# Multivariate Analysis: Correlation Analysis

### Use the Workspace Explorer to View All Plots

Partly visible in Figure 25.4 is the matrix of pairwise scatter plots between the variables. Some of these plots are hidden by the output window and the pairwise correlation plot.

To use the Workspace Explorer to view all the scatter plots:

1. Close the pairwise correlation plot.

2. Press ALT+X to open the Workspace Explorer.

You can use the Workspace Explorer to manage the display of plots. The Workspace Explorer is described in the section Workspace Explorer of Chapter 11: Techniques for Exploring Data.

3. Select the entry in the Workspace Explorer labeled Multivariate Correlation Analysis, as shown in Figure 25.5.

4. Click .

The scatter plots that are associated with the analysis appear in front of other windows.

5. Click to close the Workspace Explorer.

Figure 25.5: Selecting a Group of Plots

The workspace is now arranged as shown in Figure 25.6. The ellipses show where the specified percentage of the data should lie, assuming a bivariate normal distribution. Under bivariate normality, the percentage of observations falling inside the ellipse should closely agree with the specified level. The plots also contain a gradient shading that indicates a nested sequence of ellipses. The darkest shading occurs at the bivariate means for each pair of variables. The lightest shading corresponds to 0.9999 probability.

Variables that are bivariate normal have most of their observations close to the bivariate mean and have a bivariate density that is proportional to the gradient shading. The plot of `wind_kts` versus `latitude` shows that these two variables are not bivariate normal. Similarly, `min_pressure` and `latitude` are not bivariate normal.

Figure 25.6: A Matrix of Scatter Plots

The variables `wind_kts` and `min_pressure` are highly correlated and linearly related. In contrast, `wind_kts` is not correlated with `latitude` or `radius_eye`, although you can still notice certain relationships:

• Cyclones with high wind speeds occur only at lower latitudes.

• Cyclones north of 43 degrees of latitude tend to have wind speeds less than 75 knots.

• The size of a cyclone’s eye seems to be unrelated to the speed of its winds.

You can observe similar relationships between `min_pressure` and the `latitude` and `radius_eye` variables.

The matrix of scatter plots also reveals an aspect of the data that might not be apparent from univariate plots. The plots that display `wind_kts` or `radius_eye` show a granular appearance that indicates the data are rounded. Most of the wind speed measurements are rounded to the nearest five knots, whereas the values for the eye radius are rounded to the nearest 2.5 nautical miles. (You can also find observations for these variables that are not rounded.)

Figure 25.7 shows another use of the scatter plot matrix. Some observations with extreme values of `min_pressure` and `wind_kts` are selected. The marker shape and color for these observations were changed to make them more noticeable. You can use this technique to investigate whether outliers for one pair of variables are, in fact, multivariate outliers with respect to multivariate normality. Most of the selected data in Figure 25.7 are inside the 80% ellipse for the `radius_eye` versus `latitude` scatter plot. This indicates that these data are not far from the mean in those variables. However, a few observations (corresponding to Hurricane Hugo when it was category 5) do appear to be multivariate outliers in these variables.

Figure 25.7: Selecting Bivariate Outliers