Curve fitting, least squares, optimization
IntroductionConsider a series of given data points in -dimensional space, , where is a vector, for all . Define a function through
- When the method is known as univariate regression, while if we have multivariate regression.
- Provided that all the functions are linear, the method is called linear regression, otherwise it is known as nonlinear regression.
- Also, based on the type of the functions we may have polynomial regression, regression by orthogonal polynomials, and so on.
Solving The ProblemSince the sum of residuals function is convex on its entire domain, a necessary and sufficient condition for a tuple of parameters to be a solution to the above optimization problem is that
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