# feval

Predict responses of multinomial regression model using one input for each predictor

*Since R2023a*

## Description

returns the predicted response of `Ypred`

= feval(`mdl`

,`X`

)_{1},X_{2},...,X_{p}`mdl`

to the new input predictors
`X`

where _{1},X_{2},...,X_{p}*p* is the number of predictor variables used to fit
`mdl`

.

## Examples

### Predict Responses Using One Input for Each Predictor

Load the `fisheriris`

sample data set.

`load fisheriris`

The `species`

column vector contains names of three iris flower species: setosa, versicolor, and virginica. The matrix `meas`

contains of four types of measurements for the flowers: the length and width of sepals and petals in centimeters.

Divide the species and measurement data into training and test data by using the `cvpartition`

function. Get the indices of the training data rows by using the `training`

function.

```
n = length(species);
partition = cvpartition(n,'Holdout',0.05);
idx_train = training(partition);
```

Create training data by using the indices of the training data rows to create a matrix of measurements and a vector of species labels.

meastrain = meas(idx_train,:); speciestrain = species(idx_train,:);

Fit a multinomial regression model using the training data.

MnrModel = fitmnr(meastrain,speciestrain)

MnrModel = Multinomial regression with nominal responses Value SE tStat pValue _______ ______ ________ __________ (Intercept_setosa) 86.305 12.541 6.8817 5.9158e-12 x1_setosa -1.0728 3.5795 -0.29971 0.7644 x2_setosa 23.846 3.1238 7.6336 2.2835e-14 x3_setosa -27.289 3.5009 -7.795 6.4409e-15 x4_setosa -59.58 7.0214 -8.4855 2.1472e-17 (Intercept_versicolor) 42.637 5.2214 8.1659 3.1906e-16 x1_versicolor 2.4652 1.1263 2.1887 0.028619 x2_versicolor 6.6808 1.474 4.5325 5.829e-06 x3_versicolor -9.4292 1.2946 -7.2837 3.248e-13 x4_versicolor -18.286 2.0833 -8.7775 1.671e-18 143 observations, 276 error degrees of freedom Dispersion: 1 Chi^2-statistic vs. constant model: 302.0378, p-value = 1.5168e-60

`MnrModel`

is a multinomial regression model object that contains the results of fitting a nominal multinomial regression model to the data. By default, `virginica`

is the reference category. The table output shows coefficient statistics for each predictor in `meas`

. The small *p*-values in the column `pValue`

indicate that all coefficients, at the 95% confidence level, have a statistically significant effect on `MnrModel`

. For example, the *p*-value for the term `x3_setosa`

indicates that the flower petal length has a statistically significant effect on $$\mathrm{ln}\left(\frac{{\pi}_{setosa}}{{\pi}_{virginica}}\right)$$, where $${\pi}_{setosa}$$ and $${\pi}_{virginica}$$ are category probabilities.

Get the indices of the test data rows, by using the `test`

function. Create test data by using the indices of the test data rows to create a matrix of measurements and a vector of species labels.

idx_test = test(partition); meastest = meas(idx_test,:); speciestest = species(idx_test,:);

Predict the iris species corresponding to the data point in `meas`

that is not included in the training data.

speciespredict = feval(MnrModel,meastest(:,1),meastest(:,2),meastest(:,3),meastest(:,4))

`speciespredict = `*7x1 cell*
{'setosa' }
{'setosa' }
{'setosa' }
{'setosa' }
{'setosa' }
{'versicolor'}
{'versicolor'}

Compare the predicted iris species with the iris species corresponding to the data point in `species`

that is not included in the training data.

speciestest

`speciestest = `*7x1 cell*
{'setosa' }
{'setosa' }
{'setosa' }
{'setosa' }
{'setosa' }
{'versicolor'}
{'versicolor'}

The output shows that the model accurately predicts the iris species of the data points that not included in the training data.

## Input Arguments

`mdl`

— Multinomial regression model object

`MultinomialRegression`

model object

Multinomial regression model object, specified as a `MultinomialRegression`

model object created with the `fitmnr`

function.

`X`_{1},X_{2},...,X_{p}

— New predictor input values

scalars | vectors

_{1},X

_{2},...,X

_{p}

New predictor input values, specified as *p* scalars or vectors,
where *p* is the number of predictor variables used to fit
`mdl`

.

If you pass

`X`

as a collection of vectors, then each vector must have the same size. Each row of the_{1},X_{2},...,X_{p}`X`

corresponds to an observation._{i}If you pass

`X`

as a mixture of vectors and scalars,_{1},X_{2},...,X_{p}`feval`

expands each scalar argument into a constant vector of the same size as the vector arguments.

**Example: **`feval(mdl,[0.1; 0.2],[0.3; 0.4])`

evaluates the
two-predictor model `mdl`

at the points ```
p1 = [0.1
0.3]
```

and `p2 = [0.2 0.4]`

.

**Data Types: **`single`

| `double`

`XNew`

— New predictor input values

table | *n*-by-*p* matrix

New predictor input values, specified
as a table or an *n*-by-*p* matrix, where *n*
is the number of observations to predict, and *p* is the number of predictor
variables used to fit `mdl`

.

If

`XNew`

is a table, it must contain all the names of the predictors used to fit`mdl`

. You can find the predictor names in the`mdl.PredictorNames`

property.If

`XNew`

is a matrix, it must have the same number of columns as the number of estimated coefficients. You can find the number of estimated coefficients in the`mdl.NumPredictors`

property. You can specify`XNew`

as a matrix only when all names in`mdl.PredictorNames`

refer to numeric predictors.

**Example: **`feval(mdl,[6.2 3.4; 5.9 3.0])`

evaluates the two-predictor
model `mdl`

at the points `p1 = [6.2 3.4]`

and
`p2 = [5.9 3.0]`

.

**Data Types: **`single`

| `double`

| `string`

| `cell`

| `categorical`

## Output Arguments

`Ypred`

— Predicted response categories for input data

categorical array | character array | logical vector | numeric vector | cell array of character vectors

Predicted response categories, returned as an *n*-by-1 categorical
or character array, logical or numeric vector, or cell array of character vectors, where
*n* is the number of observations to predict.
`Ypred`

has the same data type as
`mdl.ClassNames`

.

## Alternative Functionality

## Version History

**Introduced in R2023a**

## See Also

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