Select the method or formula of your choice.

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 |

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

e_{i} | i ^{th} residual |

i ^{th} observed response value | |

i ^{th} fitted response |

Standardized residuals are also called "internally Studentized residuals."

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

e _{i} | i ^{th} residual |

h _{i} | i ^{th} diagonal element of X(X'X)^{–1}X' |

s ^{2} | mean square error |

X | design matrix |

X' | transpose of the design matrix |

Also called the externally Studentized residuals. The formula is:

Another presentation of this formula is:

The model that estimates the *i*^{th} observation omits the *i*^{th} observation from the data set. Therefore, the *i*^{th} observation cannot influence the estimate. Each deleted residual has a student's t-distribution with degrees of freedom.

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

e_{i} | i^{th} residual |

s_{(i)}^{2} | mean square error calculated without the i^{th} observation |

h_{i} | i ^{th} diagonal element of X(X'X)^{–1}X' |

n | number of observations |

p | number of terms, including the constant |

SSE | sum of squares for error |

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 |

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 |