Plastic Film Data (Page 256, Johnson and Wichern)
Summary Statistics

The CORR Procedure

3 Variables: Y1 Y2 Y3

Simple Statistics
Variable N Mean Std Dev Sum Minimum Maximum Label
Y1 20 6.78500 0.47381 135.70000 5.80000 7.60000 Tear Resistance
Y2 20 9.31500 0.51736 186.30000 8.30000 10.10000 Gloss
Y3 20 3.93500 1.97625 78.70000 0.80000 8.40000 Opacity

Pearson Correlation Coefficients, N = 20
Prob > |r| under H0: Rho=0
  Y1 Y2 Y3
Y1
Tear Resistance
1.00000
 
-0.16865
0.4772
-0.01346
0.9551
Y2
Gloss
-0.16865
0.4772
1.00000
 
0.09830
0.6801
Y3
Opacity
-0.01346
0.9551
0.09830
0.6801
1.00000
 

Plastic Film Data (Page 256, Johnson and Wichern)
Multivariate Analysis of Variance

The GLM Procedure

Class Level Information
Class Levels Values
Additive 2 High (1.5%) Low (1.0%)
Extrusn 2 High (10%) Low (-10%)

Number of Observations Read 20
Number of Observations Used 20

Plastic Film Data (Page 256, Johnson and Wichern)
Multivariate Analysis of Variance

The GLM Procedure
 
Dependent Variable: Y1 Tear Resistance

Source DF Sum of Squares Mean Square F Value Pr > F
Model 3 2.50150000 0.83383333 7.56 0.0023
Error 16 1.76400000 0.11025000    
Corrected Total 19 4.26550000      

R-Square Coeff Var Root MSE Y1 Mean
0.586449 4.893724 0.332039 6.785000

Source DF Type I SS Mean Square F Value Pr > F
Additive 1 0.76050000 0.76050000 6.90 0.0183
Extrusn 1 1.74050000 1.74050000 15.79 0.0011
Additive*Extrusn 1 0.00050000 0.00050000 0.00 0.9471

Source DF Type III SS Mean Square F Value Pr > F
Additive 1 0.76050000 0.76050000 6.90 0.0183
Extrusn 1 1.74050000 1.74050000 15.79 0.0011
Additive*Extrusn 1 0.00050000 0.00050000 0.00 0.9471

Plastic Film Data (Page 256, Johnson and Wichern)
Multivariate Analysis of Variance

The GLM Procedure
 
Dependent Variable: Y2 Gloss

Source DF Sum of Squares Mean Square F Value Pr > F
Model 3 2.45750000 0.81916667 4.99 0.0125
Error 16 2.62800000 0.16425000    
Corrected Total 19 5.08550000      

R-Square Coeff Var Root MSE Y2 Mean
0.483237 4.350807 0.405278 9.315000

Source DF Type I SS Mean Square F Value Pr > F
Additive 1 0.61250000 0.61250000 3.73 0.0714
Extrusn 1 1.30050000 1.30050000 7.92 0.0125
Additive*Extrusn 1 0.54450000 0.54450000 3.32 0.0874

Source DF Type III SS Mean Square F Value Pr > F
Additive 1 0.61250000 0.61250000 3.73 0.0714
Extrusn 1 1.30050000 1.30050000 7.92 0.0125
Additive*Extrusn 1 0.54450000 0.54450000 3.32 0.0874

Plastic Film Data (Page 256, Johnson and Wichern)
Multivariate Analysis of Variance

The GLM Procedure
 
Dependent Variable: Y3 Opacity

Source DF Sum of Squares Mean Square F Value Pr > F
Model 3 9.28150000 3.09383333 0.76 0.5315
Error 16 64.92400000 4.05775000    
Corrected Total 19 74.20550000      

R-Square Coeff Var Root MSE Y3 Mean
0.125078 51.19151 2.014386 3.935000

Source DF Type I SS Mean Square F Value Pr > F
Additive 1 4.90050000 4.90050000 1.21 0.2881
Extrusn 1 0.42050000 0.42050000 0.10 0.7517
Additive*Extrusn 1 3.96050000 3.96050000 0.98 0.3379

Source DF Type III SS Mean Square F Value Pr > F
Additive 1 4.90050000 4.90050000 1.21 0.2881
Extrusn 1 0.42050000 0.42050000 0.10 0.7517
Additive*Extrusn 1 3.96050000 3.96050000 0.98 0.3379

Plastic Film Data (Page 256, Johnson and Wichern)
Multivariate Analysis of Variance

The GLM Procedure
Multivariate Analysis of Variance

E = Error SSCP Matrix
  Y1 Y2 Y3
Y1 1.764 0.02 -3.07
Y2 0.02 2.628 -0.552
Y3 -3.07 -0.552 64.924

Partial Correlation Coefficients from the Error SSCP Matrix / Prob > |r|
DF = 16 Y1 Y2 Y3
Y1
1.000000
 
0.009289
0.9718
-0.286871
0.2643
Y2
0.009289
0.9718
1.000000
 
-0.042259
0.8721
Y3
-0.286871
0.2643
-0.042259
0.8721
1.000000
 

Plastic Film Data (Page 256, Johnson and Wichern)
Multivariate Analysis of Variance

The GLM Procedure
Multivariate Analysis of Variance

H = Type III SSCP Matrix for Additive*Extrusn
  Y1 Y2 Y3
Y1 0.0005 0.0165 0.0445
Y2 0.0165 0.5445 1.4685
Y3 0.0445 1.4685 3.9605

Canonical Analysis

H = Type III SSCP Matrix for Additive*Extrusn
E = Error SSCP Matrix
  Canonical
Correlation		 Adjusted
Canonical
Correlation		 Approximate
Standard
Error		 Squared
Canonical
Correlation		 Eigenvalues of Inv(E)*H
= CanRsq/(1-CanRsq)		 Test of H0: The canonical correlations in the
current row and all that follow are zero
  Eigenvalue Difference Proportion Cumulative Likelihood
Ratio		 Approximate
F Value		 Num DF Den DF Pr > F
1 0.472117 0.386084 0.188476 0.222894 0.2868   1.0000 1.0000 0.77710576 1.34 3 14 0.3018

The F statistic is exact.


Canonical Structure
  Total Between Within
Can1 Can1 Can1
Y1 0.0500 1.0000 0.0314
Y2 0.8834 1.0000 0.8499
Y3 0.5082 1.0000 0.4612

Canonical Coefficients
  Standardized Raw
Can1 Can1
Y1 0.25843624 0.54543782
Y2 1.11248172 2.15031881
Y3 0.53954206 0.27301346

MANOVA Test Criteria and Exact F Statistics for the
Hypothesis of No Overall Additive*Extrusn Effect
H = Type III SSCP Matrix for Additive*Extrusn
E = Error SSCP Matrix

S=1 M=0.5 N=6
Statistic Value F Value Num DF Den DF Pr > F
Wilks' Lambda 0.77710576 1.34 3 14 0.3018
Pillai's Trace 0.22289424 1.34 3 14 0.3018
Hotelling-Lawley Trace 0.28682614 1.34 3 14 0.3018
Roy's Greatest Root 0.28682614 1.34 3 14 0.3018

H = Type III SSCP Matrix for Extrusn
  Y1 Y2 Y3
Y1 1.7405 -1.5045 0.8555
Y2 -1.5045 1.3005 -0.7395
Y3 0.8555 -0.7395 0.4205

Canonical Analysis

H = Type III SSCP Matrix for Extrusn
E = Error SSCP Matrix
  Canonical
Correlation		 Adjusted
Canonical
Correlation		 Approximate
Standard
Error		 Squared
Canonical
Correlation		 Eigenvalues of Inv(E)*H
= CanRsq/(1-CanRsq)		 Test of H0: The canonical correlations in the
current row and all that follow are zero
  Eigenvalue Difference Proportion Cumulative Likelihood
Ratio		 Approximate
F Value		 Num DF Den DF Pr > F
1 0.786220 0.766480 0.092614 0.618142 1.6188   1.0000 1.0000 0.38185838 7.55 3 14 0.0030

The F statistic is exact.


Canonical Structure
  Total Between Within
Can1 Can1 Can1
Y1 0.8828 1.0000 0.7807
Y2 -0.5748 -1.0000 -0.5529
Y3 0.1293 1.0000 0.0633

Canonical Coefficients
  Standardized Raw
Can1 Can1
Y1 1.23977489 2.61658389
Y2 -0.70050425 -1.35400649
Y3 0.28382256 0.14361694

MANOVA Test Criteria and Exact F Statistics for
the Hypothesis of No Overall Extrusn Effect
H = Type III SSCP Matrix for Extrusn
E = Error SSCP Matrix

S=1 M=0.5 N=6
Statistic Value F Value Num DF Den DF Pr > F
Wilks' Lambda 0.38185838 7.55 3 14 0.0030
Pillai's Trace 0.61814162 7.55 3 14 0.0030
Hotelling-Lawley Trace 1.61877188 7.55 3 14 0.0030
Roy's Greatest Root 1.61877188 7.55 3 14 0.0030

H = Type III SSCP Matrix for Additive
  Y1 Y2 Y3
Y1 0.7605 0.6825 1.9305
Y2 0.6825 0.6125 1.7325
Y3 1.9305 1.7325 4.9005

Canonical Analysis

H = Type III SSCP Matrix for Additive
E = Error SSCP Matrix
  Canonical
Correlation		 Adjusted
Canonical
Correlation		 Approximate
Standard
Error		 Squared
Canonical
Correlation		 Eigenvalues of Inv(E)*H
= CanRsq/(1-CanRsq)		 Test of H0: The canonical correlations in the
current row and all that follow are zero
  Eigenvalue Difference Proportion Cumulative Likelihood
Ratio		 Approximate
F Value		 Num DF Den DF Pr > F
1 0.690627 0.656702 0.126855 0.476965 0.9119   1.0000 1.0000 0.52303490 4.26 3 14 0.0247

The F statistic is exact.


Canonical Structure
  Total Between Within
Can1 Can1 Can1
Y1 0.7721 1.0000 0.6876
Y2 0.3687 1.0000 0.5055
Y3 0.4214 1.0000 0.2877

Canonical Coefficients
  Standardized Raw
Can1 Can1
Y1 1.19977862 2.53217051
Y2 0.66510642 1.28558594
Y3 0.54048251 0.27348934

MANOVA Test Criteria and Exact F Statistics for
the Hypothesis of No Overall Additive Effect
H = Type III SSCP Matrix for Additive
E = Error SSCP Matrix

S=1 M=0.5 N=6
Statistic Value F Value Num DF Den DF Pr > F
Wilks' Lambda 0.52303490 4.26 3 14 0.0247
Pillai's Trace 0.47696510 4.26 3 14 0.0247
Hotelling-Lawley Trace 0.91191832 4.26 3 14 0.0247
Roy's Greatest Root 0.91191832 4.26 3 14 0.0247

Plastic Film Data (Page 256, Johnson and Wichern)
Multivariate Analysis of Variance

The GLM Procedure
Least Squares Means
Adjustment for Multiple Comparisons: Bonferroni

Additive Y1 LSMEAN H0:LSMean1=LSMean2
Pr > |t|
High (1.5%) 6.98000000 0.0183
Low (1.0%) 6.59000000  

Additive Y1 LSMEAN 98.3333% Confidence Limits
High (1.5%) 6.980000 6.699333 7.260667
Low (1.0%) 6.590000 6.309333 6.870667

Least Squares Means for Effect Additive
i j Difference Between
Means		 Simultaneous 98.3333% Confidence
Limits for LSMean(i)-LSMean(j)
1 2 0.390000 -0.006924 0.786924

Additive Y2 LSMEAN H0:LSMean1=LSMean2
Pr > |t|
High (1.5%) 9.49000000 0.0714
Low (1.0%) 9.14000000  

Additive Y2 LSMEAN 98.3333% Confidence Limits
High (1.5%) 9.490000 9.147425 9.832575
Low (1.0%) 9.140000 8.797425 9.482575

Least Squares Means for Effect Additive
i j Difference Between
Means		 Simultaneous 98.3333% Confidence
Limits for LSMean(i)-LSMean(j)
1 2 0.350000 -0.134474 0.834474

Additive Y3 LSMEAN H0:LSMean1=LSMean2
Pr > |t|
High (1.5%) 4.43000000 0.2881
Low (1.0%) 3.44000000  

Additive Y3 LSMEAN 98.3333% Confidence Limits
High (1.5%) 4.430000 2.727272 6.132728
Low (1.0%) 3.440000 1.737272 5.142728

Least Squares Means for Effect Additive
i j Difference Between
Means		 Simultaneous 98.3333% Confidence
Limits for LSMean(i)-LSMean(j)
1 2 0.990000 -1.418021 3.398021

Plastic Film Data (Page 256, Johnson and Wichern)
Multivariate Analysis of Variance

The GLM Procedure
Least Squares Means
Adjustment for Multiple Comparisons: Bonferroni

Extrusn Y1 LSMEAN H0:LSMean1=LSMean2
Pr > |t|
High (10%) 7.08000000 0.0011
Low (-10%) 6.49000000  

Extrusn Y1 LSMEAN 98.3333% Confidence Limits
High (10%) 7.080000 6.799333 7.360667
Low (-10%) 6.490000 6.209333 6.770667

Least Squares Means for Effect Extrusn
i j Difference Between
Means		 Simultaneous 98.3333% Confidence
Limits for LSMean(i)-LSMean(j)
1 2 0.590000 0.193076 0.986924

Extrusn Y2 LSMEAN H0:LSMean1=LSMean2
Pr > |t|
High (10%) 9.06000000 0.0125
Low (-10%) 9.57000000  

Extrusn Y2 LSMEAN 98.3333% Confidence Limits
High (10%) 9.060000 8.717425 9.402575
Low (-10%) 9.570000 9.227425 9.912575

Least Squares Means for Effect Extrusn
i j Difference Between
Means		 Simultaneous 98.3333% Confidence
Limits for LSMean(i)-LSMean(j)
1 2 -0.510000 -0.994474 -0.025526

Extrusn Y3 LSMEAN H0:LSMean1=LSMean2
Pr > |t|
High (10%) 4.08000000 0.7517
Low (-10%) 3.79000000  

Extrusn Y3 LSMEAN 98.3333% Confidence Limits
High (10%) 4.080000 2.377272 5.782728
Low (-10%) 3.790000 2.087272 5.492728

Least Squares Means for Effect Extrusn
i j Difference Between
Means		 Simultaneous 98.3333% Confidence
Limits for LSMean(i)-LSMean(j)
1 2 0.290000 -2.118021 2.698021