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

## Syntax

**PCA_VAR **(**X**, Mask, Standardize, Number, Number of PC, Return)

**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)).
Value Standardize 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**- is a switch to select the return output (1 = Final communality (default), 2 = Loading/weights, 3 = Fitted values, 4 = Residuals).
Value Return 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., rows) with missing values are removed.
- The PC_VAR function is available starting with version 1.60 APACHE.

## Files Examples

## Related Links

- Wikipedia - Principal component analysis.
- Wikipedia - Regression analysis.
- Wikipedia - Ordinary least squares.

## References

- J. Edward Jackson; A User's Guide to Principal Components; Wiley-Interscience; (Sep 10, 2003), ISBN: 471471348.
- I.T. Jolliffe; Principal Component Analysis; Springer; 2nd Edition(Oct 01, 2002), ISBN: 0387954422.
- John Y. Campbell, Andrew W. Lo, A. Craig MacKinlay, Andrew Y. Lo; The Econometrics of Financial Markets; Princeton University Press; 2nd edition(Dec 09, 1996), ISBN: 691043019.
- 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.

## Comments

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