PCA+Using+Only+Correlation+Matrix

PCA Using Only Correlation Matrix (PCA Analysis | Regression | Multivariate Methods) (GWU EMSE-271)
Index | Topics (Logical Lectures) | Lectures | Problems | Readings | Nomenclature | Concepts

Minitab provides two ways to conduct a Principal Components Analysis:
 * The first is under Stat | Multivariate Methods | Principal Components and can be used with original or standardized data.
 * The second uses matrix operations to solve from a correlation matrix (Calc | Matrix | Egien Analysis)

NOTE: Can't do solely in Excel with only a correlation matrix, need to use Minitab's analysis features to get Eigenvalues. Most of the Minitab soltions in this are are not a lot of help. The session notes don't have any useful information. Goverment.mpj has a little.

Here are my notes on trying to recreate the posted Government.mpj solution with my scratched notes from Session 12.
 * Paste data into Minitab.
 * Using the Data | Copy | Columns to Matrix function, copy the data to a matrix; suggest naming the matrix.
 * Check by displaying the matrix using the Data | Display Data function.
 * Label columns to receive output: Eigenvalues and one column each for the Eigenvectors (U in Van Dorps Examples).
 * Use the Calc | Matrix | Egien Analysis function to compute the Eigenvalues (storing the Eigenvalues in the labeled column), uncheck the use names check box if you name the columns.
 * Check progress by displaying the matrix loading using Data | Display Data function.
 * Copy the Eigenvectors matrix to columns in Minitab.


 * Would like to be able to compute Z-Scores - TBD (Why?)

I remember seeing somewhere that you can conduct a Principal Components Analysis with only the eigenvalues and the eigenvectors. Will reference here when I can find it.

My next steps:
 * Switch to excel using the government.xls and druguse.xls spreadsheets as templates. (May try to compute the loading factors in Minitab and transfer.
 * One reason to transfer is that the only place I have found and example to do Bartlett's spherecitiy test is in excel.
 * Then use the Principal Components Analysis check sheet to help with data analysis.


 * Sources:**
 * EMSE 271, Fall 2009