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After training regression models in Regression Learner, you can compare models based on model statistics, visualize results in a response plot or by plotting the actual versus predicted response, and evaluate models using the residual plot.

If you use

*k*-fold cross-validation, then the app computes the model statistics using the observations in the*k*validation folds and reports the average values. It makes predictions on the observations in the validation folds and the plots show these predictions. It also computes the residuals on the observations in the validation folds.**Note**When you import data into the app, if you accept the defaults, the app automatically uses cross-validation. To learn more, see Choose Validation Scheme.

If you use holdout validation, the app computes the model statistics using the observations in the validation fold and makes predictions on these observations. The app uses these predictions in the plots and also computes the residuals based on the predictions.

If you use resubstitution validation, the scores are resubstitution model statistics based on all the training data, and the predictions are resubstitution predictions.

After training a model in Regression Learner, check the
**Models** pane to see which model has the best overall score.
The best **RMSE (Validation)** is highlighted in a box. This score
is the root mean squared error (RMSE) on the validation set. The score estimates the
performance of the trained model on new data. Use the score to help you choose the
best model.

For cross-validation, the score is the RMSE on all observations, counting each observation when it was in a holdout (validation) fold.

For holdout validation, the score is the RMSE on the held-out observations.

For resubstitution validation, the score is the resubstitution RMSE on all the training data.

The best overall score might not be the best model for your goal. Sometimes a model with a slightly lower overall score is the better model for your goal. You want to avoid overfitting, and you might want to exclude some predictors where data collection is expensive or difficult.

You can view model statistics in the **Current Model Summary**
pane and use these statistics to assess and compare models. The **Training
Results** statistics are calculated on the validation set. The
**Test Results** statistics, if displayed, are calculated on an
imported test set. For more information, see Evaluate Test Set Model Performance.

To copy the information in the **Current Model Summary** pane,
right-click the pane and select **Copy text**.

**Model Statistics**

Statistic | Description | Tip |
---|---|---|

RMSE | Root mean squared error. The RMSE is always positive and its units match the units of your response. | Look for smaller values of the RMSE. |

R-Squared | Coefficient of determination. R-squared is always smaller than 1 and usually larger than 0. It compares the trained model with the model where the response is constant and equals the mean of the training response. If your model is worse than this constant model, then R-Squared is negative. | Look for an R-Squared close to 1. |

MSE | Mean squared error. The MSE is the square of the RMSE. | Look for smaller values of the MSE. |

MAE | Mean absolute error. The MAE is always positive and similar to the RMSE, but less sensitive to outliers. | Look for smaller values of the MAE. |

You can sort models based on the different model statistics. To select a statistic
for model sorting, use the **Sort by** list at the top of the
**Models** pane.

You can also delete unwanted models listed in the **Models**
pane. Select the model you want to delete and click the **Delete selected
model** button in the upper right of the pane, or right-click the
model and select **Delete model**. You cannot delete the last
remaining model in the **Models** pane.

View the regression model results by using the response plot, which displays the
predicted response versus the record number. After you train a regression model, the
app automatically opens the response plot for that model. If you train an "All"
model, the app opens the response plot for the first model only. To view the
response plot for another model, select the model in the **Models**
pane. On the **Regression Learner** tab, in the
**Plots** section, click the arrow to open the gallery, and
then click **Response** in the **Validation
Results** group. If you are using holdout or cross-validation, then the
predicted response values are the predictions on the held-out (validation)
observations. In other words, each prediction is obtained using a model that was
trained without using the corresponding observation.

To investigate your results, use the controls on the right. You can:

Plot predicted and/or true responses. Use the check boxes under

**Plot**to make your selection.Show prediction errors, drawn as vertical lines between the predicted and true responses, by selecting the

**Errors**check box.Choose the variable to plot on the

*x*-axis under**X-axis**. You can choose the record number or one of your predictor variables.Plot the response as markers, or as a box plot under

**Style**. You can select**Box plot**only when the variable on the*x*-axis has few unique values.A box plot displays the typical values of the response and any possible outliers. The central mark indicates the median, and the bottom and top edges of the box are the 25th and 75th percentiles, respectively. Vertical lines, called whiskers, extend from the boxes to the most extreme data points that are not considered outliers. The outliers are plotted individually using the

`'+'`

symbol. For more information about box plots, see`boxplot`

.

To export the response plots you create in the app to figures, see Export Plots in Regression Learner App.

Use the Predicted vs. Actual plot to check model performance. Use this plot to
understand how well the regression model makes predictions for different response
values. To view the Predicted vs. Actual plot after training a model, on the
**Regression Learner** tab, in the **Plots**
section, click the arrow to open the gallery, and then click **Predicted vs.
Actual (Validation)** in the **Validation Results**
group.

When you open the plot, the predicted response of your model is plotted against the actual, true response. A perfect regression model has a predicted response equal to the true response, so all the points lie on a diagonal line. The vertical distance from the line to any point is the error of the prediction for that point. A good model has small errors, which means the predictions are scattered near the line.

Usually a good model has points scattered roughly symmetrically around the
diagonal line. If you can see any clear patterns in the plot, it is likely that you
can improve your model. Try training a different model type or making your current
model type more flexible using the **Advanced** options in the
**Model Type** section. If you are unable to improve your
model, it is possible that you need more data, or that you are missing an important
predictor.

To export the Predicted vs. Actual plots you create in the app to figures, see Export Plots in Regression Learner App.

Use the residuals plot to check model performance. To view the residuals plot
after training a model, on the **Regression Learner** tab, in the
**Plots** section, click the arrow to open the gallery, and
then click **Residuals (Validation)** in the **Validation
Results** group. The residuals plot displays the difference between the
predicted and true responses. Choose the variable to plot on the
*x*-axis under **X-axis**. Choose the true
response, predicted response, record number, or one of your predictors.

Usually a good model has residuals scattered roughly symmetrically around 0. If you can see any clear patterns in the residuals, it is likely that you can improve your model. Look for these patterns:

Residuals are not symmetrically distributed around 0.

Residuals change significantly in size from left to right in the plot.

Outliers occur, that is, residuals that are much larger than the rest of the residuals.

A clear, nonlinear pattern appears in the residuals.

Try training a different model type, or making your current model type more
flexible using the **Advanced** options in the **Model
Type** section. If you are unable to improve your model, it is possible
that you need more data, or that you are missing an important predictor.

To export the residuals plots you create in the app to figures, see Export Plots in Regression Learner App.

Visualize the results of models trained in Regression Learner by using the plot
options in the **Plots** section of the **Regression
Learner** tab. You can rearrange the layout of the plots to compare
results across multiple models: use the options in the **Layout**
button, drag and drop plots, or select the options provided by the Document Actions
arrow located to the right of the model plot tabs.

For example, after training two models in Regression Learner, display a plot for each model and change the plot layout to compare the plots by using one of these procedures:

Click

**Layout**and select**Compare models**in the**Plots**section of the**Regression Learner**tab.Click the second model tab name, and then drag and drop the second model tab to the right.

Click the Document Actions arrow located to the far right of the model plot tabs. Select the

`Tile All`

option and specify a 1-by-2 layout.

Note that you can click the Hide plot options button in the top right of the plots to make more room for the plots.

After training a model in Regression Learner, you can evaluate the model performance on a test set in the app. This process allows you to check whether the validation metrics provide good estimates for the model performance on new data.

Import a test data set into Regression Learner.

If the test data set is in the MATLAB

^{®}workspace, then in the**Testing**section on the**Regression Learner**tab, click**Test Data**and select**From Workspace**.If the test data set is in a file, then in the

**Testing**section, click**Test Data**and select**From File**. Select a file type in the list, such as a spreadsheet, text file, or comma-separated values (`.csv`

) file, or select**All Files**to browse for other file types such as`.dat`

.

In the Import Test Data dialog box, select the test data set from the

**Test Data Set Variable**list. The test set must have the same variables as the predictors imported for training and validation.Compute the test set metrics.

To compute test metrics for a single model, select the trained model in the

**Models**pane. On the**Regression Learner**tab, in the**Testing**section, click**Test All**and select**Test Selected**.To compute test metrics for all trained models, click

**Test All**and select**Test All**in the**Testing**section.

The app computes the test set performance of each model trained on the full data set, including training and validation data.

Compare the validation metrics with the test metrics.

In the

**Current Model Summary**pane, the app displays the validation metrics and test metrics under the**Training Results**section and**Test Results**section, respectively. You can check if the validation metrics give good estimates for the test metrics.You can also visualize the test results using plots.

Display a predicted vs. actual plot. In the

**Plots**section on the**Regression Learner**tab, click the arrow to open the gallery, and then click**Predicted vs. Actual (Test)**in the**Test Results**group.Display a residuals plot. In the

**Plots**section, click the arrow to open the gallery, and then click**Residuals (Test)**in the**Test Results**group.

For an example, see Check Model Performance Using Test Set in Regression Learner App. For an example that uses test set metrics in a hyperparameter optimization workflow, see Train Regression Model Using Hyperparameter Optimization in Regression Learner App.

- Train Regression Models in Regression Learner App
- Select Data and Validation for Regression Problem
- Choose Regression Model Options
- Feature Selection and Feature Transformation Using Regression Learner App
- Export Plots in Regression Learner App
- Export Regression Model to Predict New Data
- Train Regression Trees Using Regression Learner App