# Bivariate Symbolic Regression Method

### Description

This function fits an bivariate regression model for interval-valued variables, based on bivariate exponential family of distributions, and return the fitted values, the residuals, rho, phi and the goodness-of-fit measure deviance

### Usage

1 |

### Arguments

`formula1` |
an object of class " |

`lig1` |
the link function to be considered in the first model: identity, inverse or log |

`formula2` |
an object of class " |

`lig2` |
the link function to be considered in the second model: identity, inverse or log |

`data` |
an optional data frame containing the variables in the model. |

`...` |
other arguments. |

### Details

This function fits an bivariate regression model for interval-valued variables considering the bivariate Gaussian distribution in the random component Y = [Y1, Y2]. It is possible consider any pair of interval features for the bivariate random vector Y. For example, the lower and upper interval bounds or the midpoint and the range of intervals, respectively. It also possible to choice different link functions (identity, inverse or log) to connect the random variables Y1 and Y2 with the respective linear predictors.

### Value

`bivar`

returns an object of class "`bivar`

" including at least the following elements:

`coefficients1` |
a named vector of coefficients for the explanatory variables of the model "1". |

`coefficients2` |
a named vector of coefficients for the explanatory variables of the model "2". |

`fitted.values1` |
the fitted values for the response variable Y1 . |

`fitted.values2` |
the fitted values for the response variable Y2. |

`residuals1` |
the ordinary residual for the response variable Y1. |

`residuals2` |
the ordinary residual for the response variable Y2. |

`residual.deviance` |
the global residual for the bivariate vector Y=[Y1, Y2]. |

`Rho` |
the estimative for the correlation coefficient between Y1 and Y2. |

`Phi` |
the estimative of the dispersion parameter. |

`D` |
the goodness-of-fit measure deviance for the current model. |

### Note

`lig1`

and `lig2`

must be "`identity`

", "`inverse`

" or "`log`

" for identity, inverse or logarithmic link functions, respectively.

### Author(s)

Eufrasio de A. Lima Neto eufrasio@de.ufpb.br , Claudio A. V. de Souza Filho and Pedro R. D. Marinho

### References

Lima Neto, E. A., Cordeiro, G. and De Carvalho, F.A.T. (2011). Bivariate symbolic regression models for
interval-valued variables. *Journal of Statistical Computation and Simulation (Print)*, 81, 1727–1744.

### See Also

`summary.bivar`

, `coef.bivar`

, `fitted.bivar`

, `residuals.bivar`

, `formula`

### Examples

1 2 3 | ```
data("soccer.bivar", package = "iRegression")
ex.bivar <- bivar("yMin~t1Min+t2Min", "identity", "yMax~t1Max+t2Max", "identity", data=soccer.bivar)
ex.bivar
``` |