The SAS System          13:03 Friday, December 1, 2006 233

                                                                                                     

                                        The DISCRIM Procedure                                         

                                                                                                     

                       Observations      14          DF Total                13                      

                       Variables          8          DF Within Classes       11                      

                       Classes            3          DF Between Classes       2                      

                                                                                                      

                                                                                                     

                                       Class Level Information                                       

                                                                                                      

                        Variable                                                  Prior              

               Known    Name        Frequency       Weight    Proportion    Probability               

                                                                                                     

               E        E                   5       5.0000      0.357143       0.333333              

               L        L                   5       5.0000      0.357143       0.333333              

               M        M                   4       4.0000      0.285714       0.333333              

                                            The SAS System          13:03 Friday, December 1, 2006 234

                                                                                                     

                                        The DISCRIM Procedure                                        

                                      Within-Class SSCP Matrices                                     

                                                                                                     

                                              Known = E                                               

                                                                                                     

           Variable             FreqA             FreqB             FreqC            ClustA          

                                                                                                      

           FreqA          3297.200000        984.200000       2087.400000       -118.688721          

           FreqB           984.200000        533.200000       1233.400000        -27.377958          

           FreqC          2087.400000       1233.400000       2934.800000        -48.768093          

           ClustA         -118.688721        -27.377958        -48.768093          5.727342          

           ClustB           92.028575         32.838097         71.104766         -2.842346          

           ClustC           97.839659        -76.238331       -211.147553         -5.100506          

           dbhA             95.738157         17.720863         16.705819         -6.347068          

           dbhC             -3.903879         -2.720325         -3.617752          0.447492          

                                                                                                     

                                              Known = E                                              

                                                                                                     

           Variable            ClustB            ClustC              dbhA              dbhC          

                                                                                                     

           FreqA            92.028575         97.839659         95.738157         -3.903879          

           FreqB            32.838097        -76.238331         17.720863         -2.720325          

           FreqC            71.104766       -211.147553         16.705819         -3.617752          

           ClustA           -2.842346         -5.100506         -6.347068          0.447492          

           ClustB            2.940590          1.961979          2.102198         -0.138772          

           ClustC            1.961979         59.474998          5.224842          0.654575          

           dbhA              2.102198          5.224842          9.180947         -0.947068          

           dbhC             -0.138772          0.654575         -0.947068          0.161735          

                                                                                                      

------------------------------------------------------------------------------------------------------

                                                                                                     

                                                                                                      

                                              Known = L                                              

                                                                                                      

           Variable             FreqA             FreqB             FreqC            ClustA          

                                                                                                     

           FreqA           1576.00000        2004.00000        4806.00000         -48.13521          

           FreqB           2004.00000        3550.80000        7040.20000         -27.40419          

           FreqC           4806.00000        7040.20000       28174.80000        -229.55747          

           ClustA           -48.13521         -27.40419        -229.55747           3.69403          

           ClustB           -39.30934         -16.60900          22.35297           1.23448          

           ClustC            -7.27049           8.09570         -53.56219           1.30532          

           dbhA            -176.02143        -100.78225        -676.46634          10.62318          

           dbhC              -1.23434          -1.41882         -37.71696           0.38397          

                                                                                                     

                                              Known = L                                              

                                                                                                      

           Variable            ClustB            ClustC              dbhA              dbhC          

                                                                                                      

           FreqA            -39.30934          -7.27049        -176.02143          -1.23434          

           FreqB            -16.60900           8.09570        -100.78225          -1.41882          

           FreqC             22.35297         -53.56219        -676.46634         -37.71696          

           ClustA             1.23448           1.30532          10.62318           0.38397          

           ClustB             3.20995           0.22919           8.13741          -0.31764          

                                            The SAS System          13:03 Friday, December 1, 2006 235

                                                                                                     

                                        The DISCRIM Procedure                                        

                                      Within-Class SSCP Matrices                                     

                                                                                                      

                                              Known = L                                              

                                                                                                      

           Variable            ClustB            ClustC              dbhA              dbhC          

                                                                                                     

           ClustC             0.22919           0.60138           2.38177           0.17919          

           dbhA               8.13741           2.38177          65.17794           0.11697          

           dbhC              -0.31764           0.17919           0.11697           0.11343           

                                                                                                     

------------------------------------------------------------------------------------------------------

                                                                                                      

                                                                                                     

                                              Known = M                                               

                                                                                                     

           Variable             FreqA             FreqB             FreqC            ClustA          

                                                                                                      

           FreqA            621.00000        -803.50000        -524.00000          41.43094          

           FreqB           -803.50000        6768.75000        7891.50000         -43.63896          

           FreqC           -524.00000        7891.50000       10625.00000          -6.57327          

           ClustA            41.43094         -43.63896          -6.57327           3.00937          

           ClustB           -41.42910          70.12295          57.35609          -2.71224          

           ClustC            22.60445         -79.10841         -92.06829           1.27433          

           dbhA              14.81448         -17.99293          -6.09364           1.06132          

           dbhC             -37.64284          34.41282          40.64867          -2.14940          

                                                                                                     

                                              Known = M                                              

                                                                                                     

           Variable            ClustB            ClustC              dbhA              dbhC          

                                                                                                     

           FreqA            -41.42910          22.60445          14.81448         -37.64284          

           FreqB             70.12295         -79.10841         -17.99293          34.41282          

           FreqC             57.35609         -92.06829          -6.09364          40.64867          

           ClustA            -2.71224           1.27433           1.06132          -2.14940          

           ClustB             2.81383          -1.66664          -0.97777           2.50916          

           ClustC            -1.66664           1.35158           0.48328          -1.49536          

           dbhA              -0.97777           0.48328           0.37572          -0.78057          

           dbhC               2.50916          -1.49536          -0.78057           2.97413          

                                                                                                      

------------------------------------------------------------------------------------------------------

                                            The SAS System          13:03 Friday, December 1, 2006 236

                                                                                                      

                                        The DISCRIM Procedure                                        

                                                                                                      

                                   Pooled Within-Class SSCP Matrix                                   

                                                                                                     

           Variable             FreqA             FreqB             FreqC            ClustA          

                                                                                                     

           FreqA           5494.20000        2184.70000        6369.40000        -125.39298          

           FreqB           2184.70000       10852.75000       16165.10000         -98.42111          

           FreqC           6369.40000       16165.10000       41734.60000        -284.89883          

           ClustA          -125.39298         -98.42111        -284.89883          12.43074          

           ClustB            11.29013          86.35205         150.81383          -4.32011          

           ClustC           113.17362        -147.25104        -356.77804          -2.52086          

           dbhA             -65.46879        -101.05432        -665.85417           5.33743          

           dbhC             -42.78106          30.27368          -0.68604          -1.31793          

                                                                                                      

                                   Pooled Within-Class SSCP Matrix                                   

                                                                                                      

           Variable            ClustB            ClustC              dbhA              dbhC          

                                                                                                     

           FreqA             11.29013         113.17362         -65.46879         -42.78106          

           FreqB             86.35205        -147.25104        -101.05432          30.27368          

           FreqC            150.81383        -356.77804        -665.85417          -0.68604          

           ClustA            -4.32011          -2.52086           5.33743          -1.31793          

           ClustB             8.96438           0.52453           9.26183           2.05274          

           ClustC             0.52453          61.42795           8.08989          -0.66159          

           dbhA               9.26183           8.08989          74.73461          -1.61066          

           dbhC               2.05274          -0.66159          -1.61066           3.24930          

                                                                                                     

                                                                                                     

                                      Between-Class SSCP Matrix                                      

                                                                                                     

           Variable             FreqA             FreqB             FreqC            ClustA          

                                                                                                     

           FreqA            138.72857        -419.91429       -1755.32857           9.53221          

           FreqB           -419.91429        8101.60714        5049.11429        -200.17627          

           FreqC          -1755.32857        5049.11429       22220.32857        -113.98795          

           ClustA             9.53221        -200.17627        -113.98795           4.95208          

           ClustB            -4.02457          95.43389          47.70448          -2.36465          

           ClustC            35.82142        -259.08908        -447.42332           6.24021          

           dbhA             -49.27206          91.27859         625.67474          -1.93426          

           dbhC               7.84221         -91.15257         -96.62123           2.22974          

                                                                                                      

                                      Between-Class SSCP Matrix                                      

                                                                                                      

           Variable            ClustB            ClustC              dbhA              dbhC          

                                                                                                     

           FreqA             -4.02457          35.82142         -49.27206           7.84221          

           FreqB             95.43389        -259.08908          91.27859         -91.15257          

           FreqC             47.70448        -447.42332         625.67474         -96.62123           

           ClustA            -2.36465           6.24021          -1.93426           2.22974          

           ClustB             1.13144          -2.87548           0.72417          -1.04917          

           ClustC            -2.87548          12.57269         -11.44639           3.51193          

           dbhA               0.72417         -11.44639          17.99005          -2.21424          

           dbhC              -1.04917           3.51193          -2.21424           1.10868           

                                            The SAS System          13:03 Friday, December 1, 2006 237

                                                                                                     

                                        The DISCRIM Procedure                                        

                                                                                                     

                                       Total-Sample SSCP Matrix                                       

                                                                                                     

           Variable             FreqA             FreqB             FreqC            ClustA          

                                                                                                      

           FreqA           5632.92857        1764.78571        4614.07143        -115.86077          

           FreqB           1764.78571       18954.35714       21214.21429        -298.59738          

           FreqC           4614.07143       21214.21429       63954.92857        -398.88678          

           ClustA          -115.86077        -298.59738        -398.88678          17.38282          

           ClustB             7.26557         181.78594         198.51831          -6.68476          

           ClustC           148.99505        -406.34012        -804.20135           3.71936          

           dbhA            -114.74086          -9.77573         -40.17943           3.40317          

           dbhC             -34.93884         -60.87889         -97.30727           0.91181          

                                                                                                     

                                       Total-Sample SSCP Matrix                                      

                                                                                                     

           Variable            ClustB            ClustC              dbhA              dbhC          

                                                                                                     

           FreqA              7.26557         148.99505        -114.74086         -34.93884          

           FreqB            181.78594        -406.34012          -9.77573         -60.87889          

           FreqC            198.51831        -804.20135         -40.17943         -97.30727          

           ClustA            -6.68476           3.71936           3.40317           0.91181          

           ClustB            10.09582          -2.35095           9.98601           1.00357          

           ClustC            -2.35095          74.00064          -3.35650           2.85034          

           dbhA               9.98601          -3.35650          92.72465          -3.82490          

           dbhC               1.00357           2.85034          -3.82490           4.35797          

                                            The SAS System          13:03 Friday, December 1, 2006 238

                                                                                                     

                                        The DISCRIM Procedure                                        

                                   Within-Class Covariance Matrices                                  

                                                                                                     

                                        Known = E,     DF = 4                                         

                                                                                                     

           Variable             FreqA             FreqB             FreqC            ClustA          

                                                                                                      

           FreqA          824.3000000       246.0500000       521.8500000       -29.6721804          

           FreqB          246.0500000       133.3000000       308.3500000        -6.8444896          

           FreqC          521.8500000       308.3500000       733.7000000       -12.1920232          

           ClustA         -29.6721804        -6.8444896       -12.1920232         1.4318356          

           ClustB          23.0071438         8.2095243        17.7761916        -0.7105865          

           ClustC          24.4599148       -19.0595827       -52.7868882        -1.2751264          

           dbhA            23.9345393         4.4302158         4.1764549        -1.5867671          

           dbhC            -0.9759698        -0.6800813        -0.9044381         0.1118730          

                                                                                                     

                                        Known = E,     DF = 4                                        

                                                                                                     

           Variable            ClustB            ClustC              dbhA              dbhC          

                                                                                                     

           FreqA           23.0071438        24.4599148        23.9345393        -0.9759698          

           FreqB            8.2095243       -19.0595827         4.4302158        -0.6800813          

           FreqC           17.7761916       -52.7868882         4.1764549        -0.9044381          

           ClustA          -0.7105865        -1.2751264        -1.5867671         0.1118730          

           ClustB           0.7351475         0.4904948         0.5255495        -0.0346930          

           ClustC           0.4904948        14.8687496         1.3062104         0.1636438          

           dbhA             0.5255495         1.3062104         2.2952369        -0.2367671          

           dbhC            -0.0346930         0.1636438        -0.2367671         0.0404338          

                                                                                                      

------------------------------------------------------------------------------------------------------

                                                                                                     

                                                                                                      

                                        Known = L,     DF = 4                                        

                                                                                                      

           Variable             FreqA             FreqB             FreqC            ClustA          

                                                                                                     

           FreqA           394.000000        501.000000       1201.500000        -12.033802          

           FreqB           501.000000        887.700000       1760.050000         -6.851046          

           FreqC          1201.500000       1760.050000       7043.700000        -57.389367          

           ClustA          -12.033802         -6.851046        -57.389367          0.923507          

           ClustB           -9.827336         -4.152250          5.588244          0.308619          

           ClustC           -1.817622          2.023924        -13.390549          0.326330          

           dbhA            -44.005358        -25.195562       -169.116585          2.655795          

           dbhC             -0.308585         -0.354705         -9.429241          0.095994          

                                                                                                     

                                        Known = L,     DF = 4                                         

                                                                                                     

           Variable            ClustB            ClustC              dbhA              dbhC          

                                                                                                      

           FreqA            -9.827336         -1.817622        -44.005358         -0.308585          

           FreqB            -4.152250          2.023924        -25.195562         -0.354705           

           FreqC             5.588244        -13.390549       -169.116585         -9.429241          

           ClustA            0.308619          0.326330          2.655795          0.095994          

           ClustB            0.802488          0.057297          2.034352         -0.079411          

                                            The SAS System          13:03 Friday, December 1, 2006 239

                                                                                                      

                                        The DISCRIM Procedure                                        

                                   Within-Class Covariance Matrices                                  

                                                                                                      

                                        Known = L,     DF = 4                                        

                                                                                                      

           Variable            ClustB            ClustC              dbhA              dbhC          

                                                                                                     

           ClustC            0.057297          0.150344          0.595443          0.044799          

           dbhA              2.034352          0.595443         16.294486          0.029244          

           dbhC             -0.079411          0.044799          0.029244          0.028357          

                                                                                                     

------------------------------------------------------------------------------------------------------

                                                                                                      

                                                                                                     

                                        Known = M,     DF = 3                                         

                                                                                                     

           Variable             FreqA             FreqB             FreqC            ClustA          

                                                                                                      

           FreqA           207.000000       -267.833333       -174.666667         13.810315          

           FreqB          -267.833333       2256.250000       2630.500000        -14.546321          

           FreqC          -174.666667       2630.500000       3541.666667         -2.191090          

           ClustA           13.810315        -14.546321         -2.191090          1.003124          

           ClustB          -13.809699         23.374316         19.118696         -0.904081          

           ClustC            7.534816        -26.369470        -30.689429          0.424777          

           dbhA              4.938160         -5.997644         -2.031215          0.353774          

           dbhC            -12.547612         11.470941         13.549557         -0.716467          

                                                                                                     

                                        Known = M,     DF = 3                                        

                                                                                                     

           Variable            ClustB            ClustC              dbhA              dbhC          

                                                                                                     

           FreqA           -13.809699          7.534816          4.938160        -12.547612          

           FreqB            23.374316        -26.369470         -5.997644         11.470941          

           FreqC            19.118696        -30.689429         -2.031215         13.549557          

           ClustA           -0.904081          0.424777          0.353774         -0.716467          

           ClustB            0.937945         -0.555545         -0.325925          0.836385          

           ClustC           -0.555545          0.450525          0.161093         -0.498454          

           dbhA             -0.325925          0.161093          0.125238         -0.260189          

           dbhC              0.836385         -0.498454         -0.260189          0.991378          

                                                                                                      

------------------------------------------------------------------------------------------------------

                                            The SAS System          13:03 Friday, December 1, 2006 240

                                                                                                      

                                        The DISCRIM Procedure                                        

                                                                                                      

                          Pooled Within-Class Covariance Matrix,     DF = 11                         

                                                                                                     

           Variable             FreqA             FreqB             FreqC            ClustA          

                                                                                                     

           FreqA           499.472727        198.609091        579.036364        -11.399362          

           FreqB           198.609091        986.613636       1469.554545         -8.947373          

           FreqC           579.036364       1469.554545       3794.054545        -25.899894          

           ClustA          -11.399362         -8.947373        -25.899894          1.130067          

           ClustB            1.026376          7.850186         13.710348         -0.392738          

           ClustC           10.288511        -13.386458        -32.434367         -0.229169          

           dbhA             -5.951708         -9.186756        -60.532197          0.485221          

           dbhC             -3.889187          2.752153         -0.062368         -0.119812          

                                                                                                      

                          Pooled Within-Class Covariance Matrix,     DF = 11                         

                                                                                                      

           Variable            ClustB            ClustC              dbhA              dbhC          

                                                                                                     

           FreqA             1.026376         10.288511         -5.951708         -3.889187          

           FreqB             7.850186        -13.386458         -9.186756          2.752153          

           FreqC            13.710348        -32.434367        -60.532197         -0.062368          

           ClustA           -0.392738         -0.229169          0.485221         -0.119812          

           ClustB            0.814943          0.047685          0.841985          0.186613          

           ClustC            0.047685          5.584359          0.735445         -0.060145          

           dbhA              0.841985          0.735445          6.794055         -0.146424          

           dbhC              0.186613         -0.060145         -0.146424          0.295391          

                                                                                                     

                                                                                                     

                             Between-Class Covariance Matrix,     DF = 2                             

                                                                                                     

           Variable             FreqA             FreqB             FreqC            ClustA          

                                                                                                     

           FreqA            14.863776        -44.990816       -188.070918          1.021308           

           FreqB           -44.990816        868.029337        540.976531        -21.447458          

           FreqC          -188.070918        540.976531       2380.749490        -12.212995          

           ClustA            1.021308        -21.447458        -12.212995          0.530580          

           ClustB           -0.431204         10.225060          5.111195         -0.253355          

           ClustC            3.838010        -27.759544        -47.938213          0.668594           

           dbhA             -5.279150          9.779849         67.036579         -0.207242          

           dbhC              0.840237         -9.766347        -10.352274          0.238901          

                                                                                                      

                             Between-Class Covariance Matrix,     DF = 2                             

                                                                                                      

           Variable            ClustB            ClustC              dbhA              dbhC          

                                                                                                     

           FreqA            -0.431204          3.838010         -5.279150          0.840237          

           FreqB            10.225060        -27.759544          9.779849         -9.766347          

           FreqC             5.111195        -47.938213         67.036579        -10.352274          

           ClustA           -0.253355          0.668594         -0.207242          0.238901          

           ClustB            0.121226         -0.308087          0.077590         -0.112411          

           ClustC           -0.308087          1.347073         -1.226399          0.376278          

           dbhA              0.077590         -1.226399          1.927505         -0.237239          

           dbhC             -0.112411          0.376278         -0.237239          0.118787          

                                            The SAS System          13:03 Friday, December 1, 2006 241

                                                                                                     

                                        The DISCRIM Procedure                                        

                                                                                                     

                             Total-Sample Covariance Matrix,     DF = 13                              

                                                                                                     

           Variable             FreqA             FreqB             FreqC            ClustA          

                                                                                                      

           FreqA           433.302198        135.752747        354.928571         -8.912367          

           FreqB           135.752747       1458.027473       1631.862637        -22.969029          

           FreqC           354.928571       1631.862637       4919.609890        -30.683599          

           ClustA           -8.912367        -22.969029        -30.683599          1.337140          

           ClustB            0.558890         13.983534         15.270639         -0.514212          

           ClustC           11.461157        -31.256933        -61.861643          0.286105          

           dbhA             -8.826220         -0.751979         -3.090725          0.261782          

           dbhC             -2.687603         -4.682992         -7.485175          0.070139          

                                                                                                     

                             Total-Sample Covariance Matrix,     DF = 13                             

                                                                                                     

           Variable            ClustB            ClustC              dbhA              dbhC          

                                                                                                     

           FreqA             0.558890         11.461157         -8.826220         -2.687603          

           FreqB            13.983534        -31.256933         -0.751979         -4.682992          

           FreqC            15.270639        -61.861643         -3.090725         -7.485175          

           ClustA           -0.514212          0.286105          0.261782          0.070139          

           ClustB            0.776601         -0.180843          0.768154          0.077198          

           ClustC           -0.180843          5.692357         -0.258192          0.219257          

           dbhA              0.768154         -0.258192          7.132666         -0.294223          

           dbhC              0.077198          0.219257         -0.294223          0.335229          

                                            The SAS System          13:03 Friday, December 1, 2006 242

                                                                                                     

                                        The DISCRIM Procedure                                        

                          Within-Class Correlation Coefficients  /  Pr > |r|                         

                                                                                                     

                                              Known = E                                               

                                                                                                     

   Variable      FreqA      FreqB      FreqC     ClustA     ClustB     ClustC       dbhA       dbhC  

                                                                                                      

   FreqA       1.00000    0.74228    0.67103   -0.86369    0.93462    0.22094    0.55026   -0.16905  

                           0.1508     0.2150     0.0592     0.0199     0.7210     0.3366     0.7858  

                                                                                                     

   FreqB       0.74228    1.00000    0.98598   -0.49543    0.82931   -0.42812    0.25328   -0.29294  

                0.1508                0.0020     0.3961     0.0825     0.4720     0.6810     0.6324  

                                                                                                     

   FreqC       0.67103    0.98598    1.00000   -0.37616    0.76541   -0.50539    0.10177   -0.16605  

                0.2150     0.0020                0.5326     0.1315     0.3851     0.8706     0.7896  

                                                                                                     

   ClustA     -0.86369   -0.49543   -0.37616    1.00000   -0.69260   -0.27636   -0.87529    0.46495  

                0.0592     0.3961     0.5326                0.1949     0.6527     0.0519     0.4301  

                                                                                                      

   ClustB      0.93462    0.82931    0.76541   -0.69260    1.00000    0.14836    0.40459   -0.20123  

                0.0199     0.0825     0.1315     0.1949                0.8118     0.4993     0.7455  

                                                                                                      

   ClustC      0.22094   -0.42812   -0.50539   -0.27636    0.14836    1.00000    0.22360    0.21105  

                0.7210     0.4720     0.3851     0.6527     0.8118                0.7177     0.7333  

                                                                                                     

   dbhA        0.55026    0.25328    0.10177   -0.87529    0.40459    0.22360    1.00000   -0.77720  

                0.3366     0.6810     0.8706     0.0519     0.4993     0.7177                0.1219  

                                                                                                     

   dbhC       -0.16905   -0.29294   -0.16605    0.46495   -0.20123    0.21105   -0.77720    1.00000  

                0.7858     0.6324     0.7896     0.4301     0.7455     0.7333     0.1219             

                                                                                                      

------------------------------------------------------------------------------------------------------

                                            The SAS System          13:03 Friday, December 1, 2006 243

                                                                                                      

                                        The DISCRIM Procedure                                        

                          Within-Class Correlation Coefficients  /  Pr > |r|                          

                                                                                                     

                                              Known = L                                              

                                                                                                      

   Variable      FreqA      FreqB      FreqC     ClustA     ClustB     ClustC       dbhA       dbhC  

                                                                                                      

   FreqA       1.00000    0.84714    0.72123   -0.63086   -0.55267   -0.23616   -0.54921   -0.09232  

                           0.0701     0.1691     0.2538     0.3340     0.7021     0.3377     0.8826  

                                                                                                      

   FreqB       0.84714    1.00000    0.70387   -0.23928   -0.15557    0.17519   -0.20949   -0.07070  

                0.0701                0.1846     0.6983     0.8027     0.7781     0.7352     0.9101  

                                                                                                     

   FreqC       0.72123    0.70387    1.00000   -0.71156    0.07433   -0.41149   -0.49919   -0.66718  

                0.1691     0.1846                0.1777     0.9054     0.4913     0.3919     0.2186  

                                                                                                     

   ClustA     -0.63086   -0.23928   -0.71156    1.00000    0.35849    0.87578    0.68463    0.59318  

                0.2538     0.6983     0.1777                0.5535     0.0516     0.2022     0.2917  

                                                                                                     

   ClustB     -0.55267   -0.15557    0.07433    0.35849    1.00000    0.16496    0.56258   -0.52641  

                0.3340     0.8027     0.9054     0.5535                0.7909     0.3235     0.3621  

                                                                                                      

   ClustC     -0.23616    0.17519   -0.41149    0.87578    0.16496    1.00000    0.38043    0.68610  

                0.7021     0.7781     0.4913     0.0516     0.7909                0.5276     0.2009  

                                                                                                      

   dbhA       -0.54921   -0.20949   -0.49919    0.68463    0.56258    0.38043    1.00000    0.04302  

                0.3377     0.7352     0.3919     0.2022     0.3235     0.5276                0.9452  

                                                                                                     

   dbhC       -0.09232   -0.07070   -0.66718    0.59318   -0.52641    0.68610    0.04302    1.00000  

                0.8826     0.9101     0.2186     0.2917     0.3621     0.2009     0.9452             

                                                                                                     

------------------------------------------------------------------------------------------------------

                                            The SAS System          13:03 Friday, December 1, 2006 244

                                                                                                     

                                        The DISCRIM Procedure                                        

                          Within-Class Correlation Coefficients  /  Pr > |r|                         

                                                                                                      

                                              Known = M                                              

                                                                                                     

   Variable      FreqA      FreqB      FreqC     ClustA     ClustB     ClustC       dbhA       dbhC  

                                                                                                     

   FreqA       1.00000   -0.39191   -0.20400    0.95839   -0.99108    0.78024    0.96986   -0.87590  

                           0.6081     0.7960     0.0416     0.0089     0.2198     0.0301     0.1241  

                                                                                                     

   FreqB      -0.39191    1.00000    0.93055   -0.30576    0.50811   -0.82708   -0.35679    0.24254  

                0.6081                0.0694     0.6942     0.4919     0.1729     0.6432     0.7575  

                                                                                                      

   FreqC      -0.20400    0.93055    1.00000   -0.03676    0.33172   -0.76829   -0.09645    0.22867  

                0.7960     0.0694                0.9632     0.6683     0.2317     0.9036     0.7713  

                                                                                                      

   ClustA      0.95839   -0.30576   -0.03676    1.00000   -0.93205    0.63186    0.99811   -0.71845  

                0.0416     0.6942     0.9632                0.0679     0.3681     0.0019     0.2815  

                                                                                                     

   ClustB     -0.99108    0.50811    0.33172   -0.93205    1.00000   -0.85462   -0.95096    0.86736  

                0.0089     0.4919     0.6683     0.0679                0.1454     0.0490     0.1326  

                                                                                                     

   ClustC      0.78024   -0.82708   -0.76829    0.63186   -0.85462    1.00000    0.67819   -0.74584  

                0.2198     0.1729     0.2317     0.3681     0.1454                0.3218     0.2542  

                                                                                                     

   dbhA        0.96986   -0.35679   -0.09645    0.99811   -0.95096    0.67819    1.00000   -0.73841  

                0.0301     0.6432     0.9036     0.0019     0.0490     0.3218                0.2616  

                                                                                                      

   dbhC       -0.87590    0.24254    0.22867   -0.71845    0.86736   -0.74584   -0.73841    1.00000  

                0.1241     0.7575     0.7713     0.2815     0.1326     0.2542     0.2616             

                                                                                                      

------------------------------------------------------------------------------------------------------

                                            The SAS System          13:03 Friday, December 1, 2006 245

                                                                                                     

                                        The DISCRIM Procedure                                        

                                                                                                      

                      Pooled Within-Class Correlation Coefficients  /  Pr > |r|                      

                                                                                                      

   Variable      FreqA      FreqB      FreqC     ClustA     ClustB     ClustC       dbhA       dbhC  

                                                                                                     

   FreqA       1.00000    0.28292    0.42063   -0.47981    0.05087    0.19481   -0.10217   -0.32019  

                           0.3729     0.1733     0.1144     0.8752     0.5440     0.7520     0.3103  

                                                                                                      

   FreqB       0.28292    1.00000    0.75956   -0.26796    0.27685   -0.18035   -0.11221    0.16121  

                0.3729                0.0042     0.3998     0.3837     0.5749     0.7284     0.6167  

                                                                                                     

   FreqC       0.42063    0.75956    1.00000   -0.39554    0.24657   -0.22283   -0.37702   -0.00186  

                0.1733     0.0042                0.2031     0.4398     0.4864     0.2270     0.9954  

                                                                                                     

   ClustA     -0.47981   -0.26796   -0.39554    1.00000   -0.40925   -0.09123    0.17511   -0.20737   

                0.1144     0.3998     0.2031                0.1865     0.7780     0.5862     0.5178  

                                                                                                     

   ClustB      0.05087    0.27685    0.24657   -0.40925    1.00000    0.02235    0.35783    0.38035  

                0.8752     0.3837     0.4398     0.1865                0.9450     0.2534     0.2226  

                                                                                                      

   ClustC      0.19481   -0.18035   -0.22283   -0.09123    0.02235    1.00000    0.11940   -0.04683  

                0.5440     0.5749     0.4864     0.7780     0.9450                0.7117     0.8851  

                                                                                                      

   dbhA       -0.10217   -0.11221   -0.37702    0.17511    0.35783    0.11940    1.00000   -0.10336  

                0.7520     0.7284     0.2270     0.5862     0.2534     0.7117                0.7492  

                                                                                                     

   dbhC       -0.32019    0.16121   -0.00186   -0.20737    0.38035   -0.04683   -0.10336    1.00000  

                0.3103     0.6167     0.9954     0.5178     0.2226     0.8851     0.7492             

                                            The SAS System          13:03 Friday, December 1, 2006 246

                                                                                                      

                                        The DISCRIM Procedure                                        

                                                                                                     

                         Between-Class Correlation Coefficients  /  Pr > |r|                         

                                                                                                     

   Variable      FreqA      FreqB      FreqC     ClustA     ClustB     ClustC       dbhA       dbhC  

                                                                                                     

   FreqA       1.00000   -0.39609   -0.99977    0.36368   -0.32123    0.85772   -0.98628    0.63234  

                           0.7407     0.0136     0.7630     0.7918     0.3438     0.1056     0.5642  

                                                                                                     

   FreqB      -0.39609    1.00000    0.37632   -0.99939    0.99678   -0.81180    0.23909   -0.96179  

                0.7407                0.7544     0.0223     0.0511     0.3970     0.8463     0.1765  

                                                                                                     

   FreqC      -0.99977    0.37632    1.00000   -0.34363    0.30086   -0.84650    0.98959   -0.61560  

                0.0136     0.7544                0.7767     0.8055     0.3574     0.0919     0.5778  

                                                                                                      

   ClustA      0.36368   -0.99939   -0.34363    1.00000   -0.99898    0.79085   -0.20493    0.95161  

                0.7630     0.0223     0.7767                0.0288     0.4193     0.8686     0.1989  

                                                                                                      

   ClustB     -0.32123    0.99678    0.30086   -0.99898    1.00000   -0.76240    0.16051   -0.93676  

                0.7918     0.0511     0.8055     0.0288                0.4480     0.8974     0.2276  

                                                                                                     

   ClustC      0.85772   -0.81180   -0.84650    0.79085   -0.76240    1.00000   -0.76109    0.94065  

                0.3438     0.3970     0.3574     0.4193     0.4480                0.4493     0.2204  

                                                                                                     

   dbhA       -0.98628    0.23909    0.98959   -0.20493    0.16051   -0.76109    1.00000   -0.49580  

                0.1056     0.8463     0.0919     0.8686     0.8974     0.4493                0.6698  

                                                                                                     

   dbhC        0.63234   -0.96179   -0.61560    0.95161   -0.93676    0.94065   -0.49580    1.00000  

                0.5642     0.1765     0.5778     0.1989     0.2276     0.2204     0.6698             

                                            The SAS System          13:03 Friday, December 1, 2006 247

                                                                                                     

                                        The DISCRIM Procedure                                        

                                                                                                      

                          Total-Sample Correlation Coefficients  /  Pr > |r|                         

                                                                                                      

   Variable      FreqA      FreqB      FreqC     ClustA     ClustB     ClustC       dbhA       dbhC  

                                                                                                     

   FreqA       1.00000    0.17079    0.24310   -0.37026    0.03047    0.23077   -0.15876   -0.22300  

                           0.5594     0.4023     0.1925     0.9177     0.4273     0.5877     0.4435  

                                                                                                      

   FreqB       0.17079    1.00000    0.60931   -0.52020    0.41556   -0.34310   -0.00737   -0.21182  

                0.5594                0.0207     0.0565     0.1395     0.2298     0.9800     0.4672  

                                                                                                      

   FreqC       0.24310    0.60931    1.00000   -0.37831    0.24705   -0.36967   -0.01650   -0.18432  

                0.4023     0.0207                0.1823     0.3945     0.1933     0.9554     0.5282  

                                                                                                     

   ClustA     -0.37026   -0.52020   -0.37831    1.00000   -0.50461    0.10370    0.08477    0.10476  

                0.1925     0.0565     0.1823                0.0657     0.7242     0.7733     0.7215  

                                                                                                     

   ClustB      0.03047    0.41556    0.24705   -0.50461    1.00000   -0.08601    0.32638    0.15130  

                0.9177     0.1395     0.3945     0.0657                0.7700     0.2548     0.6056  

                                                                                                     

   ClustC      0.23077   -0.34310   -0.36967    0.10370   -0.08601    1.00000   -0.04052    0.15872  

                0.4273     0.2298     0.1933     0.7242     0.7700                0.8906     0.5878  

                                                                                                      

   dbhA       -0.15876   -0.00737   -0.01650    0.08477    0.32638   -0.04052    1.00000   -0.19027  

                0.5877     0.9800     0.9554     0.7733     0.2548     0.8906                0.5147  

                                                                                                      

   dbhC       -0.22300   -0.21182   -0.18432    0.10476    0.15130    0.15872   -0.19027    1.00000  

                0.4435     0.4672     0.5282     0.7215     0.6056     0.5878     0.5147             

                                            The SAS System          13:03 Friday, December 1, 2006 248

                                                                                                     

                                        The DISCRIM Procedure                                        

                                          Simple Statistics                                          

                                                                                                      

                                             Total-Sample                                            

                                                                                                     

                                                                               Standard              

               Variable        N           Sum          Mean      Variance    Deviation              

                                                                                                      

               FreqA          14     447.00000      31.92857     433.30220      20.8159              

               FreqB          14     487.00000      34.78571          1458      38.1841               

               FreqC          14          1009      72.07143          4920      70.1399              

               ClustA         14      30.61405       2.18672       1.33714       1.1563              

               ClustB         14      12.42322       0.88737       0.77660       0.8812              

               ClustC         14      39.01811       2.78701       5.69236       2.3859              

               dbhA           14       4.12101       0.29436       7.13267       2.6707               

               dbhC           14      -3.34209      -0.23872       0.33523       0.5790              

                                                                                                     

------------------------------------------------------------------------------------------------------

                                                                                                     

                                                                                                      

                                              Known = E                                              

                                                                                                     

                                                                               Standard              

               Variable        N           Sum          Mean      Variance    Deviation              

                                                                                                      

               FreqA           5     177.00000      35.40000     824.30000      28.7106              

               FreqB           5      37.00000       7.40000     133.30000      11.5456              

               FreqC           5     144.00000      28.80000     733.70000      27.0869              

               ClustA          5      14.24289       2.84858       1.43184       1.1966              

               ClustB          5       2.90476       0.58095       0.73515       0.8574              

               ClustC          5      20.27827       4.05565      14.86875       3.8560              

               dbhA            5      -3.97805      -0.79561       2.29524       1.5150              

               dbhC            5       0.62048       0.12410       0.04043       0.2011              

                                                                                                     

------------------------------------------------------------------------------------------------------

                                                                                                     

                                                                                                     

                                              Known = L                                              

                                                                                                     

                                                                               Standard              

               Variable        N           Sum          Mean      Variance    Deviation              

                                                                                                     

               FreqA           5     140.00000      28.00000     394.00000      19.8494              

               FreqB           5     179.00000      35.80000     887.70000      29.7943              

               FreqC           5     611.00000     122.20000          7044      83.9268              

               ClustA          5      10.94798       2.18960       0.92351       0.9610              

               ClustB          5       4.34386       0.86877       0.80249       0.8958              

               ClustC          5      10.06258       2.01252       0.15034       0.3877              

               dbhA            5       8.90902       1.78180      16.29449       4.0366              

               dbhC            5      -1.76724      -0.35345       0.02836       0.1684              

                                                                                                     

------------------------------------------------------------------------------------------------------

                                            The SAS System          13:03 Friday, December 1, 2006 249

                                                                                                     

                                        The DISCRIM Procedure                                         

                                          Simple Statistics                                          

                                                                                                     

                                              Known = M                                              

                                                                                                     

                                                                               Standard              

               Variable        N           Sum          Mean      Variance    Deviation              

                                                                                                     

               FreqA           4     130.00000      32.50000     207.00000      14.3875              

               FreqB           4     271.00000      67.75000          2256      47.5000              

               FreqC           4     254.00000      63.50000          3542      59.5119              

               ClustA          4       5.42318       1.35579       1.00312       1.0016              

               ClustB          4       5.17460       1.29365       0.93794       0.9685              

               ClustC          4       8.67726       2.16931       0.45053       0.6712              

               dbhA            4      -0.80995      -0.20249       0.12524       0.3539              

               dbhC            4      -2.19534      -0.54883       0.99138       0.9957              

                                                                                                     

------------------------------------------------------------------------------------------------------

                                            The SAS System          13:03 Friday, December 1, 2006 250

                                                                                                     

                                        The DISCRIM Procedure                                        

                                                                                                     

                                Total-Sample Standardized Class Means                                

                                                                                                      

                    Variable                 E                 L                 M                   

                                                                                                      

                    FreqA         0.1667680258      -.1887292473      0.0274515269                   

                    FreqB         -.7172015497      0.0265630204      0.8632981617                   

                    FreqC         -.6169300153      0.7146937682      -.1222046910                   

                    ClustA        0.5723716230      0.0024893528      -.7185762197                   

                    ClustB        -.3477111035      -.0211077452      0.4610235609                   

                    ClustC        0.5317341387      -.3246163873      -.2588971892                   

                    dbhA          -.4081201106      0.5569485556      -.1860355562                   

                    dbhC          0.6266393930      -.1981504140      -.5356112238                   

                                                                                                     

                                                                                                      

                             Pooled Within-Class Standardized Class Means                            

                                                                                                      

                    Variable                 E                 L                 M                   

                                                                                                     

                    FreqA          0.155328928      -0.175783766       0.025568548                   

                    FreqB         -0.871867554       0.032291391       1.049470204                   

                    FreqC         -0.702505046       0.813829715      -0.139155836                    

                    ClustA         0.622607485       0.002707838      -0.781644154                   

                    ClustB        -0.339432896      -0.020605218       0.450047642                   

                    ClustC         0.536851193      -0.327740279      -0.261388643                   

                    dbhA          -0.418166656       0.570658757      -0.190615126                   

                    dbhC           0.667559315      -0.211089753      -0.570586952                    

                                                                                                     

                                                                                                     

                                 Pooled Covariance Matrix Information                                

                                                                                                     

                                                 Natural Log of the                                   

                                   Covariance    Determinant of the                                  

                                  Matrix Rank     Covariance Matrix                                  

                                                                                                      

                                            8              20.58002                                  

                                            The SAS System          13:03 Friday, December 1, 2006 251

                                                                                                     

                                        The DISCRIM Procedure                                        

                                                                                                      

                              Pairwise Squared Distances Between Groups                              

                                                                                                      

                                   2         _   _       -1  _   _                                   

                                  D (i|j) = (X - X )' COV   (X - X )                                 

                                              i   j           i   j                                  

                                                                                                     

                                                                                                      

                                      Squared Distance to Known                                      

                                                                                                     

                           From                                                                      

                           Known              E             L             M                          

                                                                                                      

                           E                  0      11.17767      19.97527                          

                           L           11.17767             0      23.82850                          

                           M           19.97527      23.82850             0                          

                                                                                                     

                                                                                                      

                       F Statistics, NDF=8, DDF=4 for Squared Distance to Known                      

                                                                                                     

                           From                                                                      

                           Known              E             L             M                          

                                                                                                      

                           E                  0       1.27019       2.01770                          

                           L            1.27019             0       2.40692                          

                           M            2.01770       2.40692             0                          

                                                                                                     

                                                                                                      

                       Prob > Mahalanobis Distance for Squared Distance to Known                     

                                                                                                     

                           From                                                                      

                           Known              E             L             M                          

                                                                                                      

                           E             1.0000        0.4354        0.2598                          

                           L             0.4354        1.0000        0.2066                          

                           M             0.2598        0.2066        1.0000                          

                                                                                                     

                        Pairwise Generalized Squared Distances Between Groups                        

                                                                                                     

                                   2         _   _       -1  _   _                                   

                                  D (i|j) = (X - X )' COV   (X - X )                                 

                                              i   j           i   j                                  

                                                                                                      

                                                                                                     

                                Generalized Squared Distance to Known                                

                                                                                                      

                           From                                                                      

                           Known              E             L             M                          

                                                                                                     

                           E                  0      11.17767      19.97527                          

                           L           11.17767             0      23.82850                          

                           M           19.97527      23.82850             0                          

                                            The SAS System          13:03 Friday, December 1, 2006 252

                                                                                                     

                                        The DISCRIM Procedure                                        

                                                                                                      

                                     Univariate Test Statistics                                      

                                                                                                      

                               F Statistics,    Num DF=2,   Den DF=11                                

                                                                                                     

                    Total       Pooled      Between                                                  

                 Standard     Standard     Standard                 R-Square                         

    Variable    Deviation    Deviation    Deviation    R-Square    / (1-RSq)    F Value    Pr > F    

                                                                                                     

    FreqA         20.8159      22.3489       3.8554      0.0246       0.0253       0.14    0.8718     

    FreqB         38.1841      31.4104      29.4623      0.4274       0.7465       4.11    0.0466    

    FreqC         70.1399      61.5959      48.7929      0.3474       0.5324       2.93    0.0956    

    ClustA         1.1563       1.0630       0.7284      0.2849       0.3984       2.19    0.1582    

    ClustB         0.8812       0.9027       0.3482      0.1121       0.1262       0.69    0.5201    

    ClustC         2.3859       2.3631       1.1606      0.1699       0.2047       1.13    0.3591    

    dbhA           2.6707       2.6065       1.3883      0.1940       0.2407       1.32    0.3053    

    dbhC           0.5790       0.5435       0.3447      0.2544       0.3412       1.88    0.1990    

                                                                                                      

                                                                                                     

                                          Average R-Square                                            

                                                                                                     

                                  Unweighted              0.2268454                                  

                                  Weighted by Variance    0.3436799                                  

                                                                                                     

                                                                                                      

                            Multivariate Statistics and F Approximations                             

                                                                                                     

                                         S=2    M=2.5    N=1                                         

                                                                                                     

           Statistic                        Value    F Value    Num DF    Den DF    Pr > F           

                                                                                                     

           Wilks' Lambda               0.04786501       1.79        16         8    0.2051           

           Pillai's Trace              1.54512169       2.12        16        10    0.1147           

           Hotelling-Lawley Trace      7.50335734       1.88        16         4    0.2866           

           Roy's Greatest Root         5.05027910       3.16         8         5    0.1105           

                                                                                                     

                    NOTE: F Statistic for Roy's Greatest Root is an upper bound.                     

                            NOTE: F Statistic for Wilks' Lambda is exact.                            

                                            The SAS System          13:03 Friday, December 1, 2006 253

                                                                                                      

                                        The DISCRIM Procedure                                        

                                                                                                     

                                     Linear Discriminant Function                                    

                                                                                                     

                                    _     -1 _                              -1 _                     

                     Constant = -.5 X' COV   X      Coefficient Vector = COV   X                     

                                     j        j                                 j                    

                                                                                                      

                                                                                                     

                                Linear Discriminant Function for Known                                

                                                                                                     

                          Variable             E             L             M                         

                                                                                                      

                          Constant     -17.45676     -12.56128     -12.80423                         

                          FreqA          0.23043       0.11294       0.10949                         

                          FreqB         -0.03371      -0.07345       0.14592                         

                          FreqC          0.01324       0.08519      -0.06972                         

                          ClustA         7.14465       5.24883       4.11349                         

                          ClustB         3.87164       1.71830       5.73590                         

                          ClustC         0.70912       0.64270       0.40157                         

                          dbhA          -0.82441       0.41465      -1.50089                         

                          dbhC           3.95869       2.37264      -4.40804                         

                                            The SAS System          13:03 Friday, December 1, 2006 254

                                                                                                     

                                        The DISCRIM Procedure                                         

                      Classification Summary for Calibration Data: WORK.SPECIES                      

                      Resubstitution Summary using Linear Discriminant Function                      

                                                                                                      

                                Generalized Squared Distance Function                                

                                                                                                      

                                      2         _       -1   _                                       

                                     D (X) = (X-X )' COV  (X-X )                                     

                                      j          j            j                                      

                                                                                                     

                          Posterior Probability of Membership in Each Known                          

                                                                                                     

                                               2                    2                                

                            Pr(j|X) = exp(-.5 D (X)) / SUM exp(-.5 D (X))                            

                                               j        k           k                                

                                                                                                      

                                                                                                     

                       Number of Observations and Percent Classified into Known                      

                                                                                                      

                      From                                                                           

                      Known             E            L            M        Total                     

                                                                                                     

                                        6            4           11           21                     

                                    28.57        19.05        52.38       100.00                     

                                                                                                     

                      E                 5            0            0            5                     

                                   100.00         0.00         0.00       100.00                     

                                                                                                     

                      L                 1            4            0            5                     

                                    20.00        80.00         0.00       100.00                     

                                                                                                      

                      M                 1            0            3            4                     

                                    25.00         0.00        75.00       100.00                      

                                                                                                     

                      Total            13            8           14           35                     

                                    37.14        22.86        40.00       100.00                     

                                                                                                     

                      Priors      0.33333      0.33333      0.33333                                   

                                                                                                     

                                                                                                     

                                   Error Count Estimates for Known                                   

                                                                                                     

                                            E           L           M       Total                     

                                                                                                     

                     Rate              0.0000      0.2000      0.2500      0.1500                    

                     Priors            0.3333      0.3333      0.3333                                

                                            The SAS System          13:03 Friday, December 1, 2006 255

                                                                                                      

                                        The DISCRIM Procedure                                        

                      Classification Results for Calibration Data: WORK.SPECIES                      

                      Resubstitution Results using Linear Discriminant Function                      

                                                                                                     

                                Generalized Squared Distance Function                                 

                                                                                                     

                                      2         _       -1   _                                       

                                     D (X) = (X-X )' COV  (X-X )                                     

                                      j          j            j                                      

                                                                                                      

                          Posterior Probability of Membership in Each Known                          

                                                                                                     

                                               2                    2                                

                            Pr(j|X) = exp(-.5 D (X)) / SUM exp(-.5 D (X))                            

                                               j        k           k                                 

                                                                                                     

                                                                                                     

           Number of Observations and Average Posterior Probabilities Classified into Known          

                                                                                                     

                            From                                                                      

                            Known             E            L            M                            

                                                                                                     

                                              6            4           11                            

                                         0.8308       0.8026       0.8871                            

                                                                                                      

                            E                 5            0            0                            

                                         0.9596        .            .                                

                                                                                                      

                            L                 1            4            0                            

                                         0.6722       0.9960        .                                 

                                                                                                     

                            M                 1            0            3                            

                                         0.7464        .           1.0000                            

                                                                                                     

                            Total            13            8           14                            

                                         0.8617       0.8993       0.9113                            

                                                                                                     

                            Priors      0.33333      0.33333      0.33333                            

                                                                                                     

                                                                                                      

                         Posterior Probability Error Rate Estimates for Known                        

                                                                                                     

                     Estimate               E           L           M       Total                    

                                                                                                     

                     Stratified       -0.2807      0.2032      0.2500      0.0575                    

                     Unstratified      0.0399      0.3833     -0.0936      0.1099                    

                     Priors            0.3333      0.3333      0.3333                                

                                            The SAS System          13:03 Friday, December 1, 2006 256

                                                                                                     

                                        The DISCRIM Procedure                                        

                          Classification Summary for Test Data: WORK.SPECIES                         

                      Classification Summary using Linear Discriminant Function                      

                                                                                                      

                                Generalized Squared Distance Function                                

                                                                                                      

                                      2         _       -1   _                                       

                                     D (X) = (X-X )' COV  (X-X )                                     

                                      j          j            j                                      

                                                                                                     

                          Posterior Probability of Membership in Each Known                          

                                                                                                     

                                               2                    2                                

                            Pr(j|X) = exp(-.5 D (X)) / SUM exp(-.5 D (X))                            

                                               j        k           k                                

                                                                                                      

                                                                                                     

                       Number of Observations and Percent Classified into Known                       

                                                                                                     

                      From                                                                           

                      Known             E            L            M        Total                     

                                                                                                     

                                        6            4           11           21                      

                                    28.57        19.05        52.38       100.00                     

                                                                                                     

                      E                 5            0            0            5                     

                                   100.00         0.00         0.00       100.00                     

                                                                                                      

                      L                 1            4            0            5                     

                                    20.00        80.00         0.00       100.00                     

                                                                                                      

                      M                 1            0            3            4                     

                                    25.00         0.00        75.00       100.00                      

                                                                                                     

                      Total            13            8           14           35                     

                                    37.14        22.86        40.00       100.00                     

                                                                                                     

                      Priors      0.33333      0.33333      0.33333                                   

                                                                                                     

                                                                                                     

                                   Error Count Estimates for Known                                   

                                                                                                     

                                            E           L           M       Total                     

                                                                                                     

                     Rate              0.0000      0.2000      0.2500      0.1500                    

                     Priors            0.3333      0.3333      0.3333                                

                                            The SAS System          13:03 Friday, December 1, 2006 257

                                                                                                      

                                        The DISCRIM Procedure                                        

                          Classification Results for Test Data: WORK.SPECIES                         

                      Classification Results using Linear Discriminant Function                      

                                                                                                     

                                Generalized Squared Distance Function                                 

                                                                                                     

                                      2         _       -1   _                                       

                                     D (X) = (X-X )' COV  (X-X )                                     

                                      j          j            j                                      

                                                                                                      

                          Posterior Probability of Membership in Each Known                          

                                                                                                     

                                               2                    2                                

                            Pr(j|X) = exp(-.5 D (X)) / SUM exp(-.5 D (X))                            

                                               j        k           k                                 

                                                                                                     

                                                                                                     

           Number of Observations and Average Posterior Probabilities Classified into Known          

                                                                                                     

                            From                                                                      

                            Known             E            L            M                            

                                                                                                     

                                              6            4           11                            

                                         0.8308       0.8026       0.8871                            

                                                                                                      

                            E                 5            0            0                            

                                         0.9596        .            .                                

                                                                                                      

                            L                 1            4            0                            

                                         0.6722       0.9960        .                                

                                                                                                     

                            M                 1            0            3                            

                                         0.7464        .           1.0000                            

                                                                                                     

                            Total            13            8           14                            

                                         0.8617       0.8993       0.9113                            

                                                                                                     

                            Priors      0.33333      0.33333      0.33333                            

                                                                                                     

                                                                                                      

                         Posterior Probability Error Rate Estimates for Known                        

                                                                                                     

                     Estimate               E           L           M       Total                    

                                                                                                     

                     Stratified       -0.2807      0.2032      0.2500      0.0575                    

                     Unstratified      0.0399      0.3833     -0.0936      0.1099                    

                     Priors            0.3333      0.3333      0.3333