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

MSE | mean square error |

R^{2} is also known as the coefficient of determination.

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

y _{i} | i ^{th} observed response value |

mean response | |

i ^{th} fitted response |

While the calculations for adjusted R^{2} can produce negative values, Minitab displays zero for these cases.

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

i^{th} observed response value | |

i^{th} fitted response | |

mean response | |

n | number of observations |

p | number of terms in the model |

While the calculations for R^{2}(pred) can produce negative values, Minitab displays zero for these cases.

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

y _{i} | i ^{th} observed response value |

mean response | |

n | number of observations |

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

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

X | design matrix |

Assesses your model's predictive ability.

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

n | number of observations |

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

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

The calculation of the log-likelihood depends on the estimation method for the analysis.

Minitab uses the following equation for the log-likelihood:

The weights for the analysis are either the specified weights or given by the following equation:

This calculation of the log-likelihood assumes that the standard deviations are from normal distributions and that the natural log of the standard deviation follows a linear model.

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

n | the number of rows with no missing data |

R | the sum of squares for error for the model |

the trigamma function | |

v_{i} | the degrees of freedom for the i^{th} standard deviation |

the gamma function | |

S_{i} | the i^{th} sample standard deviation |

the row of the design matrix associated with the i^{th} standard deviation | |

the maximum likelihood estimates of the model coefficients |

AICc is not calculated when .

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

p | the number of coefficients in the model, including the constant |

n | the number of rows in the data with no missing data |

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

p | the number of coefficients in the model, not counting the constant |

n | the number of rows in the data with no missing data |

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

SSE_{p} | sum of squared errors for the model under consideration |

MSE_{m} | mean square error for the model with all candidate terms |

n | number of observations |

p | number of terms in the model, including the constant |