Results: cruiseship.sas

The SAS System

The REG Procedure

Model: MODEL1

Dependent Variable: Crew

The REG Procedure

MODEL1

Fit

Crew

Number of Observations

Number of Observations Read 158
Number of Observations Used 158

Analysis of Variance

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 6 1781.51273 296.91879 307.99 <.0001
Error 151 145.57091 0.96405    
Corrected Total 157 1927.08364      

Fit Statistics

Root MSE 0.98186 R-Square 0.9245
Dependent Mean 7.79418 Adj R-Sq 0.9215
Coeff Var 12.59733    

Parameter Estimates

Parameter Estimates
Variable DF Parameter
Estimate		 Standard
Error		 t Value Pr > |t|
Intercept 1 -0.52134 1.05703 -0.49 0.6226
Age 1 -0.01254 0.01420 -0.88 0.3783
Tonnage 1 0.01324 0.01189 1.11 0.2673
passengers 1 -0.14976 0.04759 -3.15 0.0020
Length 1 0.40348 0.11445 3.53 0.0006
Cabins 1 0.80163 0.08922 8.98 <.0001
PassDens 1 -0.00065774 0.01581 -0.04 0.9669

The SAS System

The REG Procedure

Model: MODEL1

Dependent Variable: Crew

Observation-wise Statistics

Crew

Diagnostic Plots

Fit Diagnostics

Panel of fit diagnostics for Crew.

Residual Plots

Panel 1

Panel of scatterplots of residuals by regressors for Crew.

The SAS System

The REG Procedure

Model: MODEL2

Dependent Variable: Crew

MODEL2

Forward Selection Method

Crew

Number of Observations

Number of Observations Read 158
Number of Observations Used 158

Step 1

Forward Selection: Step 1

ANOVA

Variable Cabins Entered: R-Square = 0.9041 and C(p) = 37.7724

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 1 1742.20623 1742.20623 1470.08 <.0001
Error 156 184.87741 1.18511    
Corrected Total 157 1927.08364      

Parameter Estimates

Variable Parameter
Estimate		 Standard
Error		 Type II SS F Value Pr > F
Intercept 1.21585 0.19219 47.42985 40.02 <.0001
Cabins 0.74500 0.01943 1742.20623 1470.08 <.0001

Bounds on condition number: 1, 1

Step 2

Forward Selection: Step 2

ANOVA

Variable Length Entered: R-Square = 0.9160 and C(p) = 15.9524

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 2 1765.16987 882.58494 844.90 <.0001
Error 155 161.91377 1.04460    
Corrected Total 157 1927.08364      

Parameter Estimates

Variable Parameter
Estimate		 Standard
Error		 Type II SS F Value Pr > F
Intercept -1.11083 0.52803 4.62312 4.43 0.0370
Length 0.46728 0.09966 22.96364 21.98 <.0001
Cabins 0.57823 0.03997 218.57136 209.24 <.0001

Bounds on condition number: 4.8017, 19.207

Step 3

Forward Selection: Step 3

ANOVA

Variable passengers Entered: R-Square = 0.9220 and C(p) = 5.8566

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 3 1776.83077 592.27692 607.05 <.0001
Error 154 150.25287 0.97567    
Corrected Total 157 1927.08364      

Parameter Estimates

Variable Parameter
Estimate		 Standard
Error		 Type II SS F Value Pr > F
Intercept -1.38854 0.51659 7.04897 7.22 0.0080
passengers -0.13173 0.03810 11.66090 11.95 0.0007
Length 0.51775 0.09742 27.55895 28.25 <.0001
Cabins 0.83856 0.08463 95.78071 98.17 <.0001

Bounds on condition number: 23.045, 149.51

Step 4

Forward Selection: Step 4

ANOVA

Variable Tonnage Entered: R-Square = 0.9240 and C(p) = 3.8468

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 4 1780.69639 445.17410 465.28 <.0001
Error 153 146.38725 0.95678    
Corrected Total 157 1927.08364      

Parameter Estimates

Variable Parameter
Estimate		 Standard
Error		 Type II SS F Value Pr > F
Intercept -0.81871 0.58487 1.87482 1.96 0.1636
Tonnage 0.01632 0.00812 3.86562 4.04 0.0462
passengers -0.14985 0.03879 14.27515 14.92 0.0002
Length 0.39755 0.11350 11.73877 12.27 0.0006
Cabins 0.79084 0.08711 78.86111 82.42 <.0001

Bounds on condition number: 24.894, 279.25

No other variable met the 0.1500 significance level for entry into the model.

Selection Summary

Summary of Forward Selection
Step Variable
Entered		 Number
Vars In		 Partial
R-Square		 Model
R-Square		 C(p) F Value Pr > F
1 Cabins 1 0.9041 0.9041 37.7724 1470.08 <.0001
2 Length 2 0.0119 0.9160 15.9524 21.98 <.0001
3 passengers 3 0.0061 0.9220 5.8566 11.95 0.0007
4 Tonnage 4 0.0020 0.9240 3.8468 4.04 0.0462

The SAS System

The REG Procedure

Model: MODEL2

Dependent Variable: Crew

Observation-wise Statistics

Crew

Diagnostic Plots

Fit Diagnostics

Panel of fit diagnostics for Crew.

Residual Plots

Panel 1

Panel of scatterplots of residuals by regressors for Crew.

The SAS System

The REG Procedure

Model: MODEL3

Dependent Variable: Crew

MODEL3

Backward Elimination Method

Crew

Number of Observations

Number of Observations Read 158
Number of Observations Used 158

Step 0

Backward Elimination: Step 0

ANOVA

All Variables Entered: R-Square = 0.9245 and C(p) = 7.0000

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 6 1781.51273 296.91879 307.99 <.0001
Error 151 145.57091 0.96405    
Corrected Total 157 1927.08364      

Parameter Estimates

Variable Parameter
Estimate		 Standard
Error		 Type II SS F Value Pr > F
Intercept -0.52134 1.05703 0.23451 0.24 0.6226
Age -0.01254 0.01420 0.75267 0.78 0.3783
Tonnage 0.01324 0.01189 1.19502 1.24 0.2673
passengers -0.14976 0.04759 9.54788 9.90 0.0020
Length 0.40348 0.11445 11.98038 12.43 0.0006
Cabins 0.80163 0.08922 77.82131 80.72 <.0001
PassDens -0.00065774 0.01581 0.00167 0.00 0.9669

Bounds on condition number: 34.538, 625.13

Step 1

Backward Elimination: Step 1

ANOVA

Variable PassDens Removed: R-Square = 0.9245 and C(p) = 5.0017

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 5 1781.51106 356.30221 372.03 <.0001
Error 152 145.57258 0.95771    
Corrected Total 157 1927.08364      

Parameter Estimates

Variable Parameter
Estimate		 Standard
Error		 Type II SS F Value Pr > F
Intercept -0.55592 0.65083 0.69875 0.73 0.3944
Age -0.01235 0.01340 0.81467 0.85 0.3578
Tonnage 0.01292 0.00892 2.00698 2.10 0.1498
passengers -0.14863 0.03884 14.02657 14.65 0.0002
Length 0.40384 0.11376 12.06921 12.60 0.0005
Cabins 0.80217 0.08801 79.55636 83.07 <.0001

Bounds on condition number: 25.389, 375.79

Step 2

Backward Elimination: Step 2

ANOVA

Variable Age Removed: R-Square = 0.9240 and C(p) = 3.8468

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 4 1780.69639 445.17410 465.28 <.0001
Error 153 146.38725 0.95678    
Corrected Total 157 1927.08364      

Parameter Estimates

Variable Parameter
Estimate		 Standard
Error		 Type II SS F Value Pr > F
Intercept -0.81871 0.58487 1.87482 1.96 0.1636
Tonnage 0.01632 0.00812 3.86562 4.04 0.0462
passengers -0.14985 0.03879 14.27515 14.92 0.0002
Length 0.39755 0.11350 11.73877 12.27 0.0006
Cabins 0.79084 0.08711 78.86111 82.42 <.0001

Bounds on condition number: 24.894, 279.25

All variables left in the model are significant at the 0.1500 level.

Selection Summary

Summary of Backward Elimination
Step Variable
Removed		 Number
Vars In		 Partial
R-Square		 Model
R-Square		 C(p) F Value Pr > F
1 PassDens 5 0.0000 0.9245 5.0017 0.00 0.9669
2 Age 4 0.0004 0.9240 3.8468 0.85 0.3578

The SAS System

The REG Procedure

Model: MODEL3

Dependent Variable: Crew

Observation-wise Statistics

Crew

Diagnostic Plots

Fit Diagnostics

Panel of fit diagnostics for Crew.

Residual Plots

Panel 1

Panel of scatterplots of residuals by regressors for Crew.

The SAS System

The REG Procedure

Model: MODEL4

Dependent Variable: Crew

MODEL4

Stepwise Selection Method

Crew

Number of Observations

Number of Observations Read 158
Number of Observations Used 158

Step 1

Stepwise Selection: Step 1

ANOVA

Variable Cabins Entered: R-Square = 0.9041 and C(p) = 37.7724

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 1 1742.20623 1742.20623 1470.08 <.0001
Error 156 184.87741 1.18511    
Corrected Total 157 1927.08364      

Parameter Estimates

Variable Parameter
Estimate		 Standard
Error		 Type II SS F Value Pr > F
Intercept 1.21585 0.19219 47.42985 40.02 <.0001
Cabins 0.74500 0.01943 1742.20623 1470.08 <.0001

Bounds on condition number: 1, 1

Step 2

Stepwise Selection: Step 2

ANOVA

Variable Length Entered: R-Square = 0.9160 and C(p) = 15.9524

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 2 1765.16987 882.58494 844.90 <.0001
Error 155 161.91377 1.04460    
Corrected Total 157 1927.08364      

Parameter Estimates

Variable Parameter
Estimate		 Standard
Error		 Type II SS F Value Pr > F
Intercept -1.11083 0.52803 4.62312 4.43 0.0370
Length 0.46728 0.09966 22.96364 21.98 <.0001
Cabins 0.57823 0.03997 218.57136 209.24 <.0001

Bounds on condition number: 4.8017, 19.207

Step 3

Stepwise Selection: Step 3

ANOVA

Variable passengers Entered: R-Square = 0.9220 and C(p) = 5.8566

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 3 1776.83077 592.27692 607.05 <.0001
Error 154 150.25287 0.97567    
Corrected Total 157 1927.08364      

Parameter Estimates

Variable Parameter
Estimate		 Standard
Error		 Type II SS F Value Pr > F
Intercept -1.38854 0.51659 7.04897 7.22 0.0080
passengers -0.13173 0.03810 11.66090 11.95 0.0007
Length 0.51775 0.09742 27.55895 28.25 <.0001
Cabins 0.83856 0.08463 95.78071 98.17 <.0001

Bounds on condition number: 23.045, 149.51

Step 4

Stepwise Selection: Step 4

ANOVA

Variable Tonnage Entered: R-Square = 0.9240 and C(p) = 3.8468

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 4 1780.69639 445.17410 465.28 <.0001
Error 153 146.38725 0.95678    
Corrected Total 157 1927.08364      

Parameter Estimates

Variable Parameter
Estimate		 Standard
Error		 Type II SS F Value Pr > F
Intercept -0.81871 0.58487 1.87482 1.96 0.1636
Tonnage 0.01632 0.00812 3.86562 4.04 0.0462
passengers -0.14985 0.03879 14.27515 14.92 0.0002
Length 0.39755 0.11350 11.73877 12.27 0.0006
Cabins 0.79084 0.08711 78.86111 82.42 <.0001

Bounds on condition number: 24.894, 279.25

All variables left in the model are significant at the 0.1500 level.

No other variable met the 0.1500 significance level for entry into the model.

Selection Summary

Summary of Stepwise Selection
Step Variable
Entered		 Variable
Removed		 Number
Vars In		 Partial
R-Square		 Model
R-Square		 C(p) F Value Pr > F
1 Cabins   1 0.9041 0.9041 37.7724 1470.08 <.0001
2 Length   2 0.0119 0.9160 15.9524 21.98 <.0001
3 passengers   3 0.0061 0.9220 5.8566 11.95 0.0007
4 Tonnage   4 0.0020 0.9240 3.8468 4.04 0.0462

The SAS System

The REG Procedure

Model: MODEL4

Dependent Variable: Crew

Observation-wise Statistics

Crew

Diagnostic Plots

Fit Diagnostics

Panel of fit diagnostics for Crew.

Residual Plots

Panel 1

Panel of scatterplots of residuals by regressors for Crew.

The SAS System

The REG Procedure

Model: MODEL5

Dependent Variable: Crew

Adjusted R-Square Selection Method

MODEL5

Adjusted R-Square Selection Method

Crew

Number of Observations

Number of Observations Read 158
Number of Observations Used 158

Results

Number in
Model		 Adjusted
R-Square		 R-Square C(p) AIC BIC Variables in Model
4 0.9221 0.9240 3.8468 -2.0616 0.3403 Tonnage passengers Length Cabins
5 0.9220 0.9245 5.0017 -0.9434 1.6085 Age Tonnage passengers Length Cabins
5 0.9216 0.9241 5.7807 -0.1304 2.3580 Tonnage passengers Length Cabins PassDens
6 0.9215 0.9245 7.0000 1.0548 3.6995 Age Tonnage passengers Length Cabins PassDens
4 0.9214 0.9234 5.0836 -0.7800 1.5391 Age passengers Length Cabins
4 0.9214 0.9234 5.1975 -0.6624 1.6491 passengers Length Cabins PassDens
5 0.9213 0.9238 6.2396 0.3466 2.7977 Age passengers Length Cabins PassDens
3 0.9205 0.9220 5.8566 0.0565 2.1661 passengers Length Cabins
3 0.9177 0.9193 11.3414 5.5212 7.3546 Length Cabins PassDens
4 0.9173 0.9194 13.0556 7.2410 9.0506 Tonnage Length Cabins PassDens
4 0.9172 0.9193 13.2642 7.4455 9.2423 Age Length Cabins PassDens
5 0.9169 0.9195 14.9040 9.0922 10.8750 Age Tonnage Length Cabins PassDens
3 0.9163 0.9179 14.0233 8.1260 9.8295 Tonnage passengers Cabins
4 0.9161 0.9182 15.5211 9.6414 11.3015 Age Tonnage passengers Cabins
4 0.9158 0.9179 16.0199 10.1227 11.7529 Tonnage passengers Cabins PassDens
5 0.9156 0.9182 17.4272 11.5507 13.1499 Age Tonnage passengers Cabins PassDens
3 0.9154 0.9170 15.9087 9.9317 11.5458 Age Length Cabins
4 0.9150 0.9172 17.5514 11.5911 13.1308 Age Tonnage Length Cabins
3 0.9150 0.9166 16.6543 10.6402 12.2194 Tonnage Length Cabins
2 0.9149 0.9160 15.9524 9.8661 11.5035 Length Cabins
3 0.9119 0.9136 22.8065 16.3678 17.6677 passengers Cabins PassDens
4 0.9118 0.9140 23.8209 17.4641 18.6468 Age passengers Cabins PassDens
3 0.9111 0.9128 24.3993 17.8175 19.0475 Tonnage Cabins PassDens
2 0.9107 0.9118 24.2606 17.4948 18.8517 Cabins PassDens
4 0.9105 0.9128 26.3399 19.7637 20.8089 Age Tonnage Cabins PassDens
3 0.9102 0.9120 25.9993 19.2604 20.4213 Age Cabins PassDens
3 0.9095 0.9112 27.4513 20.5586 21.6576 Age passengers Cabins
2 0.9094 0.9106 26.7922 19.7480 21.0232 Tonnage Cabins
3 0.9092 0.9109 28.0871 21.1237 22.1959 Age Tonnage Cabins
2 0.9065 0.9077 32.4433 24.6647 25.7633 passengers Cabins
2 0.9057 0.9069 34.1252 26.0989 27.1466 Age Cabins
1 0.9034 0.9041 37.7724 28.8215 30.0550 Cabins
4 0.8810 0.8841 83.7391 64.7313 63.3468 Tonnage passengers Length PassDens
3 0.8808 0.8831 83.6490 64.0282 63.2283 Tonnage passengers Length
5 0.8803 0.8841 85.7237 66.7208 64.7005 Age Tonnage passengers Length PassDens
4 0.8801 0.8832 85.5252 65.9444 64.5010 Age Tonnage passengers Length
3 0.8799 0.8822 85.5364 65.2993 64.4491 Tonnage Length PassDens
4 0.8792 0.8822 87.3878 67.1996 65.6958 Age Tonnage Length PassDens
3 0.8736 0.8760 97.9249 73.3985 72.2337 Tonnage passengers PassDens
4 0.8727 0.8760 99.9243 75.3981 73.5079 Age Tonnage passengers PassDens
2 0.8727 0.8743 99.1787 73.4586 72.9576 Tonnage passengers
3 0.8727 0.8751 99.6149 74.4719 73.2662 passengers Length PassDens
2 0.8726 0.8742 99.3848 73.5882 73.0833 Tonnage PassDens
3 0.8721 0.8746 100.7638 75.1974 73.9643 Age Tonnage passengers
4 0.8719 0.8752 101.4766 76.3843 74.4486 Age passengers Length PassDens
3 0.8718 0.8743 101.3335 75.5559 74.3093 Age Tonnage PassDens
3 0.8710 0.8735 102.9483 76.5679 75.2831 Age passengers Length
2 0.8707 0.8723 103.2094 75.9739 75.3984 passengers Length
3 0.8697 0.8722 105.3930 78.0875 76.7459 Age Tonnage Length
2 0.8696 0.8713 105.3360 77.2851 76.6709 Tonnage Length
2 0.8602 0.8620 123.8373 88.2547 87.3266 Age Tonnage
1 0.8595 0.8604 125.0862 88.1049 87.9929 Tonnage
2 0.8501 0.8520 143.8894 99.3424 98.1119 passengers PassDens
3 0.8491 0.8520 145.8009 101.2951 99.1342 Age passengers PassDens
2 0.8403 0.8424 163.1054 109.2839 107.7953 Age passengers
1 0.8366 0.8377 170.5232 111.9370 111.3579 passengers
3 0.8147 0.8182 213.3524 133.7935 130.6334 Age Length PassDens
2 0.8057 0.8081 231.5057 140.3226 138.1030 Length PassDens
2 0.8041 0.8066 234.6007 141.5926 139.3454 Age Length
1 0.8013 0.8026 240.6754 142.8586 141.7407 Length
2 0.3735 0.3815 1084.442 325.2835 320.5288 Age PassDens
1 0.2770 0.2816 1282.056 346.9302 343.7862 Age
1 0.0179 0.0242 1796.613 395.3167 391.9515 PassDens

The SAS System

The REG Procedure

Model: MODEL5

Dependent Variable: Crew

Observation-wise Statistics

Crew

Diagnostic Plots

Fit Diagnostics

Panel of fit diagnostics for Crew.

Residual Plots

Panel 1

Panel of scatterplots of residuals by regressors for Crew.