Compact linear regression model
CompactLinearModel is a compact version of a full linear
regression model object LinearModel. Because a compact model does
not store the input data used to fit the model or information related to the fitting
process, a CompactLinearModel object consumes less memory than a
LinearModel object. You can still use a compact model to predict
responses using new input data, but some LinearModel object functions
do not work with a compact model.
Create a CompactLinearModel model from a full, trained LinearModel model by using compact.
CoefficientCovariance — Covariance matrix of coefficient estimatesThis property is read-only.
Covariance matrix of coefficient estimates, specified as a p-by-p matrix of numeric values. p is the number of coefficients in the fitted model.
For details, see Coefficient Standard Errors and Confidence Intervals.
Data Types: single | double
CoefficientNames — Coefficient namesThis property is read-only.
Coefficient names, specified as a cell array of character vectors, each containing the name of the corresponding term.
Data Types: cell
Coefficients — Coefficient valuesThis property is read-only.
Coefficient values, specified as a table.
Coefficients contains one row for each coefficient and these
columns:
Estimate — Estimated
coefficient value
SE — Standard error
of the estimate
tStat — t-statistic for a test that the
coefficient is zero
pValue — p-value for the
t-statistic
Use anova (only for a linear regression model) or
coefTest to perform other tests on the coefficients. Use
coefCI to find the confidence intervals of the coefficient
estimates.
To obtain any of these columns as a vector, index into the property
using dot notation. For example, obtain the estimated coefficient vector in the model
mdl:
beta = mdl.Coefficients.Estimate
Data Types: table
NumCoefficients — Number of model coefficientsThis property is read-only.
Number of model coefficients, specified as a positive integer.
NumCoefficients includes coefficients that are set to zero when
the model terms are rank deficient.
Data Types: double
NumEstimatedCoefficients — Number of estimated coefficientsThis property is read-only.
Number of estimated coefficients in the model, specified as a positive integer.
NumEstimatedCoefficients does not include coefficients that are
set to zero when the model terms are rank deficient.
NumEstimatedCoefficients is the degrees of freedom for
regression.
Data Types: double
DFE — Degrees of freedom for errorThis property is read-only.
Degrees of freedom for the error (residuals), equal to the number of observations minus the number of estimated coefficients, specified as a positive integer.
Data Types: double
LogLikelihood — LoglikelihoodThis property is read-only.
Loglikelihood of response values, specified as a numeric value, based
on the assumption that each response value follows a normal
distribution. The mean of the normal distribution is the fitted
(predicted) response value, and the variance is the
MSE.
Data Types: single | double
ModelCriterion — Criterion for model comparisonThis property is read-only.
Criterion for model comparison, specified as a structure with these fields:
AIC — Akaike information criterion.
AIC = –2*logL + 2*m, where logL is the
loglikelihood and m is the number of estimated
parameters.
AICc — Akaike information criterion corrected for
the sample size. AICc = AIC + (2*m*(m + 1))/(n – m – 1),
where n is the number of observations.
BIC — Bayesian information criterion.
BIC = –2*logL + m*log(n).
CAIC — Consistent Akaike information criterion.
CAIC = –2*logL + m*(log(n) + 1).
Information criteria are model selection tools that you can use to compare multiple models fit to the same data. These criteria are likelihood-based measures of model fit that include a penalty for complexity (specifically, the number of parameters). Different information criteria are distinguished by the form of the penalty.
When you compare multiple models, the model with the lowest information criterion value is the best-fitting model. The best-fitting model can vary depending on the criterion used for model comparison.
To obtain any of the criterion values as a scalar, index into the property using dot
notation. For example, obtain the AIC value aic in the model
mdl:
aic = mdl.ModelCriterion.AIC
Data Types: struct
MSE — Mean squared errorThis property is read-only.
Mean squared error (residuals), specified as a numeric value.
MSE = SSE / DFE,
where MSE is the mean squared error, SSE is the sum of squared errors, and DFE is the degrees of freedom.
Data Types: single | double
RMSE — Root mean squared errorThis property is read-only.
Root mean squared error (residuals), specified as a numeric value.
RMSE = sqrt(MSE),
where RMSE is the root mean squared error and MSE is the mean squared error.
Data Types: single | double
Rsquared — R-squared value for modelThis property is read-only.
R-squared value for the model, specified as a structure with two fields:
Ordinary — Ordinary (unadjusted) R-squared
Adjusted — R-squared adjusted for the number of
coefficients
The R-squared value is the proportion of the total sum of squares explained by the
model. The ordinary R-squared value relates to the SSR and
SST properties:
Rsquared = SSR/SST,
where SST is the total sum of squares, and
SSR is the regression sum of squares.
For details, see Coefficient of Determination (R-Squared).
To obtain either of these values as a scalar, index into the property using dot
notation. For example, obtain the adjusted R-squared value in the model
mdl:
r2 = mdl.Rsquared.Adjusted
Data Types: struct
SSE — Sum of squared errorsThis property is read-only.
Sum of squared errors (residuals), specified as a numeric value.
The Pythagorean theorem implies
SST = SSE + SSR,
where SST is the total sum of squares,
SSE is the sum of squared errors, and SSR is
the regression sum of squares.
Data Types: single | double
SSR — Regression sum of squaresThis property is read-only.
Regression sum of squares, specified as a numeric value. The regression sum of squares is equal to the sum of squared deviations of the fitted values from their mean.
The Pythagorean theorem implies
SST = SSE +
SSR,
where SST is the total sum
of squares, SSE is the sum of squared errors,
and SSR is the regression sum of
squares.
Data Types: single | double
SST — Total sum of squaresThis property is read-only.
Total sum of squares, specified as a numeric value. The total sum of squares is equal
to the sum of squared deviations of the response vector y from the
mean(y).
The Pythagorean theorem implies
SST = SSE + SSR,
where SST is the total sum of squares,
SSE is the sum of squared errors, and SSR is
the regression sum of squares.
Data Types: single | double
Robust — Robust fit informationThis property is read-only.
Robust fit information, specified as a structure with the fields described in this table.
| Field | Description |
|---|---|
WgtFun | Robust weighting function, such as 'bisquare' (see
'RobustOpts') |
Tune | Tuning constant. This field is empty ([]) if
WgtFun is 'ols' or if
WgtFun is a function handle for a custom weight
function with the default tuning constant 1. |
Weights | Vector of weights used in the final iteration of robust fit. This
field is empty for a CompactLinearModel
object. |
This structure is empty unless you fit the model using robust regression.
Data Types: struct
Formula — Model informationLinearFormula objectThis property is read-only.
Model information, specified as a LinearFormula object.
Display the formula of the fitted model mdl using dot
notation:
mdl.Formula
NumObservations — Number of observationsThis property is read-only.
Number of observations the fitting function used in fitting, specified
as a positive integer. NumObservations is the
number of observations supplied in the original table, dataset,
or matrix, minus any excluded rows (set with the
'Exclude' name-value pair
argument) or rows with missing values.
Data Types: double
NumPredictors — Number of predictor variablesThis property is read-only.
Number of predictor variables used to fit the model, specified as a positive integer.
Data Types: double
NumVariables — Number of variablesThis property is read-only.
Number of variables in the input data, specified as a positive integer.
NumVariables is the number of variables in the original table or
dataset, or the total number of columns in the predictor matrix and response
vector.
NumVariables also includes any variables that are not used to fit
the model as predictors or as the response.
Data Types: double
PredictorNames — Names of predictors used to fit modelThis property is read-only.
Names of predictors used to fit the model, specified as a cell array of character vectors.
Data Types: cell
ResponseName — Response variable nameThis property is read-only.
Response variable name, specified as a character vector.
Data Types: char
VariableInfo — Information about variablesThis property is read-only.
Information about variables contained in Variables, specified as a
table with one row for each variable and the columns described in this table.
| Column | Description |
|---|---|
Class | Variable class, specified as a cell array of character vectors, such
as 'double' and
'categorical' |
Range | Variable range, specified as a cell array of vectors
|
InModel | Indicator of which variables are in the fitted model, specified as a
logical vector. The value is true if the model
includes the variable. |
IsCategorical | Indicator of categorical variables, specified as a logical vector.
The value is true if the variable is
categorical. |
VariableInfo also includes any variables that are not used to fit
the model as predictors or as the response.
Data Types: table
VariableNames — Names of variablesThis property is read-only.
Names of variables, specified as a cell array of character vectors.
If the fit is based on a table or dataset, this property provides the names of the variables in the table or dataset.
If the fit is based on a predictor matrix and response vector,
VariableNames contains the values specified by the
'VarNames' name-value pair argument of the fitting
method. The default value of 'VarNames' is
{'x1','x2',...,'xn','y'}.
VariableNames also includes any variables that are not used to fit
the model as predictors or as the response.
Data Types: cell
anova | Analysis of variance for linear regression model |
coefCI | Confidence intervals of coefficient estimates of linear regression model |
coefTest | Linear hypothesis test on linear regression model coefficients |
partialDependence | Compute partial dependence |
plotEffects | Plot main effects of predictors in linear regression model |
plotInteraction | Plot interaction effects of two predictors in linear regression model |
plotPartialDependence | Create partial dependence plot (PDP) and individual conditional expectation (ICE) plots |
plotSlice | Plot of slices through fitted linear regression surface |
gather | Gather properties of linear or generalized linear regression model |
Fit a linear regression model to data and reduce the size of a full, fitted linear regression model by discarding the sample data and some information related to the fitting process.
Load the largedata4reg data set, which contains 15,000 observations and 45 predictor variables.
load largedata4regFit a linear regression model to the data.
mdl = fitlm(X,Y);
Compact the model.
compactMdl = compact(mdl);
The compact model discards the original sample data and some information related to the fitting process.
Compare the size of the full model mdl and the compact model compactMdl.
vars = whos('compactMdl','mdl'); [vars(1).bytes,vars(2).bytes]
ans = 1×2
81538 11408530
The compact model consumes less memory than the full model.
Usage notes and limitations:
When you fit a model by using fitlm or stepwiselm, you cannot supply training
data in a table that contains a logical vector, character array, categorical array,
string array, or cell array of character vectors. Also, you cannot use the 'CategoricalVars' name-value pair argument. Code generation does not
support categorical predictors. To include
categorical predictors in a model, preprocess the categorical predictors by
using dummyvar before fitting the
model.
For more information, see Introduction to Code Generation.
Usage notes and limitations:
The following object functions fully support GPU arrays:
The following object functions support model objects fitted with GPU array input arguments:
For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).
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