In many cases of regression analysis, we can find unknown relationship pattern between two response variables with many predictor variables (multi-predictor) and both of responses are correlated each other. Consequently such regression problem should be solved using bi-responses nonparametric regression model, which able to overcome high dimensionality case in multi-predictor data. One of the methods is Multivariate Adaptive Regression Spline (MARS). This paper aims to study how MARS method could be utilized on bi-responses nonparametric regression model. The study begins with obtaining model equation form. Thus we estimating regression function and weighted from its model equation. Last step is. The results also show that the properties of this model is a bias estimator and linear in observation y ɶ .

This article reviews one of the non-parametric functions, namely the MARS (Multivariate Adaptive Regression Spline) method, a complex combination of recursive partitioning and spline regression. The many advantages of the MARS function over other non-parametric regression functions are of interest to researchers. One of them is it can accommodate the additive and interaction model to improve the prediction and interpretation of the data. There are some important things in the MARS method, namely, ANOVA decomposition and Importance Variable. Decomposition ANOVA is a technique in MARS that is useful for grouping basis function based on variables engagement, whether they enter by one variable or interactions with other variables, making it easier to interpret in graphical form. In comparison, the important variables are a technique that can be used to determine which predictor variables most influence the MARS modeling. This study assesses ANOVA decomposition, and the important variables process in MARS modeling based on GCV and MSE criteria. We use the poverty rate modeling data on Java Island to implement the study results. The results show that the MARS model's interpretation of the poverty rate can be better done through ANOVA decomposition. Besides that, based on GCV and MSE criteria, the result also shows that the biggest variable importance in poverty rate modeling on Java Island is the percentage of per capita expenditure for food, while the smallest is the economic growth variable.

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