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# PCA_VAR

Returns an array of cells for the i-th principal component (or residuals).

## Syntax

**PCA**(

^{i}_VAR^{i}**X**,

**Mask**,

**Standardize**,

**Number**,

**Number of PC**,

**Return_type**)

**X**

is the independent variables data matrix, such that each column represents one variable.

**Mask**

is the boolean array to select a subset of the input variables in X. If missing, all variables in X are included.

**Standardize**

is a flag or switch to standardize the input variables prior to the analysis (i.e. standardize = 1 (default), subtract mean = 2)).

Order | Description |
---|---|

1 | standardize (subtract mean and divide by standard deviation) (default) |

2 | subtract mean (subtract mean) |

**Number**

is the input variable number.

**Number of PC**

is the number of principal components (PC) to include. If missing or zero, all components will be used.

**Return_type**

is a switch to select the return output (1 = final communality (default), 2 = loading/weights, 3 = fitted values, 4 = residuals).

Method | Description |
---|---|

1 | Final communality (default) |

2 | Loading or weights for factors |

3 | Fitted input variable (from PCs) |

4 | Residuals |

## Remarks

- The underlying model is described here.
- The PCA_VAR function must be entered as an array formula (for return-types other than 1) in a range that has the rows as the number of variables (return-type = 2) or the number of observations (return-type > 2).
- The sample data may include missing values.
- Each column in the input matrix corresponds to a separate variable.
- Each row in the input matrix corresponds to an observation.
- Observations (i.e. row) with missing values are removed.
- The PC_VAR function is available starting with version 1.60 APACHE.

## Examples

## References

- Hamilton, J .D.; Time Series Analysis , Princeton University Press (1994), ISBN 0-691-04289-6
- Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740
- Jolliffe, I.T. (2002). Principal Component Analysis, second edition (Springer).