$)$;

$\%$ Initial guesses for parameters a and b

A $=[1$; $0\mathrm{.}5]$;

tolerance $=1$e$-6$;

max$\_$iterations $=1000$;

i $=0$;

$\%$ Nonlinear regression loop

while true

i $=$ i $+1$;

a $=$ A$(1)$;

b $=$ A$(2)$;

$\%$ Construct Z matrix based on the current values of a and b

Z $=[$exp$(($ydata $-$ b$)/$ a$)/$ a$,-$exp$(($ydata $-$ b$)/$ a$)]$;

$\%$ Calculate the difference between xdata and model predictions

D $=$ xdata $-$ exp$(($ydata $-$ b$)/$ a$)$;

$\%$ Calculate parameter adjustment

dA $=($Z$\text{'}*$ Z$)\backslash ($Z$\text{'}*$ D$)$;

A $=$ A $+$ dA;

$\%$ Check for convergence

if max$($abs$($dA$))<$ tolerance $||$ i $>=$ max$\_$iterations

break

end

end

$\%$ Display estimated parameters

a$\_$estimated $=$ A$(1)$;

b$\_$estimated $=$ A$(2)$;

fprintf$(\text{'}$Estimated parameters:

a $=\%\mathrm{.}6$f

b $=\%\mathrm{.}6$f

$\text{'},$ a$\_$estimated, b$\_$estimated$)$;

$\%$ Predict y at x $=2\mathrm{.}6$ using estimated parameters

x$\_$pred $=2\mathrm{.}6$;

y$\_$pred $=$ a$\_$estimated $*$ log$($x$\_$pred$)+$ b$\_$estimated;

fprintf$(\text{'}$Predicted y at x $=2\mathrm{.}6$: $\%\mathrm{.}6$f

$\text{'},$ y$\_$pred$)$;