random

Simulate responses with random noise for linear regression model

Syntax

ysim = random(mdl,Xnew)

Description

ysim = random(mdl,Xnew) simulates responses to the predictor data in Xnew using the linear model mdl, adding random noise.

Examples

Simulate Response Data with Random Noise

Create a quadratic model of car mileage as a function of weight from the carsmall data set.

load carsmall
X = Weight;
y = MPG;
mdl = fitlm(X,y,'quadratic');

Create simulated responses to the data with random noise.

ysim = random(mdl,X);

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

plot(X,y,'o',X,ysim,'x')
legend('Data','Simulated')

Input Arguments

mdl — Linear regression model object

LinearModel object | CompactLinearModel object

Linear regression model object, specified as a LinearModel object created by using fitlm or stepwiselm, or a CompactLinearModel object created by using compact.

Xnew — New predictor input values

table | matrix

New predictor input values, specified as a table or matrix. Each row of Xnew corresponds to one observation, and each column corresponds to one variable.

• If Xnew is a table, it must contain predictors that have the same names as predictors in the PredictorNames property of mdl.

• If Xnew is a matrix, it must have the same number of variables (columns) in the same order as the predictor input used to create mdl. All variables used to create mdl must be numeric. To treat numerical predictors as categorical, specify the predictors using the CategoricalVars name-value argument when you create mdl.

Note that Xnew must also contain any predictor variables not used as predictors in the fitted model.

Data Types: single | double | table

Output Arguments

ysim — Simulated response values

numeric vector

Simulated response value, returned as a numeric vector. The simulated value is the predicted response values at Xnew perturbed by random noise. The noise is independent and normally distributed, with mean equal to zero and variance equal to the estimated error variance of the model.

Alternative Functionality

For predictions without random noise, use predict or feval. These two functions give the same predictions.

• predict accepts a single input argument containing all predictor variables, and gives confidence intervals on its predictions.

• feval accepts multiple input arguments with one input for each predictor variable.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• Use saveLearnerForCoder, loadLearnerForCoder, and codegen (MATLAB Coder) to generate code for the random function. Save a trained model by using saveLearnerForCoder. Define an entry-point function that loads the saved model by using loadLearnerForCoder and calls the random function. Then use codegen to generate code for the entry-point function.

• random can return a different sequence of numbers than MATLAB^® if either of the following is true:

  • The output is nonscalar.

  • An input parameter is invalid for the distribution.

• This table contains notes about the arguments of random. Arguments not included in this table are fully supported.

  Argument	Notes and Limitations
  mdl	Suppose you train a linear model by using fitlm and specifying 'RobustOpts' as a structure with an anonymous function handle for the RobustWgtFun field, use saveLearnerForCoder to save the model, and then use loadLearnerForCoder to load the model. In this case, loadLearnerForCoder cannot restore the Robust property into the MATLAB Workspace. However, loadLearnerForCoder can load the model at compile time within an entry-point function for code generation. For the usage notes and limitations of the model object, see Code Generation of the CompactLinearModel object.
  Xnew	Xnew must be a single-precision or double-precision matrix or a table containing numeric variables, categorical variables, or both. The number of rows, or observations, in Xnew can be a variable size, but the number of columns in Xnew must be fixed. If you want to specify Xnew as a table, then your model must be trained using a table, and you must ensure that your entry-point function for prediction: Accepts data as arrays Creates a table from the data input arguments and specifies the variable names in the table Passes the table to predict For an example of this table workflow, see Generate Code to Classify Data in Table. For more information on using tables in code generation, see Code Generation for Tables (MATLAB Coder) and Table Limitations for Code Generation (MATLAB Coder).

For more information, see Introduction to Code Generation.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced in R2012a