Regression Analysis: Finding Optimal Parameters for Non-Linear Functions

[JoeTarmet]

Sorry if this is somewhat elementary but the regression form of the sine function with data provided is y=asin(b(x-c))+d

As far as I know, all of the variables except c can be determined mathematically. My question is this, using calculus or any other method, is there a way to determine c without graphing the data?


As a follow up, is there a general formula or procedure that applies to all types of Regression (linear, Cubic, Sinusoidal, etc.)? I want to know this because I believe it is possible using statistical concepts like variance and I want to find out how many of these can be done completely by hand without graphing.

 

[Number Nine]

Your question is very confusing. Graphing isn't used to determine regression parameters, though it can be used to select general models for some very simple datasets. Generally, the parameters would be selected by minimizing some cost function (usually through least-squares), which in your case would require using some sort of non-linear optimization method, since your function is non-linear in its parameters.

 

[JoeTarmet]

Generally, the parameters would be selected by minimizing some cost function (usually through least-squares), which in your case would require using some sort of non-linear optimization method, since your function is non-linear in its parameters.

Please explain this further, I am interested in what you are saying about cost functions and optimization, but I don't understand these terms.