There is a software that does exactly that, Eureqa.

It tries to fit not only parameters of a given formula

but also finds a suitable expression. As far as I

understand it does that with genetic or at least

evolutionary algorithms.

http://phys.org/news179394947.html

http://www.nutonian.com/products/eureqa/

Regards,

Joachim

I am not sure what you mean by "nonlinear" in nonlinear regression. Do you mean that the coefficients/parameters are part of transformations or functions or are you talking about a non-linear relationship between a predictor and a reponse. For the latter, Excel provides a function for multiple regression: LINEST. You have to set up the design matrix manually from the predictors. Categorical predictors can be 0/1 coded, and continuous predictors can enter in any transformation (linear, polynomial, logarithmic, reciprocal...) to model non-linear relationships. Such model are called linear models because they are linear in the parameters.

If your model is non-linear in the parameters, I doubt that Excel comes with a useful built-in method. You would have to set up a likelihood function and use the solver to find its maximum (numerically better use the log-likelihood). And you would need to do a likelihood profiling to get confidence intervals. I suspect that all this will be cumbersome in Excel.

There is a software that does exactly that, Eureqa.

It tries to fit not only parameters of a given formula

but also finds a suitable expression. As far as I

understand it does that with genetic or at least

evolutionary algorithms.

http://phys.org/news179394947.html

http://www.nutonian.com/products/eureqa/

Regards,

Joachim

Thanks dear Jochen Wilhelm and dear Joachim Pimiskern.

Yes I meant a non-linear model/function to fit my data, sth like hougen or a gaussian one. Thanks for your kind and precious answer dear Jochen. I may use an optimization method.

Dear Joachim, the link which you've noted, I think that's useful. appreciate it.

There are some non parametric methods also. It depends on what properties has your data: convexity, nonnegativity...?

If you give us more informations we should probably guide you in a more efficient way.

You can try the standardized multiple linear regression (using beta weights) with SPSS. This is advisable if your 6 dependent variables have different units and/or scales.

There are statistical packages that does nonlinear multiple regression. SPSS is one such package. Nonetheless, you did not specify whether your data are time series or primary data. The characteristics of your data is necessary in order that you are able to use the best statistical package to process your regression. Other packages are STATA, SAS, E-VIEWs among the more popular ones.

Enter your data in Excel sheet. Take any statistical software. Go to Multiple regression window. Define independent and dependent variable when asked to define variables. Press OK. You will get results.

I am not a fan of this blind shots. First, try to identify to physical/biological basis of your problem, set up equations and then fire up your statistics software. I hate 10th grade polynomial approximations of poorly measured data of linear relations.

Hi Hamed

Use SPSS as it's perhaps the easiest if your not too statistical. You can import your data from excel to SPSS. Then I suggest running correlations to see how each of your independent variables relate to one another. If two (or more pairs) of variables are highly correlated then it is not a great idea to put them both into the same regression. Without knowing your data and variables I would suggest adding one variable at a time and using a variable addition test to see what it adds to the R2 and all the time for checking for individual significance. Not sure if SPSS can do it, but sometimes groups of variables can be left in a model even when some of them are individually insignificant (look at the t-stat or z-stat on the right of the regression output to see if individual variables are significant. At the start I would suggest leaving anything which is significant at the 10% level or below in your model. If your dependent variable is continuous use OLS, if it is coded 1,0 use logit, on an ordered scale (e.g 1-5 where 1 is low and 5 is high) use an ordered logit. If it is in categories but with no obvious high/low then use multinomial logit and choose a base or reference category against which all others are compared. Hope this helps? Marc

Hello Hamed! Unless there are some clues to what the equation should look like, I would try estimating the relationships between each independent and the dependent variable (linear / non-linear) and afterwards aggregate them into one equation. And the iuse what Marc duggested. In social sciences there is usually no hard and fast rules about formulas, for example, a = 1/b and a = 1/b + c may be both true. Could you describe your research in more details? Thanks. Ilya

It is always advice to give a brief description of the experiment and much more important the measurement levels of all the variables involved as to guide and enable the network members to be accurate in their propositions or suggestion'.

so easy;

Genetic Programming is the best way to do that whether a real formula does exist or not. in addition it cover non-linear option.

Discipulus is a very good software for this purpose.

Hello,

the parameters of multiple nonlinear or liner models can be easily estimated using Excel Solver provided with Microsoft Excel. In this way you can set your objective function as you want.

Dr Vatankhah, I figured out how to use excel solver to reach a formula but It's not robust since It just uses one series of data from the whole experimental data.

for example; parameters are: A,B,C and D. D is dependent. and 100 data exists for each parameters. I tried this:

desired objective function=D-(k*(A^a*B^b/C^c))

changing variables=k,a,b,c

case:minimize obj function

excel cannot cover my whole experimental data but one to start solving.

your mean is that A,B,C and D are variables and D is dependent variable and you want to determine regression parameters a, b, c and k. if your proposed functional form is suitable you can find regression parameters a, b, c and k for 100 experimental data. if it is necessary you can add constraints by solver. Please note that your current objective function is not suitable you should use mean squared error or mean absolute error as an objective function; that is, absolute(D-(k*(A^a*B^b/C^c)))

Thanks Dear Dr. Vatankhah, This still remains unanswered in my mind that Excel solver would change a,b,c,k not A,B,C which are independent variables. I want to say that how can I tell the Excel solver to find desired formula by considering these 100 data since I'm just allowed to specify A,B and C with one series of data. I can't specify a group of data.

If That's possible I would appreciate it if you could guide me through it.

Your model is linear after logarithmic it:

ln(D) = ln(k)+a*ln(A)+b*ln(B)-c*ln(C)

More rigorously:

ln(D) = ln(k)+a*ln(A)+b*ln(B)+c*[-ln(C)]+error

So, take the relevant 4 independent variables

1, ln(A), ln(B), [-ln(C)]

and do OLS with dependent variable the ln(D).

Good luck!

Thanks dear Demetris, I wanted to know how could I set a group of data for A,B,C and D to train an equation. this formula scheme is logarithmic and how "1" could be a parameter you might meant ln(k).

you should set 4 columns for A, B , C and D with 100 rows and fill them with your experimental data. then you make a new column for calculated formula of D

that is k*(A^a*B^b/C^c) and ...

It worked! thanks Everyone. Thanks Dr. Vatankah. But it's a little bit hard to handle it and it's not efficient. optimize one obj fun may leads to corrupt another obj fun.

Dear all,

I have also the same problem. I have 6 independent input variables with one output . I have a long series  experimental data of all variables with associated output. I want to derive the equation between that 6 variables and single output. And also, i am unknown whether the variables and output are linear or non-linear. Is there any method to solve this problem?  I will be grateful if anyone can me suggest about this.

You can go with following steps:

All the best.

MATLAB

Dear Hamed,

if I understand correctly, you search for a regression model to generate you high adjusted R2, (low DW), and best information criteria. If the data is of the same type, e.g. time series or cross-sectional, I think you need to do the following:

1) Estimate the best relationship between each independent and the dependent variable (in practice, it is often either a linear one /line/ or a non-linear one /polynomial or exponential, logarithm, less frequently logistical/),

2) Find a way to compensate for multicollinearity – the mutual influence of variables, at least, measuring it.

Basically, the simple additive model (Y = b0 + b1 * X1 + b2 * X2 + ...) or the multiplicative model (log Y = b0 + b1 * log X1 + b2 * log X2 + ...) is often enough, unless you find some non-linearity between a regressor and the dependent variable. Of course, the choice of model should depend on your theoretical assumptions. In social sciences, we may assume whatever, in natural sciences the equations are usually strictly given.

And, in case of time series, please check them for integration/unit root (at least I(1)), which may also be the cause of problems with the model. You can do it with an ADF test. The rank of integration of the dependent variables should match the corresponding rank of at least one independent variable. Also, residuals should be I(0), otherwise the relationship is spurious and you will constantly have problems with the DW criterion. NB Part of the problems with time series regressions may be solved by adding a time variable (t=1, 2, ...).

There is a range of software, which can perform all of the above-mentioned for you or you can try it "manually" using OLS (or, if your example somehow violates the OLS conditions, WLS, maximum likelihood etc.). I recommend gretl / R for statistical computations, but Matlab and others should do it too:

http://gretl.sourceforge.net

It has been a long time and I hope you'd found your answer,

you also can use "data analysis" in excel, If you can not find it in you Excel/ DATA manu, you can add it via add-in

I've done it for multi variable for dependent Y and independents: A,B and C you will get:

Y=i+a*A+b*B+c*C

this Data analysis gives you correlation coefficients: i (intercept),a,b, and c

as well as Regression statistics such as "r square"

this tutorial might help you:

https://www.youtube.com/watch?v=HgfHefwK7VQ

Thanks Reza,

Excel produces a linear eq.