Chapter 10 : Relationship of bat energy expenditure to mass and echolocation
Data Listing

Obs species TypeName Mass Type Expenditure LExpend LMass TypeNON TypeBIRD MassNON MassBird LMassNON LMassBird
1 Pteropus gouldii non-echolocating bats 779.0 1 43.70 3.77735 6.65801 1 0 779 0.0 6.65801 0.00000
2 Pteropus poliocephalus non-echolocating bats 628.0 1 34.80 3.54962 6.44254 1 0 628 0.0 6.44254 0.00000
3 Hypsignathus monstrosus non-echolocating bats 258.0 1 23.30 3.14845 5.55296 1 0 258 0.0 5.55296 0.00000
4 Eidolon helvum non-echolocating bats 315.0 1 22.40 3.10906 5.75257 1 0 315 0.0 5.75257 0.00000
5 Meliphaga virescens non-echolocating birds 24.3 2 2.46 0.90016 3.19048 0 1 0 24.3 0.00000 3.19048
6 Melipsittacus undulatus non-echolocating birds 35.0 2 3.93 1.36864 3.55535 0 1 0 35.0 0.00000 3.55535
7 Sturnus vulgaris non-echolocating birds 72.8 2 9.15 2.21375 4.28772 0 1 0 72.8 0.00000 4.28772
8 Falco spaverius non-echolocating birds 120.0 2 13.80 2.62467 4.78749 0 1 0 120.0 0.00000 4.78749
9 Falco tinnunculus non-echolocating birds 213.0 2 14.60 2.68102 5.36129 0 1 0 213.0 0.00000 5.36129
10 Corvus ossifragus non-echolocating birds 275.0 2 22.80 3.12676 5.61677 0 1 0 275.0 0.00000 5.61677
11 Larus atricilla non-echolocating birds 370.0 2 26.20 3.26576 5.91350 0 1 0 370.0 0.00000 5.91350
12 Columba livia non-echolocating birds 384.0 2 25.90 3.25424 5.95064 0 1 0 384.0 0.00000 5.95064
13 Columba livia non-echolocating birds 442.0 2 29.50 3.38439 6.09131 0 1 0 442.0 0.00000 6.09131
14 Columba livia non-echolocating birds 412.0 2 43.70 3.77735 6.02102 0 1 0 412.0 0.00000 6.02102
15 Columba livia non-echolocating birds 330.0 2 34.00 3.52636 5.79909 0 1 0 330.0 0.00000 5.79909
16 Corvus crytoleucos non-echolocating birds 480.0 2 27.80 3.32504 6.17379 0 1 0 480.0 0.00000 6.17379
17 Phyllostomas hastatus echolocating bats 93.0 3 8.83 2.17816 4.53260 0 0 0 0.0 0.00000 0.00000
18 Plecotus auritus echolocating bats 8.0 3 1.35 0.30010 2.07944 0 0 0 0.0 0.00000 0.00000
19 Pipistrellus pipistrellus echolocating bats 6.7 3 1.12 0.11333 1.90211 0 0 0 0.0 0.00000 0.00000
20 Plecotus auritus echolocating bats 7.7 3 1.02 0.01980 2.04122 0 0 0 0.0 0.00000 0.00000


Chapter 10 : Relationship of bat energy expenditure to mass and echolocation
Plot of the raw data with type variable

                                        Plot of Expenditure*Mass.  Symbol is value of Type.                                         
                                                                                                                                    
 Expenditure |                                                                                                                      
             |                                                                                                                      
          45 +                                                                                                                      
             |                                                            2                                                  1      
             |                                                                                                                      
             |                                                                                                                      
             |                                                                                                                      
          40 +                                                                                                                      
             |                                                                                                                      
             |                                                                                                                      
             |                                                                                                                      
             |                                                                                                                      
          35 +                                                                                          1                           
             |                                                2                                                                     
             |                                                                                                                      
             |                                                                                                                      
             |                                                                                                                      
          30 +                                                                2                                                     
             |                                                                                                                      
             |                                                                     2                                                
             |                                                                                                                      
             |                                                      2 2                                                             
          25 +                                                                                                                      
             |                                                                                                                      
             |                                      1  2                                                                            
             |                                              1                                                                       
             |                                                                                                                      
          20 +                                                                                                                      
             |                                                                                                                      
             |                                                                                                                      
             |                                                                                                                      
             |                                                                                                                      
          15 +                                2                                                                                     
             |                   2                                                                                                  
             |                                                                                                                      
             |                                                                                                                      
             |                                                                                                                      
          10 +                                                                                                                      
             |            2  3                                                                                                      
             |                                                                                                                      
             |                                                                                                                      
             |                                                                                                                      
           5 +                                                                                                                      
             |       2                                                                                                              
             |                                                                                                                      
             |     2                                                                                                                
             |   3                                                                                                                  
           0 +                                                                                                                      
             |                                                                                                                      
             ---+-------------+-------------+-------------+-------------+-------------+-------------+-------------+-------------+-- 
                0            100           200           300           400           500           600           700           800  
                                                                                                                                    
                                                                      Mass                                                          
                                                                                                                                    
NOTE: 2 obs hidden.                                                                                                                 


Chapter 10 : Relationship of bat energy expenditure to mass and echolocation
Plot of the raw data with type variable

                                          Plot of LExpend*LMass.  Symbol is value of Type.                                          
                                                                                                                                    
    4.0 +                                                                                                                           
        |                                                                                                                           
        |                                                                                                                           
        |                                                                                                   2             1         
        |                                                                                                                           
        |                                                                                                             1             
    3.5 +                                                                                               2                           
        |                                                                                                     2                     
        |                                                                                                       2                   
        |                                                                                                 22                        
        |                                                                                         1 2                               
        |                                                                                              1                            
    3.0 +                                                                                                                           
        |                                                                                                                           
        |                                                                                                                           
LExpend |                                                                                                                           
        |                                                                                     2                                     
        |                                                                        2                                                  
    2.5 +                                                                                                                           
        |                                                                                                                           
        |                                                                                                                           
        |                                                             2                                                             
        |                                                                   3                                                       
        |                                                                                                                           
    2.0 +                                                                                                                           
        |                                                                                                                           
        |                                                                                                                           
        |                                                                                                                           
        |                                                                                                                           
        |                                                                                                                           
    1.5 +                                                                                                                           
        |                                                                                                                           
        |                                             2                                                                             
        |                                                                                                                           
        |                                                                                                                           
        |                                                                                                                           
    1.0 +                                                                                                                           
        |                                     2                                                                                     
        |                                                                                                                           
        |                                                                                                                           
        |                                                                                                                           
        |                                                                                                                           
    0.5 +                                                                                                                           
        |                                                                                                                           
        |             3                                                                                                             
        |                                                                                                                           
        |                                                                                                                           
        |         3                                                                                                                 
    0.0 +            3                                                                                                              
        -+----------+----------+----------+----------+----------+----------+----------+----------+----------+----------+----------+-
        1.5        2.0        2.5        3.0        3.5        4.0        4.5        5.0        5.5        6.0        6.5        7.0
                                                                                                                                    
                                                                    LMass                                                           


Chapter 10 : Relationship of bat energy expenditure to mass and echolocation
Fit of Expenditure on indicator variables with REG

The REG Procedure
Model: MODEL1
Dependent Variable: Expenditure

Number of Observations Read 20
Number of Observations Used 20

Analysis of Variance
Source DF Sum of
Squares
Mean
Square
F Value Pr > F
Model 5 3367.37636 673.47527 26.50 <.0001
Error 14 355.73236 25.40945    
Corrected Total 19 3723.10872      

Root MSE 5.04078 R-Square 0.9045
Dependent Mean 19.51800 Adj R-Sq 0.8703
Coeff Var 25.82631    

Parameter Estimates
Variable DF Parameter
Estimate
Standard
Error
t Value Pr > |t| 95% Confidence Limits
Intercept 1 0.49398 3.19470 0.15 0.8793 -6.35796 7.34593
Mass 1 0.08964 0.06804 1.32 0.2089 -0.05630 0.23558
TypeNON 1 10.73340 7.06170 1.52 0.1508 -4.41244 25.87925
TypeBIRD 1 2.82276 4.26463 0.66 0.5188 -6.32397 11.96949
MassNON 1 -0.04959 0.06904 -0.72 0.4844 -0.19766 0.09848
MassBird 1 -0.02186 0.06866 -0.32 0.7549 -0.16913 0.12541


Chapter 10 : Relationship of bat energy expenditure to mass and echolocation
residual plot with Type variable

                                           Plot of resid*Mass.  Symbol is value of Type.                                            
                                                                                                                                    
        resid |                                                                                                                     
              |                                                                                                                     
         12.5 +                                                        2                                                            
              |                                                                                                                     
              |                                                                                                                     
              |                                                                                                                     
              |                                                                                                                     
         10.0 +                                                                                                                     
              |                                                                                                                     
              |                                                                                                                     
              |                                             2                                                                       
              |                                                                                                                     
          7.5 +                                                                                                                     
              |                                                                                                                     
              |                                                                                                                     
              |                                                                                                                     
              |                                                                                                                     
          5.0 +                                                                                                                     
              |                                                                                                                     
              |                                                                                                                     
              |                                                                                                                     
              |                                                                                                                     
          2.5 +                  2                                                                                                  
              |                                                                                                                     
              |                                    1                                                                  1             
              |           2                          2                                                                              
              |                                                                                                                     
          0.0 +   3          3                                                                                                      
              |                                                                                                                     
              |                                                                                                                     
              |                                           1                                        1                                
              |       2                                          2                                                                  
         -2.5 +     2                                                                                                               
              |                              2                                                                                      
              |                                                    2                                                                
              |                                                           2                                                         
              |                                                                                                                     
         -5.0 +                                                                                                                     
              |                                                                                                                     
              |                                                                                                                     
              |                                                                                                                     
              |                                                                                                                     
         -7.5 +                                                                                                                     
              |                                                                2                                                    
              |                                                                                                                     
              |                                                                                                                     
              |                                                                                                                     
        -10.0 +                                                                                                                     
              |                                                                                                                     
              ---+------------+------------+------------+------------+------------+------------+------------+------------+--        
                 0           100          200          300          400          500          600          700          800         
                                                                                                                                    
                                                                   Mass                                                             
                                                                                                                                    
NOTE: 2 obs hidden.                                                                                                                 


Chapter 10 : Relationship of bat energy expenditure to mass and echolocation
residual plot with Type variable

The UNIVARIATE Procedure
Variable: resid

Moments
N 20 Sum Weights 20
Mean 0 Sum Observations 0
Std Deviation 4.32697997 Variance 18.7227557
Skewness 1.33237673 Kurtosis 3.39626972
Uncorrected SS 355.732358 Corrected SS 355.732358
Coeff Variation . Std Error Mean 0.96754214

Basic Statistical Measures
Location Variability
Mean 0.00000 Std Deviation 4.32698
Median -0.08219 Variance 18.72276
Mode . Range 20.50868
    Interquartile Range 3.43666

Tests for Location: Mu0=0
Test Statistic p Value
Student's t t 0 Pr > |t| 1.0000
Sign M -1 Pr >= |M| 0.8238
Signed Rank S -20 Pr >= |S| 0.4749

Tests for Normality
Test Statistic p Value
Shapiro-Wilk W 0.870782 Pr < W 0.0121
Kolmogorov-Smirnov D 0.193724 Pr > D 0.0474
Cramer-von Mises W-Sq 0.170174 Pr > W-Sq 0.0118
Anderson-Darling A-Sq 1.023665 Pr > A-Sq 0.0087

Quantiles (Definition 5)
Quantile Estimate
100% Max 12.4601054
99% 12.4601054
95% 10.3888658
90% 5.3339637
75% Q3 1.0881443
50% Median -0.0821877
25% Q1 -2.3485125
10% -3.6076693
5% -5.9108521
1% -8.0485704
0% Min -8.0485704

Extreme Observations
Lowest Highest
Value Obs Value Obs
-8.04857 16 1.27702 1
-3.77313 13 1.74083 3
-3.44220 12 2.35030 8
-3.15274 9 8.31763 15
-2.50367 5 12.46011 14

   Stem Leaf                     #  Boxplot                        Normal Probability Plot                                          
      1 2                        1     *        12.5+                                            *    ++                            
      0 8                        1     0            |                                     ++*+++++++++                              
      0 0011122                  7  +--+--+      2.5+                         ++***+**+*+*                                          
     -0 4333222100              10  *-----*         |           *  *+*+**+**** *                                                    
     -0 8                        1     0        -7.5+  ++++*+++++++                                                                 
        ----+----+----+----+                         +----+----+----+----+----+----+----+----+----+----+                            
    Multiply Stem.Leaf by 10**+1                         -2        -1         0        +1        +2                                 
                                                                                                                                    
                                                                                                                                    


Chapter 10 : Relationship of bat energy expenditure to mass and echolocation
Fit of LOG Expenditure on indicator variables with REG

The REG Procedure
Model: MODEL1
Dependent Variable: LExpend

Number of Observations Read 20
Number of Observations Used 20

Analysis of Variance
Source DF Sum of
Squares
Mean
Square
F Value Pr > F
Model 5 29.46993 5.89399 163.44 <.0001
Error 14 0.50487 0.03606    
Corrected Total 19 29.97480      

Root MSE 0.18990 R-Square 0.9832
Dependent Mean 2.48220 Adj R-Sq 0.9771
Coeff Var 7.65047    

Parameter Estimates
Variable DF Parameter
Estimate
Standard
Error
t Value Pr > |t| 95% Confidence Limits
Intercept 1 -1.47052 0.24767 -5.94 <.0001 -2.00172 -0.93932
LMass 1 0.80466 0.08668 9.28 <.0001 0.61874 0.99058
TypeNON 1 1.26807 1.28542 0.99 0.3406 -1.48888 4.02502
TypeBIRD 1 -0.11032 0.38474 -0.29 0.7785 -0.93551 0.71487
LMassNON 1 -0.21487 0.22362 -0.96 0.3529 -0.69450 0.26475
LMassBird 1 0.03071 0.10283 0.30 0.7696 -0.18984 0.25127


Chapter 10 : Relationship of bat energy expenditure to mass and echolocation
Fit of LOG Expenditure on indicator variables with REG

The REG Procedure
Model: MODEL1

Test Test_of_intercepts Results for Dependent Variable LExpend
Source DF Mean
Square
F Value Pr > F
Numerator 2 0.02061 0.57 0.5773
Denominator 14 0.03606    


Chapter 10 : Relationship of bat energy expenditure to mass and echolocation
Fit of LOG Expenditure on indicator variables with REG

The REG Procedure
Model: MODEL1

Test Test_of_slopes Results for Dependent Variable LExpend
Source DF Mean
Square
F Value Pr > F
Numerator 2 0.02422 0.67 0.5265
Denominator 14 0.03606    


Chapter 10 : Relationship of bat energy expenditure to mass and echolocation
residual plot with Type variable

                                           Plot of resid*Mass.  Symbol is value of Type.                                            
                                                                                                                                    
        resid |                                                                                                                     
              |                                                                                                                     
          0.4 +                                                                                                                     
              |                                                                                                                     
              |                                                                                                                     
              |                                                                                                                     
              |                                                                                                                     
              |                                                        2                                                            
              |                                                                                                                     
          0.3 +                                                                                                                     
              |                                                                                                                     
              |                                                                                                                     
              |                                             2                                                                       
              |                                                                                                                     
              |                                                                                                                     
              |           2                                                                                                         
          0.2 +                  2                                                                                                  
              |                                                                                                                     
              |                                                                                                                     
              |                                                                                                                     
              |                                                                                                                     
              |                                                                                                                     
              |                                                                                                                     
          0.1 +   3                                                                                                                 
              |                                                                                                                     
              |                                    1                                                                                
              |   3                                                                                                   1             
              |                                                                                                                     
              |                                                                                                                     
              |                                      2                                                                              
          0.0 +              3                                                                                                      
              |       2                                                                                                             
              |                                                                                                                     
              |                                                                                    1                                
              |                                                                                                                     
              |                                                                                                                     
              |                                           1                                                                         
         -0.1 +                                                  2                                                                  
              |                                                                                                                     
              |                                                           2                                                         
              |                                                    2                                                                
              |   3                                                                                                                 
              |                                                                                                                     
              |     2                                                                                                               
         -0.2 +                                                                                                                     
              |                              2                                                                                      
              |                                                                                                                     
              |                                                                                                                     
              |                                                                2                                                    
              |                                                                                                                     
              |                                                                                                                     
         -0.3 +                                                                                                                     
              |                                                                                                                     
              ---+------------+------------+------------+------------+------------+------------+------------+------------+--        
                 0           100          200          300          400          500          600          700          800         
                                                                                                                                    
                                                                   Mass                                                             


Chapter 10 : Relationship of bat energy expenditure to mass and echolocation
residual plot with Type variable

The UNIVARIATE Procedure
Variable: resid

Moments
N 20 Sum Weights 20
Mean 0 Sum Observations 0
Std Deviation 0.1630092 Variance 0.026572
Skewness 0.43066631 Kurtosis -0.5728204
Uncorrected SS 0.504868 Corrected SS 0.504868
Coeff Variation . Std Error Mean 0.03644997

Basic Statistical Measures
Location Variability
Mean 0.00000 Std Deviation 0.16301
Median -0.00954 Variance 0.02657
Mode . Range 0.57993
    Interquartile Range 0.21621

Tests for Location: Mu0=0
Test Statistic p Value
Student's t t 0 Pr > |t| 1.0000
Sign M 0 Pr >= |M| 1.0000
Signed Rank S -4 Pr >= |S| 0.8983

Tests for Normality
Test Statistic p Value
Shapiro-Wilk W 0.96598 Pr < W 0.6688
Kolmogorov-Smirnov D 0.097033 Pr > D >0.1500
Cramer-von Mises W-Sq 0.032292 Pr > W-Sq >0.2500
Anderson-Darling A-Sq 0.236314 Pr > A-Sq >0.2500

Quantiles (Definition 5)
Quantile Estimate
100% Max 0.32840161
99% 0.32840161
95% 0.29560498
90% 0.23778465
75% Q3 0.08662378
50% Median -0.00953647
25% Q1 -0.12959051
10% -0.20051764
5% -0.23416453
1% -0.25152395
0% Min -0.25152395

Extreme Observations
Lowest Highest
Value Obs Value Obs
-0.251524 16 0.0973826 18
-0.216805 9 0.2061778 8
-0.184230 5 0.2127610 7
-0.152164 20 0.2628083 15
-0.135909 12 0.3284016 14

   Stem Leaf                     #  Boxplot                        Normal Probability Plot                                          
      3 3                        1     |        0.35+                                            *+++++                             
      2 116                      3     |            |                                  * * +*++++                                   
      1 0                        1     |            |                                ++++++                                         
      0 02558                    5  +--+--+     0.05+                         +****+**                                              
     -0 9852                     4  *-----*         |                   ++****                                                      
     -1 8542                     4  +-----+         |             +*+*+**                                                           
     -2 52                       2     |       -0.25+      *++++*+                                                                  
        ----+----+----+----+                         +----+----+----+----+----+----+----+----+----+----+                            
    Multiply Stem.Leaf by 10**-1                         -2        -1         0        +1        +2                                 
                                                                                                                                    
                                                                                                                                    


Chapter 10 : Relationship of bat energy expenditure to mass and echolocation
Fit of LOG Expenditure on indicator variables with REG

The REG Procedure
Model: MODEL1
Dependent Variable: LExpend

Number of Observations Read 20
Number of Observations Used 20

Analysis of Variance
Source DF Sum of
Squares
Mean
Square
F Value Pr > F
Model 3 29.42148 9.80716 283.59 <.0001
Error 16 0.55332 0.03458    
Corrected Total 19 29.97480      

Root MSE 0.18596 R-Square 0.9815
Dependent Mean 2.48220 Adj R-Sq 0.9781
Coeff Var 7.49187    

Parameter Estimates
Variable DF Parameter
Estimate
Standard
Error
t Value Pr > |t| 95% Confidence Limits
Intercept 1 -1.49770 0.14987 -9.99 <.0001 -1.81540 -1.17999
LMass 1 0.81496 0.04454 18.30 <.0001 0.72053 0.90938
TypeNON 1 -0.07866 0.20268 -0.39 0.7030 -0.50832 0.35100
TypeBIRD 1 0.02360 0.15760 0.15 0.8828 -0.31050 0.35770


Chapter 10 : Relationship of bat energy expenditure to mass and echolocation
Fit of LOG Expenditure on indicator variables with REG

The REG Procedure
Model: MODEL1

Test Test_of_intercepts Results for Dependent Variable LExpend
Source DF Mean
Square
F Value Pr > F
Numerator 2 0.01479 0.43 0.6593
Denominator 16 0.03458    


Chapter 10 : Relationship of bat energy expenditure to mass and echolocation
Fit of log Expenditure on indicator variables with GLM

The GLM Procedure

Class Level Information
Class Levels Values
Type 3 1 2 3

Number of Observations Read 20
Number of Observations Used 20


Chapter 10 : Relationship of bat energy expenditure to mass and echolocation
Fit of log Expenditure on indicator variables with GLM

The GLM Procedure
 
Dependent Variable: LExpend

Source DF Sum of Squares Mean Square F Value Pr > F
Model 5 29.46993221 5.89398644 163.44 <.0001
Error 14 0.50486800 0.03606200    
Corrected Total 19 29.97480021      

R-Square Coeff Var Root MSE LExpend Mean
0.983157 7.650468 0.189900 2.482201

Source DF Type I SS Mean Square F Value Pr > F
LMass 1 29.39190909 29.39190909 815.04 <.0001
Type 2 0.02957359 0.01478680 0.41 0.6713
LMass*Type 2 0.04844954 0.02422477 0.67 0.5265

Source DF Type III SS Mean Square F Value Pr > F
LMass 1 3.37875389 3.37875389 93.69 <.0001
Type 2 0.04122472 0.02061236 0.57 0.5773
LMass*Type 2 0.04844954 0.02422477 0.67 0.5265

Parameter Estimate   Standard Error t Value Pr > |t|
Intercept -1.470515265 B 0.24767033 -5.94 <.0001
LMass 0.804657049 B 0.08668453 9.28 <.0001
Type 1 1.268067693 B 1.28542004 0.99 0.3406
Type 2 -0.110322504 B 0.38474216 -0.29 0.7785
Type 3 0.000000000 B . . .
LMass*Type 1 -0.214874992 B 0.22362264 -0.96 0.3529
LMass*Type 2 0.030713281 B 0.10283304 0.30 0.7696
LMass*Type 3 0.000000000 B . . .


The X'X matrix has been found to be singular, and a generalized inverse was used to solve the normal equations. Terms whose estimates are followed by the letter 'B' are not uniquely estimable.


Chapter 10 : Relationship of bat energy expenditure to mass and echolocation
residual plot with Type variable

                                           Plot of resid*Mass.  Symbol is value of Type.                                            
                                                                                                                                    
        resid |                                                                                                                     
              |                                                                                                                     
          0.4 +                                                                                                                     
              |                                                                                                                     
              |                                                                                                                     
              |                                                                                                                     
              |                                                                                                                     
              |                                                        2                                                            
              |                                                                                                                     
          0.3 +                                                                                                                     
              |                                                                                                                     
              |                                                                                                                     
              |                                             2                                                                       
              |                                                                                                                     
              |                                                                                                                     
              |           2                                                                                                         
          0.2 +                  2                                                                                                  
              |                                                                                                                     
              |                                                                                                                     
              |                                                                                                                     
              |                                                                                                                     
              |                                                                                                                     
              |                                                                                                                     
          0.1 +   3                                                                                                                 
              |                                                                                                                     
              |                                    1                                                                                
              |   3                                                                                                   1             
              |                                                                                                                     
              |                                                                                                                     
              |                                      2                                                                              
          0.0 +              3                                                                                                      
              |       2                                                                                                             
              |                                                                                                                     
              |                                                                                    1                                
              |                                                                                                                     
              |                                                                                                                     
              |                                           1                                                                         
         -0.1 +                                                  2                                                                  
              |                                                                                                                     
              |                                                           2                                                         
              |                                                    2                                                                
              |   3                                                                                                                 
              |                                                                                                                     
              |     2                                                                                                               
         -0.2 +                                                                                                                     
              |                              2                                                                                      
              |                                                                                                                     
              |                                                                                                                     
              |                                                                2                                                    
              |                                                                                                                     
              |                                                                                                                     
         -0.3 +                                                                                                                     
              |                                                                                                                     
              ---+------------+------------+------------+------------+------------+------------+------------+------------+--        
                 0           100          200          300          400          500          600          700          800         
                                                                                                                                    
                                                                   Mass                                                             


Chapter 10 : Relationship of bat energy expenditure to mass and echolocation
Analysis of Covariance with GLM

The GLM Procedure

Class Level Information
Class Levels Values
Type 3 1 2 3

Number of Observations Read 20
Number of Observations Used 20


Chapter 10 : Relationship of bat energy expenditure to mass and echolocation
Analysis of Covariance with GLM

The GLM Procedure
 
Dependent Variable: LExpend

Source DF Sum of Squares Mean Square F Value Pr > F
Model 5 29.46993221 5.89398644 163.44 <.0001
Error 14 0.50486800 0.03606200    
Corrected Total 19 29.97480021      

R-Square Coeff Var Root MSE LExpend Mean
0.983157 7.650468 0.189900 2.482201

Source DF Type I SS Mean Square F Value Pr > F
LMass 1 29.39190909 29.39190909 815.04 <.0001
Type 2 0.02957359 0.01478680 0.41 0.6713
LMass*Type 2 0.04844954 0.02422477 0.67 0.5265

Source DF Type III SS Mean Square F Value Pr > F
LMass 1 3.37875389 3.37875389 93.69 <.0001
Type 2 0.04122472 0.02061236 0.57 0.5773
LMass*Type 2 0.04844954 0.02422477 0.67 0.5265

Parameter Estimate   Standard Error t Value Pr > |t|
Intercept -1.470515265 B 0.24767033 -5.94 <.0001
LMass 0.804657049 B 0.08668453 9.28 <.0001
Type 1 1.268067693 B 1.28542004 0.99 0.3406
Type 2 -0.110322504 B 0.38474216 -0.29 0.7785
Type 3 0.000000000 B . . .
LMass*Type 1 -0.214874992 B 0.22362264 -0.96 0.3529
LMass*Type 2 0.030713281 B 0.10283304 0.30 0.7696
LMass*Type 3 0.000000000 B . . .


The X'X matrix has been found to be singular, and a generalized inverse was used to solve the normal equations. Terms whose estimates are followed by the letter 'B' are not uniquely estimable.


Chapter 10 : Relationship of bat energy expenditure to mass and echolocation
Analysis of Covariance with MIXED

The Mixed Procedure

Model Information
Data Set WORK.BATDAT
Dependent Variable LExpend
Covariance Structure Diagonal
Estimation Method REML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Residual

Class Level Information
Class Levels Values
Type 3 1 2 3

Dimensions
Covariance Parameters 1
Columns in X 8
Columns in Z 0
Subjects 1
Max Obs Per Subject 20

Number of Observations
Number of Observations Read 20
Number of Observations Used 20
Number of Observations Not Used 0

Covariance Parameter Estimates
Cov Parm Estimate
Residual 0.03606

Fit Statistics
-2 Res Log Likelihood 2.3
AIC (smaller is better) 4.3
AICC (smaller is better) 4.7
BIC (smaller is better) 5.0

Solution for Fixed Effects
Effect Type Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept   -1.4705 0.2477 14 -5.94 <.0001 0.05 -2.0017 -0.9393
LMass   0.8047 0.08668 14 9.28 <.0001 0.05 0.6187 0.9906
Type 1 1.2681 1.2854 14 0.99 0.3406 0.05 -1.4889 4.0250
Type 2 -0.1103 0.3847 14 -0.29 0.7785 0.05 -0.9355 0.7149
Type 3 0 . . . . . . .
LMass*Type 1 -0.2149 0.2236 14 -0.96 0.3529 0.05 -0.6945 0.2647
LMass*Type 2 0.03071 0.1028 14 0.30 0.7696 0.05 -0.1898 0.2513
LMass*Type 3 0 . . . . . . .

Type 3 Tests of Fixed Effects
Effect Num DF Den DF F Value Pr > F
LMass 1 14 93.69 <.0001
Type 2 14 0.57 0.5773
LMass*Type 2 14 0.67 0.5265