predict
Predict responses of linear regression model
Syntax
Description
Examples
Predict Response Values
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 predicted responses to the data.
ypred = predict(mdl,X);
Plot the original responses and the predicted responses to see how they differ.
plot(X,y,'o',X,ypred,'x') legend('Data','Predictions')
Generate C/C++ Code for Prediction
Fit a linear regression model, and then save the model by using saveLearnerForCoder
. Define an entry-point function that loads the model by using loadLearnerForCoder
and calls the predict
function of the fitted model. Then use codegen
(MATLAB Coder) to generate C/C++ code. Note that generating C/C++ code requires MATLAB® Coder™.
This example briefly explains the code generation workflow for the prediction of linear regression models at the command line. For more details, see Code Generation for Prediction of Machine Learning Model at Command Line. You can also generate code using the MATLAB Coder app. For details, see Code Generation for Prediction of Machine Learning Model Using MATLAB Coder App.
Train Model
Load the carsmall
data set, and then fit the quadratic regression model.
load carsmall X = Weight; y = MPG; mdl = fitlm(X,y,'quadratic');
Save Model
Save the fitted quadratic model to the file QLMMdl.mat
by using saveLearnerForCoder
.
saveLearnerForCoder(mdl,'QLMMdl');
Define Entry-Point Function
Define an entry-point function named mypredictQLM
that does the following:
Accept measurements corresponding to X and optional, valid name-value pair arguments.
Load the fitted quadratic model in
QLMMdl.mat
.Return predictions and confidence interval bounds.
function [yhat,ci] = mypredictQLM(x,varargin) %#codegen %MYPREDICTQLM Predict response using linear model % MYPREDICTQLM predicts responses for the n observations in the n-by-1 % vector x using the linear model stored in the MAT-file QLMMdl.mat, and % then returns the predictions in the n-by-1 vector yhat. MYPREDICTQLM % also returns confidence interval bounds for the predictions in the % n-by-2 vector ci. CompactMdl = loadLearnerForCoder('QLMMdl'); [yhat,ci] = predict(CompactMdl,x,varargin{:}); end
Add the %#codegen
compiler directive (or pragma) to the entry-point function after the function signature to indicate that you intend to generate code for the MATLAB algorithm. Adding this directive instructs the MATLAB Code Analyzer to help you diagnose and fix violations that would result in errors during code generation.
Note: If you click the button located in the upper-right section of this example and open the example in MATLAB®, then MATLAB opens the example folder. This folder includes the entry-point function file.
Generate Code
Generate code for the entry-point function using codegen
(MATLAB Coder). Because C and C++ are statically typed languages, you must determine the properties of all variables in the entry-point function at compile time. To specify the data type and exact input array size, pass a MATLAB® expression that represents the set of values with a certain data type and array size. Use coder.Constant
(MATLAB Coder) for the names of name-value pair arguments.
If the number of observations is unknown at compile time, you can also specify the input as variable-size by using coder.typeof
(MATLAB Coder). For details, see Specify Variable-Size Arguments for Code Generation and Specify Types of Entry-Point Function Inputs (MATLAB Coder).
codegen mypredictQLM -args {X,coder.Constant('Alpha'),0.1,coder.Constant('Simultaneous'),true}
Code generation successful.
codegen
generates the MEX function mypredictQLM_mex
with a platform-dependent extension.
Verify Generated Code
Compare predictions and confidence intervals using predict
and mypredictQLM_mex
. Specify name-value pair arguments in the same order as in the -args
argument in the call to codegen
.
Xnew = sort(X); [yhat1,ci1] = predict(mdl,Xnew,'Alpha',0.1,'Simultaneous',true); [yhat2,ci2] = mypredictQLM_mex(Xnew,'Alpha',0.1,'Simultaneous',true);
The returned values from mypredictQLM_mex
might include round-off differences compared to the values from predict
. In this case, compare the values allowing a small tolerance.
find(abs(yhat1-yhat2) > 1e-6)
ans = 0x1 empty double column vector
find(abs(ci1-ci2) > 1e-6)
ans = 0x1 empty double column vector
The comparison confirms that the returned values are equal within the tolerance 1e–6
.
Plot the returned values for comparison.
h1 = plot(X,y,'k.'); hold on h2 = plot(Xnew,yhat1,'ro',Xnew,yhat2,'gx'); h3 = plot(Xnew,ci1,'r-','LineWidth',4); h4 = plot(Xnew,ci2,'g--','LineWidth',2); legend([h1; h2; h3(1); h4(1)], ... {'Data','predict estimates','MEX estimates','predict CIs','MEX CIs'}); xlabel('Weight'); ylabel('MPG');
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 | dataset array | matrix
New predictor input values, specified as a table, dataset array, or matrix. Each row of
Xnew
corresponds to one observation, and each column
corresponds to one variable.
If
Xnew
is a table or dataset array, it must contain predictors that have the same predictor names as in thePredictorNames
property ofmdl
.If
Xnew
is a matrix, it must have the same number of variables (columns) in the same order as the predictor input used to createmdl
. Note thatXnew
must also contain any predictor variables that are not used as predictors in the fitted model. Also, all variables used in creatingmdl
must be numeric. To treat numerical predictors as categorical, identify the predictors using the'CategoricalVars'
name-value pair argument when you createmdl
.
Data Types: single
| double
| table
Name-Value Arguments
Specify optional pairs of arguments as
Name1=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.
Alpha
— Significance level
0.05 (default) | numeric value in the range [0,1]
Significance level for the confidence interval, specified as the comma-separated pair
consisting of 'Alpha'
and a numeric value in the range [0,1]. The
confidence level of yci
is equal to 100(1 – Alpha
)%. Alpha
is the probability that the confidence
interval does not contain the true value.
Example: 'Alpha',0.01
Data Types: single
| double
Prediction
— Prediction type
'curve'
(default) | 'observation'
Prediction type, specified as the comma-separated pair consisting of
'Prediction'
and either
'curve'
or
'observation'
.
A regression model for the predictor variables X and the response variable y has the form
y = f(X) + ε,
where f is a fitted regression function and ε is a random noise term.
If
'Prediction'
is'curve'
, thenpredict
predicts confidence bounds for f(Xnew), the fitted responses atXnew
.If
'Prediction'
is'observation'
, thenpredict
predicts confidence bounds for y, the response observations atXnew
.
The bounds for y are wider than the bounds for f(X) because of the additional variability of the noise term.
Example: 'Prediction','observation'
Simultaneous
— Flag to compute simultaneous confidence bounds
false
(default) | true
Flag to compute simultaneous confidence bounds, specified as the comma-separated pair
consisting of 'Simultaneous'
and either true or false.
true
—predict
computes confidence bounds for the curve of response values corresponding to all predictor values inXnew
, using Scheffé's method. The range between the upper and lower bounds contains the curve consisting of true response values with 100(1 – α)% confidence.false
—predict
computes confidence bounds for the response value at each observation inXnew
. The confidence interval for a response value at a specific predictor value contains the true response value with 100(1 – α)% confidence.
With simultaneous bounds, the entire curve of true response values is within the bounds at high confidence. By contrast, non-simultaneous bounds require only the response value at a single predictor value to be within the bounds at high confidence. Therefore, simultaneous bounds are wider than non-simultaneous bounds.
Example: 'Simultaneous',true
Output Arguments
ypred
— Predicted response values
numeric vector
Predicted response values evaluated at Xnew
,
returned as a numeric vector.
yci
— Confidence intervals for responses
two-column numeric matrix
Confidence intervals for the responses, returned as a two-column matrix with each row
providing one interval. The meaning of the confidence interval depends on the settings
of the name-value pair arguments 'Alpha'
,
'Prediction'
, and 'Simultaneous'
.
Alternative Functionality
feval
returns the same predictions aspredict
. Thefeval
function can take multiple input arguments, with one input for each predictor variable, which is simpler to use with a model created from a table or dataset array. Note that thefeval
function does not give confidence intervals on its predictions.random
returns predictions with added noise.Use
plotSlice
to create a figure containing a series of plots, each representing a slice through the predicted regression surface. Each plot shows the fitted response values as a function of a single predictor variable, with the other predictor variables held constant.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
Usage notes and limitations:
Use
saveLearnerForCoder
,loadLearnerForCoder
, andcodegen
(MATLAB Coder) to generate code for thepredict
function. Save a trained model by usingsaveLearnerForCoder
. Define an entry-point function that loads the saved model by usingloadLearnerForCoder
and calls thepredict
function. Then usecodegen
to generate code for the entry-point function.To generate single-precision C/C++ code for
predict
, specify the name-value argument"DataType","single"
when you call theloadLearnerForCoder
function.This table contains notes about the arguments of
predict
. 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 theRobustWgtFun
field, usesaveLearnerForCoder
to save the model, and then useloadLearnerForCoder
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 inXnew
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).
Name-value pair arguments Names in name-value arguments must be compile-time constants. For example, to allow a user-defined significance level in the generated code, include
{coder.Constant('Alpha'),0}
in the-args
value ofcodegen
(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
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