# Regression

## SIMPLE LINEAR REGRESSION

ROUTINE | DESCRIPTION |
---|---|

RLINE | Fits a line to a set of data points using least squares. |

RONE | Analyzes a simple linear regression model. |

RINCF | Performs response control given a fitted simple linear regression model. |

RINPF | Performs inverse prediction given a fitted simple linear regression model. |

## MULTIVARIATE GENERAL LINEAR MODEL ANALYSIS

### MODEL FITTING

ROUTINE | DESCRIPTION |
---|---|

RLSE | Fits a multiple linear regression model using least squares. |

RCOV | Fits a multivariate linear regression model given the variance-covariance matrix. |

RGIVN | Fits a multivariate linear regression model via fast Givens transformations. |

RGLM | Fits a multivariate general linear model. |

RLEQU | Fits a multivariate linear regression model with linear equality restrictions imposed on the regression parameters given results from routine H B = GRGIVN after IDO = 1 and IDO = 2 and prior to IDO = 3. |

## STATISTICAL INFERENCE AND DIAGNOSTICS

ROUTINE | DESCRIPTION |
---|---|

RSTAT | Computes statistics related to a regression fit given the coefficient estimates. |

RCOVB | Computes the estimated variance-covariance matrix of the estimated regression coefficients given the matrix. R |

CESTI | Constructs an equivalent completely testable multivariate general linear hypothesis from a partially testable hypothesisH BU = G. H_{p}BU = G_{p} |

RHPSS | Computes the matrix of sums of squares and crossproducts for the multivariate general linear hypothesis given the coefficient estimates and the H BU = Gmatrix.R |

RHPTE | Performs tests for a multivariate general linear hypothesis given the hypothesis sums of squares and crossproducts matrix H BU = G and the error sums of squares and crossproducts matrix S_{H}.S_{E} |

RLOFE | Computes a lack of fit test based on exact replicates for a fitted regression model. |

RLOFN | Computes a lack of fit test based on near replicates for a fitted regression model. |

RCASE | Computes case statistics and diagnostics given data points, coefficient estimates and the matrix for a fitted general linear model.R |

ROTIN | Computes diagnostics for detection of outliers and influential data points given residuals and the matrix for a fitted general linear model.R |

## UTILITIES FOR CLASSIFICATION VARIABLES

ROUTINE | DESCRIPTION |
---|---|

GCLAS | Gets the unique values of each classification variable. |

GRGLM | Generates regressors for a general linear model. |

## VARIABLES SELECTION

ROUTINE | DESCRIPTION |
---|---|

RBEST | Selects the best multiple linear regression models. |

RSTEP | Builds multiple linear regression models using forward selection, backward selection or stepwise selection. |

GSWEP | Performs a generalized sweep of a row of a nonnegative definite matrix. |

RSUBM | Retrieves a symmetric submatrix from a symmetric matrix. |

## POLYNOMINAL REGRESSION AND SECOND-ORDER MODELS

### POLYNOMINAL REGRESSION ANALYSIS

ROUTINE | DESCRIPTION |
---|---|

RCURV | Fits a polynomial curve using least squares. |

RPOLY | Analyzes a polynomial regression model. |

## SECOND-ORDER MODEL DESIGN

ROUTINE | DESCRIPTION |
---|---|

RCOMP | Generates an orthogonal central composite design. |

## UTILITY ROUTINES FOR POLYNOMIAL MODELS AND SECOND-ORDER MODELS

ROUTINE | DESCRIPTION |
---|---|

RFORP | Fits an orthogonal polynomial regression model. |

RSTAP | Computes summary statistics for a polynomial regression model given the fit based on orthogonal polynomials. |

RCASP | Computes case statistics for a polynomial regression model given the fit based on orthogonal polynomials. |

OPOLY | Generates orthogonal polynomials with respect to x-values and specified weights. |

GCSCP | Generates centered variables, squares, and crossproducts. |

TCSCP | Transforms coefficients from a second order response surface model generated from squares and crossproducts of centered variables to a model using uncentered variables. |

## NONLINEAR REGRESSION ANALYSIS

ROUTINE | DESCRIPTION |
---|---|

RNLIN | Fits a nonlinear regression model. |

## FITTING LINEAR MODELS BASED ON CRITERIA OTHER THAN LEAST SQUARES

ROUTINE | DESCRIPTION |
---|---|

RLAV | Fits a multiple linear regression model using the least absolute values criterion. |

RLLP | Fits a multiple linear regression model using the L norm criterion._{p} |

RLMV | Fits a multiple linear regression model using the minimax criterion. |

PLSR | Performs partial least squares regression for one or more response variables and one or more predictor variables. |