STATGRAPHICS Centurion
contains a set of procedures that implement multivariate
statistical methods. These include:
1.
Correlation Analysis 
estimation of correlation coefficients between pairs of
variables.
2.
Principal Components  identification of linear
combinations of variables with large variance.
3.
Factor Analysis 
identification of unique factors in a set of
quantitative variables.
4.
Canonical Correlations 
construction of linear combinations of two sets of
variables with high intercorrelation.
5.
Cluster Analysis  separation
of observations or variables into groups with similar
characteristics.
6.
Discriminant Analysis 
construction of linear discriminant functions to help
classify observations.
7.
Bayesian Neural Network Classifier
 classification of observations given prior group
probabilities.
Correlation Analysis
The Correlation
Analysis procedure calculates correlations between pairs
of quantitative variables. Pearson productmoment
correlations, Kendall and Spearman rank correlations, and
partial correlation coefficients may be estimated. The
StatAdvisor will highlight in red all PValues that indicate
statistically significant correlations.
Correlations

MPG City 
MPG Highway 
Horsepower 
Length 
RPM 
Width 
Weight 
MPG City 

0.9439 
0.6726 
0.6662 
0.3630 
0.7205 
0.8431 


(93) 
(93) 
(93) 
(93) 
(93) 
(93) 


0.0000 
0.0000 
0.0000 
0.0003 
0.0000 
0.0000 
MPG Highway 
0.9439 

0.6190 
0.5429 
0.3135 
0.6404 
0.8107 

(93) 

(93) 
(93) 
(93) 
(93) 
(93) 

0.0000 

0.0000 
0.0000 
0.0022 
0.0000 
0.0000 
Horsepower 
0.6726 
0.6190 

0.5509 
0.0367 
0.6444 
0.7388 

(93) 
(93) 

(93) 
(93) 
(93) 
(93) 

0.0000 
0.0000 

0.0000 
0.7270 
0.0000 
0.0000 
Length 
0.6662 
0.5429 
0.5509 

0.4412 
0.8221 
0.8063 

(93) 
(93) 
(93) 

(93) 
(93) 
(93) 

0.0000 
0.0000 
0.0000 

0.0000 
0.0000 
0.0000 
RPM 
0.3630 
0.3135 
0.0367 
0.4412 

0.5397 
0.4279 

(93) 
(93) 
(93) 
(93) 

(93) 
(93) 

0.0003 
0.0022 
0.7270 
0.0000 

0.0000 
0.0000 
Width 
0.7205 
0.6404 
0.6444 
0.8221 
0.5397 

0.8750 

(93) 
(93) 
(93) 
(93) 
(93) 

(93) 

0.0000 
0.0000 
0.0000 
0.0000 
0.0000 

0.0000 
Weight 
0.8431 
0.8107 
0.7388 
0.8063 
0.4279 
0.8750 


(93) 
(93) 
(93) 
(93) 
(93) 
(93) 


0.0000 
0.0000 
0.0000 
0.0000 
0.0000 
0.0000 

Correlation
(Sample Size)
PValue
Principal Components
When many characteristics
are measured, it is not uncommon to obtain redundant
information. As a way of reducing dimensionality, the
Principal Components procedure finds linear combinations
of quantitative variables with high variability. Frequently,
a small number of such components is sufficient to explain
most of the observed variability in a data set. Constructing
models for the principal components may then be an easier
and more instructive task than attempting to model all of
the original measurements.
Factor Analysis
When a small number of
components explain most of the observed variability in a
data set, it may be possible to give a meaningful
interpretation to those factors. STATGRAPHICS allows you to
rotate the factor space in an attempt to simplify the factor
equations.
Factor Loading
Matrix After Varimax Rotation

Factor 
Factor 

1 
2 
Engine Size 
0.8598 
0.4022 
Horsepower 
0.9106 
0.006172 
Fueltank 
0.8594 
0.2957 
Passengers 
0.2096 
0.883 
Length 
0.7651 
0.5536 
Wheelbase 
0.7392 
0.5914 
Width 
0.8418 
0.3894 
U Turn Space 
0.7489 
0.3971 
Rear seat 
0.1902 
0.8742 
Luggage 
0.4323 
0.7462 
Weight 
0.917 
0.34 

Estimated 
Specific 
Variable 
Communality 
Variance 
Engine Size 
0.901 
0.09904 
Horsepower 
0.8292 
0.1708 
Fueltank 
0.8261 
0.1739 
Passengers 
0.8236 
0.1764 
Length 
0.8919 
0.1081 
Wheelbase 
0.8962 
0.1038 
Width 
0.8603 
0.1397 
U Turn Space 
0.7186 
0.2814 
Rear seat 
0.8005 
0.1995 
Luggage 
0.7437 
0.2563 
Weight 
0.9565 
0.0435 
Canonical Correlations
When the variables are
divided into two groups, it can be useful to obtain linear
combinations from each group that have high correlation
between them. These Canonical Correlations often
provide insight into the relationships between the groups.
Canonical
Correlations


Canonical 
Wilks 



Number 
Eigenvalue 
Correlation 
Lambda 
ChiSquared 
D.F. 
PValue 
1 
0.8953 
0.9462 
0.02753 
301.8 
28 
0.0000 
2 
0.4958 
0.7041 
0.2629 
112.2 
18 
0.0000 
3 
0.4629 
0.6804 
0.5215 
54.7 
10 
0.0000 
4 
0.02916 
0.1708 
0.9708 
2.486 
4 
0.6472 
Coefficients
for Canonical Variables of the First Set
Engine Size 
0.2617 
0.6984 
0.07371 
2.05 
Horsepower 
0.1275 
0.4043 
1.239 
0.7845 
Length 
0.02418 
1.063 
0.2796 
0.05425 
Wheelbase 
0.04117 
0.3449 
0.7107 
1.45 
Width 
0.0677 
0.2929 
1.512 
1.089 
Rear seat 
0.004258 
0.09294 
0.07899 
0.2616 
Weight 
0.6578 
2.425 
0.4708 
1.191 
Coefficients
for Canonical Variables of the Second Set
Mid Price 
0.2566 
0.1546 
1.211 
0.4017 
1/MPG Highway 
0.09713 
2.205 
0.1757 
1.515 
1/MPG City 
0.6521 
1.425 
0.7964 
2.809 
U Turn Space 
0.3222 
0.455 
0.3407 
1.337 
Cluster Analysis
The Cluster Analysis
procedure divides data into groups with similar
characteristics. Clustering may be done using either
observations or variables. The techniques provided for
clustering include nearest neighbor, furthest neighbor,
centroid, median, group average, Ward's method, and the
method of kmeans.
Discriminant Analysis
The Discriminant
Analysis procedure derives linear combinations of
quantitative variables that can best divide data into
groups. The resulting discriminant functions can then be
used to classify new observations.
Bayesian Neural Network Classifier
The Bayesian Neural
Network Classifier classifies observations into groups
by combining information from a training set with prior
probabilities. It can be used to predict the relative
likelihood that an observation belongs to each of several
groups.
