non linear regression equation calculator

#NON LINEAR REGRESSION EQUATION CALCULATOR SERIES#

When allowing for any type of relationship between the independent variables and the dependent variable, two issues raise their heads. (However, if all variables of interest are categorical in nature, or can be converted into categorical variables, you may also consider Correspondence Analysis.)

Nonlinear Estimation leaves it up to you to specify the nature of the relationship for example, you may specify the dependent variable to be a logarithmic function of the independent variable(s), an exponential function, a function of some complex ratio of independent measures, etc. Specifically, multiple regression (and ANOVA) assumes that the relationship between the independent variable(s) and the dependent variable is linear in nature. In fact, you may think of Nonlinear Estimation as a generalization of those methods. You may recognize research issues in these examples that are commonly addressed by such techniques as multiple regression (see Multiple Regression) or analysis of variance (see ANOVA/MANOVA). For example, we may want to compute the relationship between the dose of a drug and its effectiveness, the relationship between training and subsequent performance on a task, the relationship between the price of a house and the time it takes to sell it, etc. This makes divergence much more likely, especially as the minimum along the direction of steepest descent may correspond to a small fraction of the length of the steepest descent vector.In the most general terms, Nonlinear Estimation will compute the relationship between a set of independent variables and a dependent variable.

When the parameter values are far from optimal the direction of the steepest descent vector, which is normal (perpendicular) to the contours of the objective function, is very different from the direction of the Gauss–Newton vector. Although a reduction in the sum of squares is guaranteed when the shift vector points in the direction of steepest descent, this method often performs poorly. This method, a form of pseudo-Newton method, is similar to the one above but calculates the Hessian by successive approximation, to avoid having to use analytical expressions for the second derivatives. Calculation of the Hessian adds to the complexity of the algorithm. Although this model has better convergence properties near to the minimum, it is much worse when the parameters are far from their optimal values. In economic theory, the non-linear least squares method is applied in (i) the probit regression, (ii) threshold regression, (iii) smooth regression, (iv) logistic link regression, (v) Box–Cox transformed regressors ( m ( x, θ i ) = θ 1 + θ 2 x ( θ 3 ) The matrix H is known as the Hessian matrix. There are many similarities to linear least squares, but also some significant differences.

The basis of the method is to approximate the model by a linear one and to refine the parameters by successive iterations. It is used in some forms of nonlinear regression. Non-linear least squares is the form of least squares analysis used to fit a set of m observations with a model that is non-linear in n unknown parameters ( m ≥ n).

#NON LINEAR REGRESSION EQUATION CALCULATOR SERIES#

Approximation method in statistics Part of a series on

Non linear regression equation calculator