Complete the following steps to interpret MARS^{®}
Regression. Key output includes the model summary statistics, variable importance, the partial
dependence plots, and the regression equation.

To determine how well the model fits your data, examine
the statistics in the Model Summary table. Usually, you use the test version of the
statistics because the test version is a better representation of how the model performs
for new data. If you fit additional models, use the values in the Model Summary table to
compare how well the models fit the data.

- Test R-squared
- The higher the R
^{2}value, the better the model fits your data. R^{2}is always between 0% and 100%. Outliers have a greater effect on R^{2}than on MAD. - Test root mean squared error (RMSE)
- Smaller values indicate a better fit. Outliers have a greater effect on RMSE than on MAD.
- Test mean squared error (MSE)
- Smaller values indicate a better fit. Outliers have a greater effect on MSE than on MAD.
- Test mean absolute deviation (MAD)
- Smaller values indicate a better fit. The mean absolute deviation (MAD)
expresses accuracy in the same units as the data, which helps conceptualize
the amount of error. Outliers have less of an effect on MAD than on
R
^{2}, RMSE, and MSE.

Total predictors | 77 |
---|---|

Important predictors | 10 |

Maximum number of basis functions | 30 |

Optimal number of basis functions | 13 |

Statistics | Training | Test |
---|---|---|

R-squared | 89.61% | 87.61% |

Root mean squared error (RMSE) | 25836.5197 | 27855.6550 |

Mean squared error (MSE) | 667525749.7185 | 775937512.8264 |

Mean absolute deviation (MAD) | 17506.0038 | 17783.5549 |

In these results, the test R-squared is about 88%. The test root mean squared error is about 27,856. The test mean squared error is about 775,937,513. The test mean absolute deviation is about 17,784.

Use the relative variable importance chart to see which predictors are the most important variables to the model.

Important variables are in at least 1 basis function in the model. The variable with the highest improvement score is set as the most important variable and the other variables are ranked accordingly. Relative variable importance standardizes the importance values for ease of interpretation. Relative importance is defined as the percent improvement with respect to the most important predictor.

Relative variable importance values range from 0% to 100%. The most important variable always has a relative importance of 100%. If a variable is not in a basis function, that variable is not important.

Use the partial dependence plots, the basis functions, and the coefficients in the regression equation to determine the effect of the predictors. The effects of the predictors explain the relationship between the predictors and the response. Consider all the basis functions for a predictor to understand the effect of the predictor on the response variable.

In addition, consider the use of the important predictors and the forms of their
relationships when you build other models. For example, if the MARS^{®}
regression model includes interactions, consider whether to include those interactions
in a least-squares regression model to compare the performance of the two types of
models. In applications where you control the predictors, the effects provide a natural
way to optimize the settings to achieve a goal for the response variable.

In an additive model, one-predictor, partial dependence
plots show how the important continuous predictors affect the predicted response. The
one predictor partial dependence plot indicates how the response is expected to change
with changes in the predictor levels. For MARS^{®}
Regression, the values on the plot come from the basis functions for the predictor on the
x-axis. The contribution on the y-axis is standardized so that the minimum value on the
plot is 0.

For more examples of common basis functions, go to Regression equation for MARS® Regression.