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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 inter-correlation.

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 product-moment correlations, Kendall and Spearman rank correlations, and partial correlation coefficients may be estimated. The StatAdvisor will highlight in red all P-Values 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)
P-Value

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

Chi-Squared

D.F.

P-Value

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 k-means.

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.

 

 
 
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