nlinregr — Interactive non linear regression solver
nlinregr(Data,Names,funDef,dfunDef,pDef,YDef[,WDef][,pEst][,pLo][,pUp][,alfa]) // Start in interactive mode. [phat,yhat[,stat]]=nlinregr(Data,Names,funDef,dfunDef,pDef,YDef[,WDef][,pEst][,pLo][,pUp][,alfa]); // Run in silent command line mode. nlinregr(); // Start nlinregr with example data in interactive mode.
matrix with experimental data (dependent and independent variables) stored as column vectors.
string with space separated names for each column vector in Data. E.g 'x y z'.
string with definition of the non linear regression function yhat=f(x,p). E.g 'A+B*exp(C*x)'.
optional string with definition analytical derivatives df(x,p)/dp. e.g '[ones(x),exp(C*x),B*x.*exp(C*x)]'.
string with space separated parameter names. E.g. 'A B C'
string with name of the dependent data variables y (from Names)' E.g 'y'
optional flag selecting predefined weight strategy: =1(default): no weight factor wt=ones(y). =2: wt=(1)./y.^2. =3: wt=(1)./y.
optional column vector with initial estimate for non linear regression parameters. Default is ones(np,1). pEst is also used for internal scaling of the model parameters.
optional lower bounds on parameters as column vector or scalar (default = +%Inf).
optional upper bounds on parameters as column vector or scalar (default = -%Inf).
optional significance level for parameter confidence interval estimates (default alfa=0.05).
parameter value at the solution of the non linear regression problem.
dependent variable estimates (yhat=f(x,phat)).
optional structure with regression statistics at the solution.
weighted residual sum of squares ( ss = (wt.*res)'*(wt.*res) )
degrees of freedom ( df = length(y) - length(p) )
vector with residuals ( res = y-f(x,p) )
vector with solution of the WLSQ problem ( Minimize: ss. Subject to: plo .le. p .le. pup.)
confidence interval (at alfa significance level) for reqression parameters ( pint = devp*cdft('T',df,1-alfa/2,alfa/2) )
parameter covariance matrix ( covp = inv(df/ss*(J'*J)) where J is the Jacobi matrix of res wrt p at the solution p=phat)
parameter correlation matrix ( corp = covp./sqrt(devp2*devp2'); where devp2=devp.^2; )
standard error ( devp = sqrt(diag(covp)) ).
nlinregr is an interactive frontend for the non linear regression solver nlinlsq.
A non linear function yhat=f(x,p) is fitted to the data set y [x] using non linear regression analysis. The following optimization problem is solved:
Minimize ss=sum(((y-f(x,p)).*wt).^2) subject to: pLo .le. p .le. pUp.
Regression statistics like asymptotic confidence intervals and correlation matrix for the model parameters are calculated and presented in a solution report inspired by the nls function in R Project.
Note that new data may be loaded directly from Excel spreadsheet files when nlinregr is started in interactive mode. Use the button "Load data" from the GUI to read data from .xls files. The data in the Excel spreadsheets must be located in the upper left corner of the spreadsheet. The first row should contain Names for each column vector in Data. Numbers in subsequent rows are stored in Data. Number of columns must match number of columns in the first row.
See the Scilab Demonstrations section for some non linear regression test problems from the NIST StRG Dataset Archives. nlinregr is not able to solve all these problems. Consider using R for hard problems.
x=-[1:100]'/10; y=2+10*exp(x/2)+grand(100,1,'nor',0,1)/2; // some noisy data fun='A+B*exp(C*x)'; dfun='[ones(x), exp(C*x), B*x.*exp(C*x)]'; [p,yhat,stat]=nlinregr([x y],'x y',fun,dfun,'A B C','y',1,[1;1;1]) // fit curve directly nlinregr([x y],'x y',fun,dfun,'A B C','y',1,[1;1;1]); // solve problem interactivly from gui // Data example from R (http://www.r-project.org/). See help on nls and DNase in R. conc=[0.04882812 0.04882812 0.1953125 0.1953125 0.390625 0.390625 0.78125 0.78125 1.5625 1.5625 3.125 3.125 6.25 6.25 12.5 12.5]'; density=[0.017 0.018 0.121 0.124 0.206 0.215 0.377 0.374 0.614 0.609 1.019 1.001 1.334 1.364 1.73 1.71]'; fun='Asym./(1+exp((xmid-log(conc))./scal))'; pnames='Asym xmid scal'; dfun='[1.0./(exp((xmid-log(conc))/scal)+1), Asym*exp((xmid-log(conc))/scal)./(scal*(exp((xmid-log(conc))/scal)+1).^2), Asym*(xmid-log(conc)).*exp((xmid-log(conc))/scal)./(scal^2*(exp((xmid-log(conc))/scal)+1).^2)]'; [p,yhat,stat]=nlinregr([conc density],'conc density',fun,dfun,'Asym xmid scal','density',1,[1;1;1]); // unweighted model nlinregr([conc density],'conc density',fun,dfun,'Asym xmid scal','density',2,[1;1;1]); // weighted model