predict - Predict response of nonlinear regression model - MATLAB (original) (raw)

Predict response of nonlinear regression model

Syntax

Description

[ypred](#btbowi9%5Fsep%5Fshared-ypred) = predict([mdl](#btbowi9%5Fsep%5Fshared-mdl),[Xnew](#btbowi9%5Fsep%5Fshared-Xnew)) returns the predicted response of the nonlinear regression modelmdl to the points in Xnew.

example

[[ypred](#btbowi9%5Fsep%5Fshared-ypred),[yci](#btbowi9%5Fsep%5Fshared-yci)] = predict([mdl](#btbowi9%5Fsep%5Fshared-mdl),[Xnew](#btbowi9%5Fsep%5Fshared-Xnew),[Name,Value](#namevaluepairarguments)) specifies additional options using one or more name-value arguments. For example, you can specify the confidence level of the confidence interval and the prediction type.

example

Examples

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Create a nonlinear model of car mileage as a function of weight, and predict the response.

Create an exponential model of car mileage as a function of weight from the carsmall data. Scale the weight by a factor of 1000 so all the variables are roughly equal in size.

load carsmall X = Weight; y = MPG; modelfun = 'y ~ b1 + b2exp(-b3x/1000)'; beta0 = [1 1 1]; mdl = fitnlm(X,y,modelfun,beta0);

Create predicted responses to the data.

Xnew = X; ypred = predict(mdl,Xnew);

Plot the original responses and the predicted responses to see how they differ.

plot(X,y,'o',X,ypred,'x') legend('Data','Predicted')

Figure contains an axes object. The axes object contains 2 objects of type line. One or more of the lines displays its values using only markers These objects represent Data, Predicted.

Create a nonlinear model of car mileage as a function of weight, and examine confidence intervals of some responses.

Create an exponential model of car mileage as a function of weight from the carsmall data. Scale the weight by a factor of 1000 so all the variables are roughly equal in size.

load carsmall X = Weight; y = MPG; modelfun = 'y ~ b1 + b2exp(-b3x/1000)'; beta0 = [1 1 1]; mdl = fitnlm(X,y,modelfun,beta0);

Create predicted responses to the smallest, mean, and largest data points.

Xnew = [min(X);mean(X);max(X)]; [ypred,yci] = predict(mdl,Xnew)

ypred = 3×1

34.9469 22.6868 10.0617

yci = 3×2

32.5212 37.3726 21.4061 23.9674 7.0148 13.1086

Generate sample data from the nonlinear regression model

y=b1+b2exp(-b3x)+ϵ

where b1, b2, and b3 are coefficients, and the error term ϵ is normally distributed with mean 0 and standard deviation 0.5.

modelfun = @(b,x)(b(1)+b(2)*exp(-b(3)*x));

rng('default') % For reproducibility b = [1;3;2]; x = exprnd(2,100,1); y = modelfun(b,x) + normrnd(0,0.5,100,1);

Fit the nonlinear model using robust fitting options.

opts = statset('nlinfit'); opts.RobustWgtFun = 'bisquare'; b0 = [2;2;2]; mdl = fitnlm(x,y,modelfun,b0,'Options',opts);

Plot the fitted regression model and simultaneous 95% confidence bounds.

xrange = [min(x):.01:max(x)]'; [ypred,yci] = predict(mdl,xrange,'Simultaneous',true);

figure() plot(x,y,'ko') % observed data hold on plot(xrange,ypred,'k','LineWidth',2) plot(xrange,yci','r--','LineWidth',1.5)

Figure contains an axes object. The axes object contains 4 objects of type line. One or more of the lines displays its values using only markers

Load sample data.

S = load('reaction'); X = S.reactants; y = S.rate; beta0 = S.beta;

Specify a function handle for observation weights, then fit the Hougen-Watson model to the rate data using the specified observation weights function.

a = 1; b = 1; weights = @(yhat) 1./((a + b*abs(yhat)).^2); mdl = fitnlm(X,y,@hougen,beta0,'Weights',weights);

Compute the 95% prediction interval for a new observation with reactant levels [100,100,100] using the observation weight function.

[ypred,yci] = predict(mdl,[100,100,100],'Prediction','observation', ... 'Weights',weights)

Input Arguments

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Data Types: single | double | table

Name-Value Arguments

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Specify optional pairs of arguments asName1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: [ypred,yci] = predict(Mdl,Xnew,'Alpha',0.01,'Simultaneous',true) returns the confidence interval yci with a 99% confidence level, computed simultaneously for all predictor values.

Data Types: single | double

Data Types: string | char

Vector of real, positive value weights or a function handle.

If you specify a vector, then it must have the same number of elements as the number of observations (or rows) inXnew.
If you specify a function handle, the function must accept a vector of predicted response values as input, and returns a vector of real positive weights as output.

Given weights, W, predict estimates the error variance at observation i byMSE*(1/W(i)), where MSE is the mean squared error.

Output Arguments

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Predicted response values evaluated at Xnew, returned as a numeric vector.

Confidence intervals for the responses, returned as a two-column matrix in which each row provides one interval. The meaning of the confidence interval depends on the settings of the name-value arguments Alpha,Prediction, and Simultaneous.

Tips

For predictions with added noise, use random.
For a syntax that can be easier to use with models created from tables or dataset arrays, try feval.

References

[1] Lane, T. P. and W. H. DuMouchel. “Simultaneous Confidence Intervals in Multiple Regression.” The American Statistician. Vol. 48, No. 4, 1994, pp. 315–321. Available at https://doi.org/10.1080/00031305.1994.10476090

[2] Seber, G. A. F., and C. J. Wild. Nonlinear Regression. Hoboken, NJ: Wiley-Interscience, 2003.

Version History

Introduced in R2012a