Select the method or formula of your choice.

The expected response for the n^{th} observation at *θ**:

Term | Description |
---|---|

θ* | the final iteration |

x_{n} | vector of values for the predictors at the n^{th} observation |

v_{0} | gradient matrix = ( ∂f(, x_{n}) / ∂θθ_{p} ), the P by 1 vector of partial derivatives of f(x_{0}, ), evaluated at θ*θ |

The range in which the mean response is expected to fall given specified settings of the predictors. An approximate 100(1 - α)% confidence interval for the prediction is:

Term | Description |
---|---|

t_{α/2} | upper α/2 point of the t distribution with N – P degrees of freedom |

se fit | standard error of the fit |

n | n^{th} observation |

N | total number of observations |

P | number of free (unlocked) parameters |

fitted value | |

b | (R')^{-1}v_{0} |

R | the (upper triangular) R matrix from the QR decomposition of V^{i} for the final iteration |

v_{0} | gradient matrix = ( ∂f(x_{n}, θ) / ∂θ_{p}), the P by 1 vector of partial derivatives of f(x_{0}, θ), evaluated at θ* |

S |

The range in which the predicted response for a single new observation is expected to fall. A new observation has an approximate 100(1 - α)% prediction interval of:

Term | Description |
---|---|

t_{α/2} | upper α/2 point of the t distribution with N – P degrees of freedom |

se fit | standard error of the fit |

n | n^{th} observation |

N | total number of observations |

P | number of free (unlocked) parameters |

fitted value | |

b | (R')^{-1}v_{0} |

R | the (upper triangular) R matrix from the QR decomposition of V^{i} for the final iteration |

v_{0} | gradient matrix = ( ∂f(x_{n}, θ) / ∂θ_{p}), the P by 1 vector of partial derivatives of f(x_{0}, θ), evaluated at θ* |

S |

The approximate standard error of the fitted value is:
where **R** is the (upper triangular) **R** matrix from the QR decomposition of **V**^{i} for the final iteration. Minitab computes:
by back-solving:

Term | Description |
---|---|

n | n^{th} observation |

N | total number of observations |

P | number of free (unlocked) parameters |

x_{0} | vector of values for the predictors |

f(x_{0}, θ*) | |

v_{0} | gradient matrix = ( ∂f(x_{n}, θ) / ∂θ_{p}), the P by 1 vector of partial derivatives of f(x_{0}, θ), evaluated at θ* |

S |