Question

can you help me understanding the nonlinear fit concept, especially the highlighted function

torial 12.nb Nonlinear Fit and Parametric Plots << Statistics NonlinearFit data= {{1., 1.0, 0.126), {2., 1., 0.219), {1., 2., 0.076}, {2., 2., 0.126), {1., 0, 0.186)); NonlinearFit [data, CX1/(1taxi+bx21, (x1, x2), (a, b, c)] y1[x1, x2] 2.443 x1/1+3.32*x1 +15.159 x2

Answer 1

The concept of linear relationship suggests that two quantities are proportional to each other: doubling one causes the other to double as well. Linear relationships are often the first approximation used to describe any relationship, even though there is no unique way to define what a linear relationship is in terms of the underlying nature of the quantities. For example, a linear relationship between the height and weight of a person is different than a linear relationship between the volume and weight of a person. The second relationship makes more sense, but both are linear relationships, and they are, of course, incompatible with each other.

Nonlinear relationships, in general, are any relationship which is not linear. What is important in considering nonlinear relationships is that a wider range of possible dependencies is allowed. When there is very little information to determine what the relationship is, assuming a linear relationship is simplest one. However, additional information generally reveals the need to use a nonlinear relationship.

Here the shaded region shows the linear function applied to the data for modelling data. it is not same every case. but it will be nonlinear in unknown parameter. There is lot of nonlinear forms such as poisson model, logistic model etc. For more information you can refer the book by Seber and Lee.