FullCIs.XY {BivRegBLS} | R Documentation |

## Confidence Intervals from OLSv to OLSh by DR and BLS

### Description

Estimate the vertical and horizontal Ordinary least Square regressions, and several 'intermediate' Deming Regression (DR) and Bivariate Least Square (BLS), in a (X,Y) plot. The OLSv assumes no error on the X axis (λ=Infinity), while the OLSh assumes no error on the Y axis (λ=0). These two regressions are therefore 'extreme' regressions, while DR and BLS assume errors on both axes.

### Usage

```
FullCIs.XY(data = NULL, xcol = 1, ycol = 2,
conf.level = 0.95, npoints = 1000, nlambdas = 13)
```

### Arguments

`data` |
a data set (data frame or matrix). |

`xcol` |
a numeric vector to specify the X column(s) or a character vector with the column names. |

`ycol` |
a numeric vector to specify the Y column(s) or a character vector with the column names. |

`conf.level` |
a numeric value for the confidence level (expressed between 0 and 1). |

`npoints` |
an integer (at least 10) for the number of points to smooth the hyperbolic curves. |

`nlambdas` |
an integer for the number of intermediate DR and BLS regressions (between the OLSv and OLSh). |

### Details

The data argument is mandatory. This function is especially useful for unreplicated data with unknown λ (the ratio of the measurement error variances), as it calculates all the potential solutions from OLSv to OLSh. The different estimated regression lines are provided with the different confidence intervals.

### Value

A CIs.XY class object, a list including the following elements:

`Data.means` |
a table with the X and Y data (means of the replicated data if replicated). |

`Ellipses.CB` |
an array of dimension [ |

`Slopes` |
a table ( |

`Intercepts` |
a table ( |

`Joints` |
a table ( |

`Hyperbolic.intervals` |
an array of dimension [npoints, 6 (X values, Y predictions, confidence interval and confidence bands),nlambdas+2] with the hyperbolic confidence intervals and confidence bands from OLSv to OLSh including |

### Author(s)

Bernard G FRANCQ

### References

Francq BG, Govaerts BB. Measurement methods comparison with errors-in-variables regressions. From horizontal to vertical OLS regression, review and new perspectives. Chemometrics and Intelligent Laboratory Systems, 2014; 134:123-139.

Francq BG, Govaerts BB. Hyperbolic confidence bands of errors-in-variables regression lines applied to method comparison studies. Journal de la Societe Francaise de Statistique 2014; 155(1):23-45.

### See Also

### Examples

```
library(BivRegBLS)
data(Aromatics)
res.full=FullCIs.XY(data=Aromatics,xcol=3,ycol=4)
```

*BivRegBLS*version 1.1.1 Index]