Principal components regression.

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`y` |
A real values vector. |

`x` |
A matrix with the predictor variable(s), they have to be continuous. |

`k` |
The number of principal components to use. |

`xnew` |
If you have new data use it, otherwise leave it NULL. |

The principal components of the cross product of the independent variables are obtained and classical regression is performed. This is used in the function
`alfa.pcr`

.

A list including:

`beta` |
The beta coefficients. |

`parameters` |
The beta coefficients and their standard eror. |

`mse` |
The MSE of the linear regression, if xnew is NULL, becuase it needs the fitted values. |

`adj.rsq` |
The value of the adusted |

`per` |
The percentage of variance of the cross product of the independent variables explained by the k components. |

`est` |
The fitted or the predicted values (if xnew is not NULL). |

Michail Tsagris

R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Giorgos Athineou <athineou@csd.uoc.gr>

Jolliffe I.T. (2002). Principal Component Analysis.

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