Regression in all its forms is one type of model. It could be argued that most (all?) of statistics is about building a model or the consequences thereof. The mean is the simplest model of the expected output of some system or process.

However, model is not some special domain of statistics. There are many other models. A model of the solar system. A demographic model. An economic model. Physicists build many models, as do engineers and chemists. Boyle's Law is a model of how gases behave. In its general application a model is an abstraction of some process that we are interested in that helps us explain, predict, or visualize that process. Some models are designed more to help us understand the modeling process. So I set up a simple set of rules, and then see how a system that operates under these rules behaves. Initially, it is very hard to see how the simple rules produce anything interesting. However, we discover "emergent properties" that surprise us. With only four rules we get Conway's Game of Life: https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life.

There are many ways to start, but a great deal depends on what you are trying to do. This is by no means the only answer, and may not even be the best. If you don't already, learn a programming language. C++ is a good choice, but others will work. This will do several things. 1) it will give you a tool set that will allow you to build your own model. 2) It will help you break down problems into very small bits. 3) The idea of building flow charts in programming is very similar to building models in any system.  That said this is a great deal of effort, and there are people who have worked very hard to help you model without getting bogged down in the details and problems with programming. An example of this is: http://www.iseesystems.com/softwares/Education/StellaSoftware.aspx

There are books on ecological modeling (http://ms.mcmaster.ca/~bolker/emdbook/), and a journal titled "Ecological Modeling." Just access to a university library should provide more information then you can absorb. Taking a class in demography or ecology could be a good start. Such classes could be in any of the life sciences departments, terrestrial or aquatic, pure or applied.

Hi!

The difference is and difference of principle. The regression equation does not allow to make prognosis, to extrapolate the data or to transfer the results of the regression calculations for similarity conditions. The law of Boyle is not a regression it's the law. In short, the difference in correlation coefficient (R).If R=1 we have the functional relationship of the values or this is the law. If R less 1 , we have a regression, and strictly speaking the relationship between variables is not functional, but probabilistic. The probability of connection, the more than higher the value R. So, regression is the relationship probability for the independent variables. Physical modeling is not a function probability .

Best regards.

The regression equation does allow us to make a new prediction if the data are appropriate. Perhaps you are thinking of ANOVA rather than regression, or you are only considering a misapplication of a model of a continuous variable that is being treated as a fixed effect. I can make a regression model yield = kg/ha nitrogen, and even if I only applied nitrogen at 50, 100, 150, and 200 kg/ha I can still run the model to predict the outcome if I had applied 87.9 kg/ha.

Boyle's Law is a linear equation: pressure * volume = constant. It is a model of how pressure and volume are related. If I take a number of measurements of the volumes of a gas along with readings of pressure I can perform a linear regression (statistical model) to see how well my data conform to the model's prediction.

Laws, like Boyle's Law are useful until new data becomes available to revise or replace them.

Correlation coefficient is irrelevant to the question asked (unless I have misinterpreted the question). If you measure pressure and volume and then run a regression equation I doubt that you will get an R-square of 1. You will have measurement error. That neither proves nor disproves Boyle's Law.

I will accept that there are many terms to describe models:

deterministic versus probabilistic

Strategic versus tactical

Theoretical versus applied

There are probably other terms that could be applied to categorize models, and these might be dependent on the branch of science that is providing the dictionary.

Regression is not the relationship between independent variables. That would be multicollinearity, and that is a violation of an assumption in multivariate regression. Regression is a statistical process for estimating the relationship between the dependent and independent variables. It is not the only statistical model for doing so: Cluster analysis, Factor analysis, and other multivariate methods are other types of statistical models.

A physical model is theoretical. When you apply the model, it quickly becomes a function of probability. In general we cannot control all factors perfectly and we cannot take perfect measurements. This introduces error (error in a statistical sense), and we must then figure out if the error is consistent with the theoretical model or if the model should be revised.

Well. Apparently my English is bad English. So much to say in English I just can't. I have to say briefly

• thank dear researchers for your  interest to my question and your  answers that are loaded with information that will push me to clarify maybe a little bit my question :
• Regression analysis give us an equation that relate a dependant varialbe ( y) and one or more independant variable  ( X1, X2 ...etc). in classical regression analysis, Assuming the normality of the variables , we compute the coefficient of correlation R , and we used the table of R interpretation  to infer if there is a  significant correlation, the interpration is dependant on the degree of freedom  and the  level of significance .  At my knowledge , the limit of this analysis is that our equation is only relevant to our experimental condition!.
• Concerning Modelling of natural processes, i take an example in my field of research which is soil science, Suppose , i want to model the behavior of soil structure ( the dependant variable) in different condition of saline and sodic condition ( independant variable). the first  step for me is to set up an experiment where i vary the indendant variable ( salinity and sodicity) and then i measure the response ( soil structure changes). i can make ANOVA analysis and suppose that i have a significant effect of the different treatment. and then i  will perform a multiple regression  analysis.  i will find an equation which is highly significant. can i say that i had find a model of soil  structure change ? or just a significant correlation between a set of condition that i had imposed and soil structure changes ?

i add  to the discussion a contribution from Pr Donald Myers from the University of Arizona

"Both of these terms are rather generic, i.e. they do not refer to specific algorithms or methods. Usually when people refer to "regression" they mean "linear regression" wherein one variable (the response) is modeled as a linear function of one or more independent variables (the control variables)., i.e. Y = a +b1 X1 + ... bn Xn + e

The "e" term is the "error". There are several different ways to determine the coefficients b1,..., bn. One is "least squares", this does not depend on any statistical assumptions but then you can't do any statistical analysis of the results other than to try differrent choices of the independent variables as well as the number of independent variables.

Alternatively you can utilize various statistical assumptions (which need to be checked). E.g. that the error terms are normally distributed, have common variances, zero means..This allows you to do various statistical tests and construct confidence intervals.

It is also possible to use non-linear models but the methodology and interpretation is more complicated.

As you see this is one form of "modeling", more generally "modeling" means coming up with a mathematical description of the relationship between various variables, intended to describe some kind of phenomenon. The mathematical description can take various forms and likely involves some parameters. In any case there is the problem of deciding whether the model (and the parameter values) provide a good "model", there are different ways to evaluate the fit of a model to data. Essentially always "modeling" involves a data set. Even when the model is derived from basic principles of physics or chemistry or biology, etc it needs to be compared with data.

It is nearly often useful to do some exploratory analysis of the data to provide insight about possible model forms.

Note that "linear regression" refers to the form of the expression with respect to the (unknown) coefficients, the independent variables may be nonlinear functions of other variables.

In the statistical literature they often refer to "linear models" or "general linear models" when talking about regression. There is a good book by Raymond Myers (no relationship) on regression, it does require some knowledge of matrix analysis.

Any statistical software package will include regression analysis, if you do a search on "R package glm", you can find not only free software but also free tutorial 'material. More generally do a search (in Google) for "regression tutorials"