I have an equation of type: y = a1*x^b + a2 * x + e1 where e1 is error in the y experimental data corresponding to x. What type of least square method i should apply to get the values of e1, a1 and a2. What will be the normal equations of least square i should use for getting the reqquired values or what technique i use to get the value of e1 and a1 if i have y, x and a2 known.
Your last sentence makes little sense to me. However, if I understand your prior question, you're looking at a simple multiple regression problem in two parameters. If you're learning this regression stuff, you could hardly do better than get a copy of the book by Neter and Wasserman, "Applied Linear Statistical Models".
What type of multiple regression i should use. I have no idea of normal equations for my equation. I have experimental data of x and corresponding y but the y has some error e and the equation of x,y is of type y = a1*x^b + a2*x + e, where e is the error in y. To minimize our e what will be the normal equations or what technique i use to get the minimum value of e.
By your last post, it's reasonably clear you don't understand the nature of the usual linear statistical model used for regression (I don't mean this in a derogatory way; rather, it's just an observation). I'll reiterate that you would really benefit from getting a copy of the Neter and Wasserman book -- it's very, very good and will give you an understanding of the model being applied and the assumptions the model must make to be validly applied. For multiple linear regression, the book writes the relevant equations down in a beautiful and compact matrix notation. This may not be the answer you want, as it forces you to go out and learn the principles -- but you'll be better prepared the next time such a problem pops up. If all you're interested in is a few plug-and-chug equations, then there are numerous statistics books and web pages that do that for you too. The typical computer multiple regression tool spits out an analysis of variance of the fit, so you'll need to understand what that's telling you to intelligently use the results. Also, one of the most important tasks in analyzing a regression is looking at the residuals -- do a probability plot, time series plot, etc. -- those things tell you a lot when you know what to look for.