Dear Paul,

There are many references online, yet the following may be very useful to you.

Best wishes,

P

http://blog.minitab.com/blog/adventures-in-statistics/curve-fitting-with-linear-and-nonlinear-regression

Morning Paul,

You can apply the "curve fitting" procedure in SPSS. You can also define which curves you are goin to investigate. The program will try to fit the data into chosen curves and show you the significance levels. 

What curves to choose? It depdens only on your theory. If you expect tthe data to be inear, then you check the linear curves. If you expect the to be non linear, then you choose the appropriate type of the curve (there are 4-6 of them, can't remeber). For example, if you assume that the results should have an U-shaped form, choose the quadratic one AND the linear one. If your theory is correct, then the explained resulty and significances will be higher by a quadratic one. If not - the linear one. You need to provide data on both of them (or if you tested more, then on more). It will  indicate that you tested different solutions and that the right one was the theorized one.

SIncerely,

Eugen 

Dear Paul Ouma ,

You may use correlation analysis to check, whether your data is linear or not. If correlation value if greater than 0.8 or smaller than -0.8 then your data is linear.

There are different way to find the non linear regression models. I suggest you to use multivariate adaptive regression splines (MARS) to find the relation between variables. MARS is a collection of multiple linear regression. Please refer this paper:

 https://www.researchgate.net/publication/303011477_Quality_Assessment_of_Web_Services_Using_Multivariate_Adaptive_Regression_Splines

Conference Paper Quality Assessment of Web Services Using Multivariate Adapti...

Please refer to my paper entitled: The Prediction of LWST Values from DFT and CTM Measurements Using Linear and Nonlinear Regression Analyses. You may also try symbolic regression using Eureqa software.

The main question is what you are fitting your data for. If you are searching X to maximize Y, the linear model is wrong. If you want to "describe" how Y depends on X, you are to have a theory for such a "model". Linear dependence is a very primitive one. If you want to predict Y for a given set of X, you should consider not regression problem but consider transductive inference approach. Have a look at http://olivier.chapelle.cc/pub/trans_nips99.pdf

Hope this helps

How do I determine whether the model is linear or non linear? I think the simple method is to draw a scatterplot using the data (x,y). If all the plots are almost like a line, then the model is linear. Otherwise, it is nonlinear.

Let me to use capital letters X, Y instead, as uppercase are perhaps used   more often for  data and model, letting  lowercase x,y for dummy integration variables.

A linear model is of the form Y = A  X   +   B , with A, B: being two constants.

A nonlinear model is any other model that cannot be put in this form. For example 

Y=Y**2+2, or Y=log(X)

On which model should you choose..You have two basic approaches:

The empirical one and:

... the "incorporating evidence designed model" that is: ...if you knew some previous assumed relationships (beliefs) between implied variables, it's expected  that you could  design a better fit model.    

Both have advantages and disadvantages: but on the on the other hand: if you choose a linear model (through   any of both approaches), you'll win some  advantages (from the points of view of:  expression, modelling, computation and interpretation of results.

Moreover.: Complex numbers let us to formulate in some sense: universal models that are linear  (That is in fact Quantum Mechanics.) . 

I think you have rerceived several good alternatives. Try different. They recogniize slightly different aspects.

Johan Fellman

 So the issue for you is to choose appropriate f in y_i = f(X_i) + u_i. I suggest you to choose f so that the u_i is close to iid (independent and identically distributed). You might have to use a lots of dummies to take into account the heterogeneity in y If normality is also maintained, inference would be a lot easier.