# Statistics of Quadratic Response Surface

### Description

Computes stationary point, 1st and 2nd principal axes of the quadratic response surface, shapes and curvatures along the congruence and incongruence lines, as well as various parameters useful for `plot.siRSM`

.

### Usage

1 2 | ```
surface.stats(obj)
surface.stats.main(b, xlim, ylim)
``` |

### Arguments

`obj` |
an object of class |

`b` |
coefficients of the response surface, e.g., |

`xlim` |
x-boundaries in 3D (x,y,z)-perspective plot — used when |

`ylim` |
y-boundaries in 3D (x,y,z)-perspective plot — used when |

### Value

`u0` |
x-coordinates of surface's stationary point |

`v0` |
y-coordinates of surface's stationary point |

`p10` |
intercept in xy-plane of surface's 1st principal axis |

`p11` |
slope in xy-plane of surface's 1st principal axis |

`p20` |
intercept in xy-plane of surface's 2nd principal axis |

`p21` |
slope in xy-plane of surface's 2nd principal axis |

`ax.congr` |
slope of surface along the congruence line, |

`ax2.congr` |
curvature of surface along the congruence line, |

`ax.incongr` |
slope of surface along the incongruence line, |

`ax2.incongr` |
curvature of surface along the incongruence line, |

`pl` |
intersection of 1st axis at lower border, to be used by |

`ph` |
intersection of 1st axis at upper border, to be used by |

`sl` |
intersection of 2nd axis at lower border, to be used by |

`sh` |
intersection of 2nd axis at upper border, to be used by |

### Author(s)

Huan Cheng, Mu Zhu

### References

Edwards JR (2002), "Alternatives to difference scores: Polynomial regression analysis and response surface methodology," in Measuring and Analyzing Behavior in Organizations: Advances in Measurement and Data Analysis (F. Drasgow, N. Schmitt, Eds.), Jossey-Bass, pp. 350-400.