The model itself is a bit misleading.
A better option might be:
That produces an equivalent fit with parameters that make sense.
xdata=[0; 30; 60; 90; 120; 180; 240];
ydata=[1.607; 2.346; 2.621; 2.967; 3.238; 3.479; 3.566];
coef = ["ymax","y0","k","R2","R2adj","RMSE"];
% fun = @(x,xdata) x(1)+(x(1)-x(2))*exp(-x(3)*xdata)
fun = @(x,xdata) x(2)+(x(1)-x(2))*(1-exp(-x(3)*xdata));
x0 = [1,1,0.01];
lb = [0,0,0];
ub = [10,10,0.5];
[x,resnorm,residual,exitflag,output] = lsqcurvefit(fun,x0,xdata,ydata,lb,ub);
x
figure(1);
plot(xdata,ydata,'o',xdata,fun(x,xdata),'-');
SSresid = sum(residual.^2);
SStotal = (numel(ydata)-1) * var(ydata);
R = 1 - SSresid/SStotal;
Radj = 1 - (SSresid/SStotal) * ((numel(ydata)-1)/(numel(ydata)-1-1));
RMSE = rmse(fun(x,xdata),ydata);
r = [x R Radj RMSE];
coef = [coef;r];
figure(2);
scatter(xdata,residual);
coef
.
