When building a high-quality regression model, it is important to select the right features (or predictors), tune hyperparameters (model parameters not fit to the data), and assess model assumptions through residual diagnostics.
You can tune hyperparameters by iterating between choosing values for them, and cross-validating a model using your choices. This process yields multiple models, and the best model among them can be the one that minimizes the estimated generalization error. For example, to tune an SVM model, choose a set of box constraints and kernel scales, cross-validate a model for each pair of values, and then compare their 10-fold cross-validated mean-squared error estimates.
Certain nonparametric regression functions in Statistics and Machine Learning Toolbox™ additionally
offer automatic hyperparameter tuning through Bayesian optimization,
grid search, or random search. However,
which is the main function to implement Bayesian optimization, is
flexible enough for many other applications. For more details, see Bayesian Optimization Workflow.
||Confidence intervals of coefficient estimates of linear model|
||Linear hypothesis test on linear regression model coefficients|
||Durbin-Watson test of linear model|
||Scatter plot or added variable plot of linear model|
||Added variable plot or leverage plot for linear model|
||Adjusted response plot for linear regression model|
||Plot diagnostics of linear regression model|
||Plot main effects of each predictor in linear regression model|
||Plot interaction effects of two predictors in linear regression model|
||Plot residuals of linear regression model|
||Plot of slices through fitted linear regression surface|
||Confidence intervals of coefficient estimates of generalized linear model|
||Linear hypothesis test on generalized linear regression model coefficients|
||Analysis of deviance|
||Plot diagnostics of generalized linear regression model|
||Plot residuals of generalized linear regression model|
||Plot of slices through fitted generalized linear regression surface|
||Confidence intervals of coefficient estimates of nonlinear regression model|
||Linear hypothesis test on nonlinear regression model coefficients|
||Plot diagnostics of nonlinear regression model|
||Plot residuals of nonlinear regression model|
||Plot of slices through fitted nonlinear regression surface|
Learn about feature selection algorithms, such as sequential feature selection.
Perform Bayesian optimization using a fit function
or by calling
Create variables for Bayesian optimization.
Create the objective function for Bayesian optimization.
Set different types of constraint for Bayesian optimization.
Minimize cross-validation loss of a regression ensemble.
Visually monitor a Bayesian optimization.
Monitor a Bayesian optimization.
Understand underlying algorithms for Bayesian optimization.
Speed up cross-validation using parallel computing.
Display and interpret linear regression output statistics.
After fitting a model, examine the result and make adjustments.
Construct and analyze a linear regression model with interaction effects and interpret the results.
In linear regression, the F-statistic is the test statistic for the analysis of variance (ANOVA) approach to test the significance of the model or the components in the model. The t-statistic is useful for making inferences about the regression coefficients
Coefficient of determination (R-squared) indicates the proportionate amount of variation in the response variable y explained by the independent variables X in the linear regression model.
Estimated coefficient variances and covariances capture the precision of regression coefficient estimates.
Residuals are useful for detecting outlying y values and checking the linear regression assumptions with respect to the error term in the regression model.
The Durbin-Watson test assesses whether there is autocorrelation among the residuals or not.
Cook's distance is useful for identifying outliers in the X values (observations for predictor variables).
The hat matrix provides a measure of leverage.
Delete-1 change in covariance (
identifies the observations that are influential in the regression
After fitting a model, examine the result.
Diagnostic plots can help you examine the quality of a model.