The code attached suppose to estimate alpha and beta using least square estimate . I didn't see what is wrong with the code , it does give me good value for alpha but this is not the case for beta , its always fixed at the lower bound of it's constrains .
I might have done something wrong, but when I graph the LSQ function over a range of parameter values, it doesn't look like it has a maximum. If that is the case, it could be caused by a coding error in one of your functions. Try running the program on a problem for which you know the correct answer. That will help you locate the source of the problem.