The following statements request a correlation analysis and a scatter plot matrix for the variables in the data set Fish1
, which was created in Example 2.6.
ods graphics on; title 'Fish Measurement Data'; proc corr data=fish1 nomiss plots=matrix(histogram); var Height Width Length3 Weight3; run; ods graphics off;
The “Simple Statistics” table in Output 2.8.1 displays univariate descriptive statistics for analysis variables.
Output 2.8.1: Simple Statistics
Fish Measurement Data |
4 Variables: | Height Width Length3 Weight3 |
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Simple Statistics | ||||||
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Variable | N | Mean | Std Dev | Sum | Minimum | Maximum |
Height | 34 | 15.22057 | 1.98159 | 517.49950 | 11.52000 | 18.95700 |
Width | 34 | 5.43805 | 0.72967 | 184.89370 | 4.02000 | 6.74970 |
Length3 | 34 | 38.38529 | 4.21628 | 1305 | 30.00000 | 46.50000 |
Weight3 | 34 | 8.44751 | 0.97574 | 287.21524 | 6.23168 | 10.00000 |
The “Pearson Correlation Coefficients” table in Output 2.8.2 displays Pearson correlation statistics for pairs of analysis variables.
Output 2.8.2: Pearson Correlation Coefficients
Pearson Correlation Coefficients, N = 34 Prob > |r| under H0: Rho=0 |
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Height | Width | Length3 | Weight3 | |||||||||
Height |
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Width |
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Length3 |
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Weight3 |
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The variables are highly correlated. For example, the correlation between Height
and Width
is 0.92632.
The PLOTS=MATRIX(HISTOGRAM) option requests a scatter plot matrix for the VAR statement variables in Output 2.8.3.
Note that this graphical display is requested by enabling ODS Graphics and by specifying the PLOTS= option. For more information about ODS Graphics, see Chapter 21: Statistical Graphics Using ODS in SAS/STAT 12.3 User's Guide,.
To explore the correlation between Height
and Width
, the following statements display (in Output 2.8.4) a scatter plot with prediction ellipses for the two variables:
ods graphics on; proc corr data=fish1 nomiss plots=scatter(nvar=2 alpha=.20 .30); var Height Width Length3 Weight3; run; ods graphics off;
The PLOTS=SCATTER(NVAR=2) option requests a scatter plot for the first two variables in the VAR list. The ALPHA=.20 .30 suboption requests and prediction ellipses, respectively.
A prediction ellipse is a region for predicting a new observation from the population, assuming bivariate normality. It also approximates a region that contains a specified percentage of the population. The displayed prediction ellipse is centered at the means . For further details, see the section Confidence and Prediction Ellipses.
Note that the following statements also display (in Output 2.8.5) a scatter plot for Height
and Width
:
ods graphics on; proc corr data=fish1 plots=scatter(alpha=.20 .30); var Height Width; run; ods graphics off;
Output 2.8.5 includes the point , which was excluded from Output 2.8.4 because the observation had a missing value for Weight3
. The prediction ellipses in Output 2.8.5 also reflect the inclusion of this observation.
The following statements display (in Output 2.8.6) a scatter plot with confidence ellipses for the mean:
ods graphics on; title 'Fish Measurement Data'; proc corr data=fish1 nomiss plots=scatter(ellipse=confidence nvar=2 alpha=.05 .01); var Height Width Length3 Weight3; run; ods graphics off;
The NVAR=2 suboption within the PLOTS= option restricts the number of plots created to the first two variables in the VAR statement, and the ELLIPSE=CONFIDENCE suboption requests confidence ellipses for the mean. The ALPHA=.05 .01 suboption requests and confidence ellipses, respectively.
The confidence ellipse for the mean is centered at the means . For further details, see the section Confidence and Prediction Ellipses.