Select the method or formula of your choice.

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

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

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

α | type I error rate |

n | number of observations |

p | number of model parameters |

S ^{2}(b) | variance-covariance matrix of the coefficients |

s ^{2} | mean square error |

X | design matrix |

X _{0} | vector of given predictor values |

X'_{0} | transpose of the new vector of predictor values |

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

fitted value | |

x_{k} | k^{th} term. Each term can be a single predictor, a polynomial term, or an interaction term. |

b_{k} | estimate of k^{th} regression coefficient |

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:

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

s^{2} | mean square error |

n | number of observations |

x_{0} | new value of the predictor |

mean of the predictor | |

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

x_{0} | vector of values that produce the fitted values, one for each column in the design matrix, beginning with a 1 for the constant term |

x'_{0} | transpose of the new vector of predictor values |

X | design matrix |

For a model with multiple predictors, the equation is:

*y* = *β*_{0} + *β*_{1}*x*_{1} + … + *β _{k}x_{k}* +

The fitted equation is:

In simple linear regression, which includes only one predictor, the model is:

*y*=*ß*_{0}+ *ß*_{1}*x*_{1}+*ε*

Using regression estimates *b*_{0} for *ß*_{0}, and *b*_{1} for *ß*_{1}, the fitted equation is:

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

y | response |

x_{k} | k^{th} term. Each term can be a single predictor, a polynomial term, or an interaction term. |

ß_{k} | k^{th} population regression coefficient |

ε | error term that follows a normal distribution with a mean of 0 |

b_{k} | estimate of k^{th} population regression coefficient |

fitted response |

The prediction interval is the range in which the fitted response for a new observation is expected to fall.

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

s(Pred) | |

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

α | level of significance |

n | number of observations |

p | number of model parameters |

s ^{2} | mean square error |

X | predictor matrix |

X _{0} | matrix of given predictor values |

X'_{0} | transpose of the new vector of predictor values |