# Advanced Regression And Alternatives

**Introduction:** As an alternative of regressions we can utilize kriging models and also artificial neural nets(ANN) Linear regression models are not the only curve-fitting methods in wide use. Also, these methods are not useful for analyzing data for categorical responses.

**Generic Curve Fitting:**

Many numerical approaches have been proposed for interpolating data points. A subset of these has been developed with the intention of mitigating the effects that random errors have on curve fitting, including linear regression, kriging models, and neural nets.

All of these estimate their model parameters, β*est*, based on their experimental inputs, **x**_{1},…,**x**_{N}, and outputs, *y*_{1},…,*y _{N}*, by solving an optimization program of the form

**Curve Fitting Example:** The linear regression optimization problem for estimating the coefficients is given by

there is a formula giving the solution. The solution is given by the formula

Generally, formula optimization problems are so difficult that there is no formula giving the solution.

More commonly, a solution algorithm such as the Excel solver must be applied.

The first set is sub-optimal for the formulation ,few people would desire this fitted model based on the data compared with the model associated with the coefficients that minimize the sum of squares error are shown in Figure (b). The coefficients giving the fit in Figure (b) can be derived using the solver.