Select the method or formula of your choice.

In matrix terms, this is the formula for the general linear regression model:

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

Y | vector of responses |

X | design matrix |

β | vector of parameters |

ε | vector of independent normal random variables |

The fitted value is the predicted y or , which is the mean response value for the given predictor values using the estimated regression equation.

The standard error of the fitted value in a regression model with one predictor is:

The standard error of the fitted value in a regression model with more than one predictor is:
where

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

x_{i} | i^{th} predictor value |

mean predictor | |

X | design matrix |

n | number of observations |

s^{2} | mean square error |

The range in which the predicted response for a new observation is expected to fall. The formula is:

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

fitted response value for a given set of predictor value | |

α | level of significance |

n | number of observations |

p | number of terms in the model, including the intercept term if it is in the model |

s^{2} | mean square error |

x | predictor matrix |

x_{o} | matrix of given predictor values beginning with a column of 1s when the intercept term is in the model |

The range in which the estimated mean response for a given set of predictor values is expected to fall. The formula is:

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

fitted response value for a given set of predictor values | |

α | level of significance |

n | number of observations |

p | number of terms in the model, including the intercept term if it is in the model |

s^{2}(b) | variance-covariance matrix of coefficient |

s^{2} | mean square error |

X | predictor matrix |

X_{o} | matrix of given predictor values beginning with a column of 1s when the intercept term is in the model |