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Multivariate Analyses |

You can request a plot of the first two principal
components or the first three principal components
from the Principal Components Options dialog,
shown in Figure 40.6,
or from the **Graphs** menu,
shown in Figure 40.34. Select **Principal Components**
from the **Graphs** menu to display the **Principal Component Plots**
dialog.

In the dialog, you choose a principal component scatter plot
(**Scatter Plot**), a principal component biplot with standardized
**Y** variables (**Biplot (Std Y)**), or a principal component biplot
with centered **Y** variables (**Biplot (Raw Y)**).

A *biplot* is a joint display of two sets of variables.
The data points are first displayed in a scatter plot
of principal components.
With the approximated **Y** variable axes also displayed in the
scatter plot, the data values of the **Y** variables are graphically
estimated.

The **Y** variable axes are generated from the regression
coefficients of the **Y** variables on the principal components.
The lengths of the axes are approximately proportional to the
standard deviations of the variables.
A closer parallel between a **Y** variable axis and
a principal component axis
indicates a higher correlation between the two variables.

For a **Y** variable **Y1**, the **Y1** variable value
of a data point y in a principal component biplot
is geometrically evaluated as follows:

- A perpendicular is dropped from point y onto the
**Y1**axis. - The distance from the origin to this perpendicular is measured.
- The distance is multiplied by the length of the
**Y1**axis; this gives an approximation of the**Y1**variable value for point y.

Two sets of variables are used in creating principal component biplots.
One set is the **Y** variables. Either standardized or centered **Y**
variables are used, as specified in the Principal Component Plots
dialog, shown in Figure 40.36.

The other set is the principal component variables. These variables have variances either equal to one or equal to corresponding eigenvalues. You specify the principal component variable variance in the Multivariate Method Options dialog, shown in Figure 40.3.

Note | A biplot with principal component variable variances equal to one is called
a GH' biplot, and a biplot with principal component variable variances
equal to corresponding eigenvalues is called a JK' biplot. |

A biplot is a useful tool for examining data patterns and outliers. Figure 40.37 shows a biplot of the first two principal components from the correlation matrix and a rotating plot of the first three principal components. The biplot shows that the variable SEPALWID (highlighted axis) has a moderate negative correlation with PCR1 and a high correlation with PCR2.

**Figure 40.37:** Principal Component Plots

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