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Graphical displays may also not be particularly helpful when the data set is very large. With 12 variables, for example, there will be more than three-dimensional scatterplots. To interpret the data in a more meaningful form, it is necessary to reduce the number of variables to a few, interpretable linear combinations of the data.

Each linear combination will correspond to a principal component. There is another very useful data reduction technique called Factor Analysis discussed in a subsequent lesson.

This is an acceptably large percentage. An Alternative Method to determine the number of principal components is to look at a Scree Plot.

The number of components is determined at the point beyond which the remaining eigenvalues are all relatively small and of comparable size.

The following plot is made in Minitab. The scree plot for the variables without standardization covariance matrix. As you see, we could have stopped at the second principal component, but we continued till the third component. Relatively speaking, the contribution of the third component is small compared to the second component. Step 2 : Next, we compute the principal component scores. For example, the first principal component can be computed using the elements of the first eigenvector:.

In order to complete this formula and compute the principal component for the individual community of interest, plug in that community's values for each of these variables.

A fairly standard procedure is to use the difference between the variables and their sample means rather than the raw data. This is known as a translation of the random variables. Translation does not affect the interpretations because the variances of the original variables are the same as those of the translated variables.

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