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Industrial Statistics with Minitab by Xavier Tort-Martorell Llabres, Lluis Marco Almagro, Pere Grima Cintas

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24.2 Principal Components

Statistical method used to compute new variables function of the original ones. These new variables are called ‘principal components’ and it is expected that few of them contain most of the information in the data.

Stat > Multivariate > Principal Components

nc24uf001.eps
In case the covariance matrix is chosen, the sum of the eigenvalues is equal to the sum of the variables’ variances. In case the correlation matrix is chosen, the data will be normalized and the sum of the eigenvalues will be equal to the number of variables. In either case, the eigenvalues represent each component's contribution to the explanation of the variability of the data.

The first part on the shown output list provides information on the magnitude of the eigenvalues, ordered from highest to lowest, on the proportion they represent with respect to the total (proportion of the global variability explained by this component), and on the cumulative proportion.

nc24uf002.eps
Eigenvalues:
5.5117 + 2.0441 + 1.4691 + 0.8631 + 0.5554 + 0.2638 + 0.1386 + 0.0660 + 0.0475 + 0.0350 + 0.0056 = 11
50.1% + 18.6% ...

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