Project 2: k-Nearest Neighbors (KNN) and Naive Bayes (NB)

★ represents a unique aspect of this method, or indicates that the code requires special attention.

Data

This dataset is provided as a sample for demonstration purposes.

# Import data

dropout_data <- read.csv("dropout_data.csv")
View(dropout_data)

# Assign variable labels using attr()

attr(dropout_data$SES, "label") <- "Socioeconomic Status (1-100)"
attr(dropout_data$ParentEdu, "label") <- "Parental Education Level (1-5)"
attr(dropout_data$Attendance, "label") <- "Attendance Rate (percent)"
attr(dropout_data$HomeworkHours, "label") <- "Hours Spent on Homework (per week)"
attr(dropout_data$Motivation, "label") <- "Student Motivation (1-15)"
attr(dropout_data$PeerSupport, "label") <- "Peer Support (0-15)"
attr(dropout_data$TestAnxiety, "label") <- "Test Anxiety (0-15)"
attr(dropout_data$ExtraCurricular, "label") <- "Extracurricular Activities (number)"
attr(dropout_data$MathSelfEfficacy, "label") <- "Math Self-Efficacy (0-15)"
attr(dropout_data$FavoriteNumber, "label") <- "Favorite Number (Random Unrelated Variable)"
attr(dropout_data$Dropout, "label") <- "Dropout (1=Dropout; 0=NotDropout)"

# Check the structure of variables in this dataset

str(dropout_data)

'data.frame':   1000 obs. of  11 variables:
 $ SES             : num  37.3 58.9 46.9 58.2 60.2 ...
  ..- attr(*, "label")= chr "Socioeconomic Status (1-100)"
 $ ParentEdu       : int  3 5 4 1 3 2 4 2 1 2 ...
  ..- attr(*, "label")= chr "Parental Education Level (1-5)"
 $ Attendance      : num  82 80.2 87.6 86.3 86.5 ...
  ..- attr(*, "label")= chr "Attendance Rate (percent)"
 $ HomeworkHours   : num  4.9 2.02 2.32 3.58 3.28 ...
  ..- attr(*, "label")= chr "Hours Spent on Homework (per week)"
 $ Motivation      : num  8.33 5.53 6.66 5.8 7.9 ...
  ..- attr(*, "label")= chr "Student Motivation (1-15)"
 $ PeerSupport     : num  7.05 7.79 8.35 6.36 11.73 ...
  ..- attr(*, "label")= chr "Peer Support (0-15)"
 $ TestAnxiety     : num  7.91 3.78 4.92 7.33 5.25 ...
  ..- attr(*, "label")= chr "Test Anxiety (0-15)"
 $ ExtraCurricular : int  11 3 6 6 6 9 10 12 13 7 ...
  ..- attr(*, "label")= chr "Extracurricular Activities (number)"
 $ MathSelfEfficacy: num  8.4 5.18 6.68 6.12 8.07 ...
  ..- attr(*, "label")= chr "Math Self-Efficacy (0-15)"
 $ FavoriteNumber  : int  687 907 893 198 529 896 23 343 563 712 ...
  ..- attr(*, "label")= chr "Favorite Number (Random Unrelated Variable)"
 $ Dropout         : int  0 0 0 0 0 0 0 0 0 0 ...
  ..- attr(*, "label")= chr "Dropout (1=Dropout; 0=NotDropout)"

Remove ‘FavoriteNumber’ Variable

# Load the dplyr package
library(dplyr)

Attaching package: 'dplyr'

The following objects are masked from 'package:stats':

    filter, lag

The following objects are masked from 'package:base':

    intersect, setdiff, setequal, union

# Example data frame
#df <- data.frame(a = 1:5, b = 6:10, c = 11:15)

# Remove column 'b'
#df <- df %>% select(-b)

#Remove FavoriteNumber
dropout_data_new <- dropout_data %>% select(-FavoriteNumber)

# View the result
print(dropout_data_new)

          SES ParentEdu Attendance HomeworkHours Motivation PeerSupport
1    37.32338         3   82.01397     4.8972188  8.3253876   7.0469820
2    58.92681         5   80.15557     2.0223786  5.5268894   7.7920209
3    46.85475         4   87.55442     2.3187275  6.6618207   8.3486654
4    58.24271         1   86.30704     3.5773818  5.7951508   6.3561422
5    60.17920         3   86.45678     3.2781019  7.9022356  11.7263730
6    58.43493         2   85.86751     1.7571708  8.8391747   9.3044500
7    40.05218         4   86.06715     3.5368386  6.5493120   7.1123627
8    53.17541         2   78.28039     4.3445794  7.8496835   9.0684703
9    48.86595         1   74.82533     3.1053942  9.0893723   8.2546447
10   36.95363         2   88.31835     3.1767968  6.5271705   5.7457809
11   52.21128         1   73.70358     3.9603764  5.4657170   7.4615343
12   40.17518         4   75.20999     4.0091375  9.1315383  10.8321444
13   56.07302         4   80.15090     4.0863855  7.6552406  10.1184182
14   49.94705         5   78.39070     3.4470248  4.9629180  10.7018119
15   53.31880         4   87.45312     2.4016789  7.4493789  10.4315519
16   48.94326         5   79.05265     3.5573602  3.9125730   6.7315390
17   57.92878         1   84.52066     2.6433797  5.6436362  10.0592616
18   48.48713         2   74.53696     3.2864383  6.5280558   8.6687642
19   59.07016         1   82.10933     3.3355498  6.5182197   8.2460041
20   30.12262         4   89.81807     2.8851167  5.8965528   8.1754748
21   35.65495         2   81.70179     5.0778903  7.2673171  12.4996960
22   40.21429         3   89.56975     6.0752573  9.5173673   6.4381939
23   52.17657         3   90.00207     4.0560640  9.2251492   8.3418140
24   61.93085         3   87.87512     0.5826708  5.2878371   6.5018624
25   64.43665         5   83.64373     3.0998319  9.7816916   5.7729274
26   47.16128         4   86.00395     4.4918292  6.0205735   7.4490871
27   47.35634         1   84.19099     2.8700049  5.6082182   4.9930926
28   39.65964         2   84.65892     5.2400102  5.4445755   5.1037313
29   41.86841         4   86.88930     3.4639290  4.4002034   7.4189253
30   30.25594         3   82.48530     2.8212076  9.6624194   7.1710903
31   61.16833         4   87.63952     2.6010724  7.4433216   6.5292947
32   62.67824         3   87.77742     6.1871430  7.3956699   4.6752858
33   60.13597         3   88.60807     3.2661506  1.9211165   7.1978269
34   45.03134         3   78.54434     3.7564004  4.6217907   4.7847199
35   48.38794         2   86.05462     3.9527835  3.1427911   9.9936288
36   49.36940         4   74.43676     2.3682585  7.5661897   6.6981450
37   37.90287         3   89.20025     2.3815894  7.0993334   6.8061019
38   41.06928         4   83.29106     4.6929835  6.3879306  10.3020278
39   51.64838         5   83.76192     2.7688554  6.0807086   7.9534869
40   52.43658         2   92.22659     3.3546551  7.1559085  10.7069053
41   30.51741         5   74.88506     3.4695151  6.5292656   8.5833812
42   34.73714         1   85.75280     3.5729830  4.4610732   8.8710789
43   49.81975         5   82.36054     2.5309206  7.8159227   5.7576717
44   47.01883         2   85.91639     3.5016934  4.5698323   8.3440636
45   35.27271         4   87.07290     2.7848954  5.8444817   7.4973929
46   60.53967         1   82.13756     2.6676988  7.6365368   6.1115558
47   48.92222         3   80.08355     1.9010984  6.0477141   7.9094426
48   47.20907         3   88.68343     4.4478344 13.8299604   7.7968518
49   66.06098         3   78.76604     3.4999545  6.8005103   6.2525610
50   56.89379         3   80.33609     3.5209034  5.6175718   9.6995238
51   67.27187         3   86.63452     4.5478734  7.6648698   8.4896958
52   39.78089         4   81.20935     2.6244019  6.5970875   8.7399160
53   73.41840         2   85.65444     3.9046396  5.9442696   7.3325048
54   41.62892         2   81.64787     4.3112017  9.1376862   7.3989667
55   54.38030         4   81.17674     4.3281502  6.1127432   7.7084312
56   41.39951         1   81.13546     3.3659886  7.8944369   7.4046853
57   61.44644         3   79.22642     2.1560808  5.2756048   8.8277993
58   52.62846         4   82.00618     4.5941765  5.3913498   8.9162138
59   46.69437         3   76.93015     2.5952282  5.3547759   6.8840288
60   58.38330         5   92.35650     4.9752443  8.0751543   8.1839547
61   36.17538         4   83.13301     1.3920614  9.8116251   8.4568394
62   47.37492         3   81.95815     4.8755899  4.9736775   8.5377154
63   64.25732         1   80.98182     2.3763072  8.4996677  11.0178604
64   44.14808         4   80.51708     3.9181947  7.0723781  10.3620999
65   51.17213         3   87.86286     4.2711802  8.2899376   4.5249210
66   56.24963         2   79.83494     2.9816761  8.0465338   7.5662841
67   32.51251         2   79.06737     2.7547602  7.3921696   5.6331202
68   44.45132         1   82.87586     2.7327145 10.4191853   5.8197732
69   49.07546         1   82.67973     3.4682487  8.6470331  10.0485449
70   47.23357         3   77.70953     2.8692588  5.7093008   7.1189894
71   35.67150         1   86.44850     3.3678485  3.6341313   5.4526584
72   49.52574         1   87.32704     4.6758105  6.9105445   8.4157193
73   50.40291         1   78.62929     3.8435632  6.7212409   9.4469211
74   58.98367         4   78.60940     2.7018142  4.8301588   9.3248686
75   61.11415         1   77.98908     4.7888621  7.2768683   4.0320490
76   66.52231         5   89.08927     3.8009077  7.3011895   7.3039818
77   44.89107         1   79.19652     3.0627871  6.2342984   7.4647720
78   65.77507         4   72.32748     4.5651407  8.1539971   8.6329279
79   63.58457         4   76.61058     5.8100002  6.4925604   4.5803638
80   56.56619         1   81.06899     2.5570247  8.6596057   7.6937112
81   54.78035         1   79.06376     3.3915541  7.0473557   7.4082672
82   29.58033         5   89.49665     2.8120832  9.4811517  12.5024281
83   37.22604         4   78.39603     4.7214174  3.0208387   9.6230775
84   52.21899         5   79.62991     2.7845654  7.9514347   6.7045670
85   68.81073         5   83.36866     5.3845509  5.3239023   8.5984295
86   48.43555         4   82.96688     3.3026071  7.8852372   5.0597390
87   31.82730         1   81.26921     3.5112190  5.7623484  12.6569320
88   62.04912         3   76.03116     3.2523691  5.9762651   7.0303093
89   53.47196         5   82.68135     4.3897741  7.5829425  10.3891931
90   37.34370         3   85.12432     5.0420757 10.0993493   4.7803165
91   57.10115         2   88.38537     4.2503952  8.8168432  10.9575651
92   67.41463         1   70.30169     3.1077233  2.6892819   5.0780354
93   31.34190         1   76.52000     4.2974912  9.1211127   9.3915011
94   45.13661         5   84.97710     4.3732066  6.1378692   8.9830403
95   48.57352         2   87.42104     4.0253084  7.5748507   6.8982684
96   59.71679         5   75.94338     3.2447796  7.1456712   6.5439234
97   50.98716         2   79.82120     3.1819897  7.0102903   3.6878067
98   40.77192         4   82.44520     3.6821719  5.0532553   8.5518607
99   57.82004         2   81.26025     3.9227761  3.6355894   9.1827644
100  48.69958         3   86.08081     3.6556179  7.8669224   8.5548451
101  36.71775         4   81.75955     4.1827844  8.9597431  10.2396609
102  52.45025         3   84.66585     4.1047520  5.9760353   5.9833044
103  59.11720         3   70.23540     3.1918341  6.6354553   6.3163841
104  45.45218         5   90.04588     3.4156343  8.9605170  10.3021802
105  55.52156         3   85.82498     3.0507932  6.2014747   5.5284795
106  48.47362         4   81.08306     3.4173350  6.0522251  10.4065266
107  58.00308         5   85.74013     2.6342755  5.8422435   6.8557608
108  50.73480         3   85.76726     5.0898726  9.5747414   5.7360754
109  36.66027         5   82.29180     3.2208830  7.0827404   3.8485435
110  43.91294         5   83.60497     2.7152690  8.7089267   9.7736900
111  42.04458         3   82.51456     4.9855702  6.3632716   6.0420841
112  56.72934         2   70.09261     3.1800410  7.5850693  10.2084141
113  31.56804         3   79.73723     2.6778580 10.4655050   5.5011523
114  50.99021         3   78.34035     2.3562221 10.5732752   6.9383848
115  43.33800         2   80.20393     2.1396782  8.9529414   6.7081574
116  46.37597         5   77.60720     2.7994733  8.7852774   9.8118934
117  36.03246         3   81.81758     3.1125034  6.6329364   6.3636604
118  58.98128         5   84.45857     2.3419742  7.3826561   7.5387579
119  39.97298         2   77.00957     2.9885022  5.7515479  11.0642934
120  51.49240         3   89.20511     4.7919566  4.4232644   4.9909938
121  70.42426         3   80.27525     3.6026019  7.1691852  10.3779711
122  43.07794         3   85.48911     2.2268464  7.4242738   9.6677789
123  33.27907         5   80.99461     3.1873070  5.2393557   5.6477702
124  58.59118         2   84.23416     4.4351050  8.0887023   7.0130685
125  44.58912         2   83.13614     2.5812285  4.6063866   9.8921104
126  50.11296         2   86.32427     2.2850188  5.8422217   8.0511524
127  50.88591         4   83.25027     4.3190150  4.7776381   5.9168380
128  47.66770         1   80.86108     2.3200732  8.3596142   7.3851549
129  75.44125         5   87.65884     4.1471643  9.6518789   4.9093717
130  49.30953         4   87.70110     4.0966475  8.3567131   6.1979163
131  38.88961         2   85.92929     2.5344441  5.8972311   5.2695505
132  44.33520         5   87.95819     4.7210024  6.8522858   7.1643296
133  46.41448         5   84.13754     2.7458156  7.2522633   8.9465675
134  53.00317         2   79.05783     4.1869156  5.2709541   9.3244117
135  58.66669         3   79.72966     4.0908496  7.5760807  10.2906623
136  53.18404         1   82.57367     3.4814123  6.0964942  10.6644303
137  47.68797         1   80.01659     4.1590699  6.0412281   9.6975166
138  37.51847         5   81.53622     3.2043074  5.5968201   8.5655391
139  54.20516         3   81.56670     4.2535193  9.9867437   8.6259383
140  48.80080         3   85.43690     4.2701705  8.0588390   6.8019632
141  45.65463         1   85.44029     2.4976048  2.8934180   6.9541458
142  27.82373         3   83.27882     4.1836735  7.0873734   7.6218690
143  59.87630         1   70.48594     2.9435531  7.8366735   8.6966447
144  55.55321         1   83.27077     2.9276670  4.4963751   7.1599913
145  44.19687         3   80.03276     3.3161866  9.7905091  10.6040864
146  55.44539         1   70.54485     4.8716865 12.6711953   5.6335104
147  28.88951         3   82.81063     4.4543799  8.3018000   4.9851791
148  45.46474         1   88.33725     2.4572984  6.0336764   6.6146988
149  57.08446         5   83.08567     4.3810656  7.8445950   8.0989665
150  47.89881         5   84.69269     1.9867477  6.9701948   9.3502574
151  45.29114         3   84.88599     4.8459516 10.1276790  10.9017923
152  65.37787         1   81.08170     4.1679756  4.4329483   8.0887499
153  33.89602         5   89.08630     3.8656489  5.1250092   3.7885709
154  56.75105         1   82.88736     3.9944065  8.0491265   9.2758945
155  43.72287         2   77.77697     5.0651266  7.7327342   5.8933177
156  47.30895         4   77.47076     4.0812083  8.1298776   6.3825789
157  62.07717         2   80.81583     3.4845739  5.2008885   7.0628201
158  47.32974         4   81.83380     2.0849330  5.5883502   9.1310125
159  54.14745         1   78.02822     4.3732581  8.0140983   9.2007292
160  57.12973         1   79.06997     2.8686118  3.4589949   9.0728584
161  70.70020         3   76.20033     2.2816441  5.7992973   8.7572335
162  28.56980         4   82.87903     3.1452401  7.9707596   2.4904862
163  39.46196         2   79.03595     2.9477023 11.7379564   7.1944746
164  33.53453         4   90.30887     3.3445061  8.4256438   8.4854734
165  35.37358         1   79.44309     2.5091423  7.6640614   6.2579506
166  39.20106         4   86.53161     3.7615593  4.8746268   7.6694702
167  35.05152         1   79.38119     4.0653943  6.5729971   4.0870206
168  45.18605         3   81.79089     4.1788599  6.6462538  10.7907909
169  62.05890         5   84.91420     3.9101965 10.9741679   4.0696771
170  38.71593         3   78.52684     1.4147627  8.3039687   8.7550626
171  64.11160         3   83.99773     4.0030464  5.9930237   8.0324429
172  64.16786         3   78.41153     3.9198187  5.8566078   8.7338788
173  59.59333         2   82.17995     3.2534143  6.7832593   5.5170099
174  33.30466         5   80.61202     3.9731717  5.9104601   4.9987489
175  56.57573         2   80.35205     3.2423357  5.9646369   5.5602476
176  31.71674         3   78.21080     3.9134044  5.4265084  11.5067317
177  52.91744         1   85.52055     3.8074100  6.9883856  10.5571721
178  63.24200         4   84.74253     4.3194408  6.1511844   5.6620115
179  71.94937         2   85.61404     2.9205442  8.2753593   9.4945062
180  44.75475         5   76.38988     3.5944863  8.2870569   5.7272277
181  49.72341         5   95.39283     4.8142574  7.0255079   5.5434734
182  44.45525         3   85.20180     3.7130320  6.3700188   8.1585852
183  53.66690         1   79.66175     3.9171746 12.3343421  10.2074847
184  37.95363         4   76.53115     4.1186591  9.3026360   4.4837198
185  40.90214         5   80.62201     2.2457822  6.6642129   7.0228097
186  66.88778         4   85.09209     4.4982966  7.1963556   8.1153816
187  39.63422         5   80.75920     4.3334402  8.3696065   9.0396276
188  53.40869         4   81.21205     3.1584304  5.1952334   7.6865049
189  40.82703         2   86.58977     3.7087176 10.1236557   6.3735687
190  48.29160         4   82.92748     3.8672505  3.7879757   6.9122819
191  69.96995         2   79.89273     3.7062340  8.8354036   8.5060084
192  79.34735         2   90.27208     3.9112319  8.7506979   6.3030436
193  33.34362         4   92.85203     4.1440455  4.6151345   8.9799523
194  56.96958         2   84.14223     4.4737309  8.3571921  10.0296580
195  37.79948         5   77.62367     3.7053160  6.3285818   8.3996101
196  64.65549         2   85.83601     2.9894467  6.1663026   5.6804001
197  27.00910         5   78.89721     3.6449127  7.5918423   7.8714385
198  43.49055         1   75.05709     3.9058650  6.3686819  10.4642981
199  43.65778         2   92.83350     4.7467706  7.4592324   4.9687926
200  28.27559         3   79.90474     2.7704276  7.6746330   5.7308631
201  30.10315         2   76.48139     1.0973196  5.2099534   8.2469571
202  74.65965         1   85.25020     4.7010106  9.9480657   4.9292892
203  30.15539         5   84.86358     4.4610868  8.8728827   9.7107543
204  32.78476         2   81.71151     3.2174722  4.0302607   7.2254042
205  51.05069         3   90.42666     3.5834112  8.6819965   8.9562417
206  50.05922         5   86.07155     3.9415963  8.6078990   6.7842508
207  53.65288         5   89.55401     2.8787004  4.8777333  10.0961792
208  41.46670         3   85.07472     4.7861373  9.4472490   5.0047559
209  63.49469         3   84.40776     2.4996637  7.1568944   8.3488614
210  43.78033         5   79.26093     4.3251010  4.4211453   7.2381868
211  49.11798         1   85.68503     2.4351776  4.7600708  11.2117971
212  69.33717         3   79.27522     2.9336466  9.1222717   8.6721512
213  61.21918         1   88.94005     5.2545750  9.3849627   7.4912448
214  50.48345         3   85.45505     3.1505089  4.2263428   8.3892967
215  52.33301         1   87.87453     2.5405845  8.3887012  10.2145104
216  41.44752         4   80.41379     4.6058887  6.8010698   4.8594969
217  41.78449         2   86.07734     5.3078278  6.6333259   7.7322944
218  59.18604         5   75.83314     4.3285425  4.3829158   9.9002929
219  43.39209         4   77.47146     4.3506499 10.8964991  10.2159846
220  53.68796         2   86.05654     5.3157231  6.7330012   7.9368539
221  52.76726         4   75.51709     2.8863231  5.6194097   7.1786413
222  49.99481         1   76.70263     2.9662924  4.5757548   8.2371852
223  59.35334         3   76.26695     4.4033475  6.9855518   2.6186103
224  52.08261         4   77.96804     4.0064013  4.1181437   8.8546079
225  55.25699         1   80.34413     2.3907140  6.0378964   4.1033498
226  35.52665         2   77.32852     5.4049133  7.4319163   7.6675553
227  42.36537         3   88.51401     2.9037024 10.1709113   7.3841430
228  54.52622         4   80.27399     2.3370157  8.0740122   6.5795296
229  43.27349         3   84.21785     1.9990721  8.6023413   7.1755732
230  60.97044         5   78.22843     4.0471316 10.2989874   6.5186334
231  44.86647         4   83.43385     5.0537730  6.2941385   9.2757614
232  43.53866         3   86.91533     3.5380249  5.2484267  11.7544167
233  50.59540         4   89.95969     3.3577284  9.2219558   7.3355248
234  42.56104         2   84.60240     2.3666682  6.4621560   9.9857193
235  37.82293         2   83.27815     2.7816047  5.8050031   9.3643756
236  46.08316         3   80.52468     3.4428398  9.4896392   9.4392958
237  42.62845         3   86.13851     3.1354561  8.7045397   6.9607351
238  39.59600         2   79.69760     2.7669743  7.1478533   7.8798750
239  56.28786         3   88.83135     4.3646305  7.1885603  14.1708979
240  44.72931         4   82.87358     2.4108329  4.9156838   8.8860294
241  50.62138         3   79.94499     4.1368895  9.4998566   6.2895211
242  44.93118         3   83.37920     2.1878432  5.4259736   6.1048530
243  53.22975         2   87.51611     3.8077647  7.8554200   8.7591376
244  54.15356         3   92.07890     4.7897198  5.6739028   6.8305080
245  42.77465         2   81.18602     2.4623742 10.0243103   6.2006283
246  52.58672         3   80.95559     3.1840659  9.0629809   6.6372161
247  21.95723         1   83.28135     4.1325712  7.8774936   7.2194156
248  36.91866         5   87.91893     3.3440068  7.0723383   8.5946258
249  57.80147         1   88.58130     5.2820705  9.3899846   7.2693053
250  68.34534         4   80.89182     3.7983471  4.5266137   8.5506782
251  59.28460         1   89.79317     4.7002198 10.2472803   6.2936580
252  53.60214         5   81.51981     3.6893413  5.0488104   6.1579170
253  46.85209         1   76.38197     1.7366717 10.2336676   4.4795414
254  49.81187         2   78.72764     4.0788049  3.3635794  11.2032330
255  49.73361         4   87.38661     4.5217837  8.8822924   5.8604016
256  57.01215         2   82.91718     3.2304116  6.5759460   7.8647947
257  63.40694         4   87.38713     3.2616039  8.0156441   6.5921651
258  39.85112         5   76.47054     3.4783655  5.7287273   7.9160007
259  50.29792         3   90.72874     1.8996483  7.9987516  10.1791567
260  57.13069         5   81.05798     2.6461313  4.0665535   6.7322549
261  67.75584         4   87.27098     4.3355602  5.5733033  10.8047627
262  42.31781         5   81.05143     3.4877247  6.6122366   9.6207803
263  63.01508         3   80.68174     2.6569649 10.6599723   8.0418326
264  44.53803         1   83.21113     2.2780742  7.1957121  10.3619914
265  44.90637         2   75.05383     3.3784175  7.7974647   9.2769103
266  34.21204         2   88.49854     4.7111741  5.8851283   7.2583192
267  39.61601         2   83.01641     5.4051049  8.1610521   3.9797189
268  42.26864         3   81.17960     2.9383532  5.6788116   6.0940998
269  38.16226         2   81.23388     4.0836304  6.6533620   6.8461221
270  50.39438         2   85.93865     4.0946767  9.0174492   8.3376260
271  57.13328         5   87.14163     2.8804706  6.7117344  10.1388241
272  38.47194         4   84.18191     2.8490592  8.1029538   8.3571869
273  51.36610         1   86.41476     3.3153649  3.7653140   7.5765366
274  41.47842         5   88.45246     2.3323809  8.2850040   9.5203210
275  49.62226         1   80.36982     2.3135335  6.3013159   6.9202410
276  34.91515         5   80.73890     3.6547767  8.0054238   3.5799625
277  22.37481         4   75.23941     2.9337471 13.8410041   6.4643321
278  34.96977         3   84.65677     6.0480087  5.0551171   9.8673601
279  52.55258         3   83.58175     3.8758895  7.8889825  10.4325890
280  53.75735         1   88.17062     4.3876838  8.2377669  10.0526734
281  56.16410         3   87.52416     4.5555655  7.0997595  11.3131685
282  41.14104         5   83.17561     3.9069010  6.1035721   6.0588950
283  42.98435         2   80.80744     3.4729048  7.6099515   6.4192278
284  42.97848         4   84.87876     3.4642080  7.0258906   7.0422812
285  46.71991         3   78.56321     2.9421292  4.5999357   8.2820908
286  36.50900         4   82.33790     2.2204122  8.5980509   9.2149883
287  64.53542         5   88.30440     3.2594664  6.6869506   8.8773054
288  41.75684         1   80.43251     2.7952920 12.1201681   6.7315107
289  64.41097         5   82.48919     3.8293621  4.9693312  11.1881950
290  47.66810         5   77.89582     2.8605998  5.6293299   8.5354321
291  68.96651         1   80.56919     3.0036128 11.0245488  10.8386656
292  54.58244         2   85.88833     4.5470678  6.4735744   9.9200040
293  55.82903         4   78.94168     3.6769166  5.3096057   5.7276806
294  59.22130         4   90.83969     2.1211130  5.0263398   6.5200310
295  49.90190         4   82.58611     4.1816209  7.4495551   9.1730529
296  48.92708         1   80.41636     3.8306416 11.2753874   7.8219001
297  53.55558         4   79.89352     2.9527241  8.0988796   8.1731198
298  52.66174         5   85.53734     4.2766678  4.1209559   7.2476028
299  40.99818         3   82.53004     4.9625460  4.2773750   8.0858082
300  37.83760         3   79.82873     5.0068698  7.6084146   7.6466988
301  60.39080         2   84.34603     4.4135420  5.4003725   5.3887397
302  40.90412         5   81.28268     2.6791495  4.8107836  10.6503254
303  47.68848         1   84.46418     3.8757054  8.6936620   9.0851762
304  51.18723         1   87.91495     3.9111520  9.3618127   8.3591363
305  43.68276         1   77.06922     3.0776867  7.2464782   7.2803694
306  30.86993         1   83.13891     3.3873608  7.6719014   6.2598477
307  40.68082         5   73.78748     3.0913504  8.5345064   9.1823905
308  57.67062         4   84.98859     3.2193662  8.5530904   8.0688982
309  30.58522         1   84.44953     3.1735824  8.3743454   7.8124542
310  43.03093         5   69.14142     5.0284190  6.0578046   5.0802193
311  73.35646         3   81.61785     3.1889044  5.4980398   8.5881920
312  51.16955         3   83.46161     3.1141544  4.8569341   7.1482724
313  43.03403         5   91.33623     3.4567459  4.8948295   7.1326057
314  43.00288         5   85.17092     2.6119774  8.2848068   6.6970172
315  60.67046         2   80.52043     2.7109178  7.9663775   6.0380973
316  53.88054         2   84.90908     3.6358596  5.1490326   3.6223391
317  60.23815         2   86.02423     5.8195016  7.9676780   8.0674916
318  51.47905         1   85.08049     4.0623050  7.2157289   6.6067317
319  42.94863         4   88.71571     3.8033819  6.6149313   7.8685086
320  60.01294         4   76.04660     2.3849481  7.6638769   9.0911306
321  75.60049         4   86.34832     5.9464205  6.1786920   6.5184559
322  41.60884         2   81.36024     4.1315298  8.0436420   7.9793619
323  39.75867         5   85.15489     3.8971329  6.5376162   8.9046854
324  40.81363         1   77.93341     3.4458565  7.2333999   6.4287993
325  52.73838         2   86.30072     4.0834100  6.5757152   6.2629793
326  44.40444         4   80.00496     2.3651602  3.6829311   8.0661976
327  57.45461         3   87.82205     3.2053974 11.0554472   8.3484613
328  46.25259         5   81.66691     2.6941351  5.4599813   7.1507776
329  51.02224         4   77.42300     2.8888818  8.3979867  10.7731830
330  36.24486         2   82.45906     5.2617384  7.6050209   8.9204403
331  47.25879         5   86.49319     3.5096456  6.2512310   5.6651036
332  58.62024         5   81.70604     2.9025832 10.1743314   6.3871441
333  31.68790         4   79.59359     2.3130670 10.2121376  10.6365396
334  53.32296         3   81.59562     3.8918669  7.2176538  12.4832073
335  51.92098         4   73.72286     4.0610060  5.4431897   8.3892847
336  31.70576         4   86.57953     4.6632197  5.7229928   5.9389624
337  49.89156         5   89.43372     4.4059851  2.9704328   6.8351586
338  50.37434         1   82.51437     1.9159008 10.1619657   7.2889568
339  26.88312         3   88.56154     2.6529377  5.6783791   8.6395183
340  48.78951         2   85.00763     3.1971914  8.0698087   4.5819188
341  56.54854         2   88.60340     4.6446443  8.1215844   7.7652305
342  49.96327         3   76.73115     3.1233180  8.5737618  11.2560408
343  33.43687         4   83.89074     3.6727242  7.7228793   8.3515989
344  35.45154         1   82.88205     4.0860056  4.4253926   6.4095143
345  56.17323         5   75.44652     4.9564776  6.8549583   9.6678430
346  44.65381         3   81.49361     2.9182657  5.9833916   9.6033596
347  48.05166         3   81.24416     5.2537486  4.9673986   5.6430030
348  49.69976         4   86.87084     2.8567763  7.6524503   8.1318578
349  38.51846         4   79.55156     4.1321959  7.8723376   5.2151108
350  59.81332         3   80.28564     2.8628456  7.2552553   6.8848307
351  67.68132         1   75.73517     1.9880649  4.5408955   6.8781484
352  49.86758         4   84.96846     3.9174938 10.6249511  10.1354209
353  47.84437         4   88.26552     2.7987287  6.6203567  10.4065910
354  40.69891         2   77.16365     3.9166287  6.5634165   5.4679237
355  53.15034         5   77.63224     1.9659520  6.6346756   6.7667334
356  49.45965         1   82.81626     3.2640002  7.3278049   6.0773030
357  57.70931         5   77.04005     2.9854894  6.5250495   7.6148853
358  55.45649         4   76.12009     2.5983569  9.1142665   7.2835844
359  58.86586         3   79.86063     1.6820942  6.1017483   8.6245347
360  66.60010         4   81.21182     4.2405311  4.5674448   8.6311587
361  46.24868         2   77.23316     4.7751192  6.1333056   7.4772574
362  48.24115         5   84.91613     2.7576590  9.3000466  11.2747593
363  49.29004         2   78.94569     3.8312491  6.1700879   9.7377339
364  48.23924         2   81.87480     4.3676298  7.5409173   9.6313175
365  38.30496         3   84.98301     3.4326001  7.6219973   9.2966216
366  48.36752         2   85.40788     5.1970409  7.0809804   5.1344775
367  56.77950         2   82.26426     2.9721314  8.5812736   8.3997100
368  48.63615         4   85.94282     4.0889863 11.8231425   4.5014281
369  75.15831         4   78.46463     3.0897165  8.5155442   8.2287917
370  43.96108         5   80.15148     2.8255801  6.5366546   5.8319208
371  45.72109         3   87.51931     4.6272348  5.9987946   5.8628590
372  38.12306         1   82.97056     2.7134665  8.0183601   9.0262583
373  48.80942         3   78.43305     3.2322910  7.2185802   5.9857637
374  41.45204         4   90.72567     2.1321973  9.3072476  10.5603356
375  55.40684         5   84.94234     4.4660651  7.3153291   5.8159090
376  31.66697         4   92.25328     1.9509791  7.1687301   8.6964944
377  48.31651         5   80.58116     1.9846318 13.2623519   6.3321786
378  64.96190         3   79.38548     2.9245427  6.1262545   8.1783036
379  37.68266         5   80.54277     2.8294922 10.2245905   8.0405766
380  52.01144         5   77.89364     2.0847789  4.0865317   9.1702367
381  40.39230         2   85.23445     0.7890092  6.6225204   7.7035297
382  46.95556         4   84.01523     2.2567848  5.0087390   6.8897865
383  47.47348         2   95.75794     3.3072441  6.8384408   8.2782144
384  52.26503         2   83.37544     1.9306494  5.7759790   7.1412885
385  40.60178         4   84.06689     5.2180620  7.2040528   5.1513145
386  52.52180         1   82.08515     5.5169113  7.3504478   6.6192186
387  60.04796         2   77.72452     2.5793782  8.3216465   6.0339141
388  62.94717         2   83.63994     3.5285109  8.6788343   4.9550650
389  56.32484         1   75.81988     5.3187431  5.1490810   6.9822458
390  51.22108         4   84.72812     3.4815680  9.5282620   7.3156138
391  29.96823         3   82.12920     3.8022776  7.2746674   8.9538205
392  42.44291         4   76.49023     2.0769477  7.1524361   6.9066347
393  55.46281         3   87.44723     4.3168226  5.3485557   4.9413439
394  32.04617         5   83.01130     3.2152758  9.8180637   5.2312983
395  44.88512         3   81.48079     1.5662020  6.4983678   7.8005504
396  66.39641         2   80.93552     4.5454379  7.1615526   8.8937384
397  58.62242         5   81.77963     3.3297673  8.5781426   7.4758376
398  41.04113         5   83.38111     5.2664950  8.3702018   9.1248297
399  45.05039         3   84.41922     3.8731853  8.0516745   8.8160388
400  25.63154         1   84.97513     3.7251309  6.8972746  13.6464574
401  51.64748         5   80.86058     3.9079804  6.1038996   4.6871616
402  36.58115         3   82.49431     2.8122349  8.6503767   8.7254817
403  42.36605         3   89.46610     3.0220845  5.4290891   7.4566691
404  59.75904         1   83.84462     2.5072643  4.3629613   8.2676068
405  67.79858         2   85.68994     4.4854913  9.8834000   4.9670216
406  41.90713         4   81.34750     2.5601366  9.5527557   3.9480172
407  46.79716         5   82.66647     1.8193189  6.1888603   7.7003152
408  35.57263         2   73.99681     3.9675052 11.8090695  13.0420932
409  46.52752         2   83.88062     2.4099375  4.1206150   6.6689074
410  51.12504         4   81.59046     4.1127910 11.0437161   6.2440588
411  48.88750         2   86.96479     4.3552843  8.0130794   6.8012161
412  54.33484         3   86.71892     2.2384115 10.8454313   3.3003287
413  51.29705         5   81.19971     3.9437720  7.4730851   9.2346767
414  53.59262         5   85.52642     2.4941477  7.4503521   9.2325681
415  56.23857         5   86.07620     2.0568945  5.4331655   9.1635582
416  68.48629         3   79.49196     4.0285414 10.1016666   6.9724474
417  53.05990         3   78.56297     2.8590211  4.9521500   8.9506366
418  48.64412         4   83.12281     4.1469127  6.0095218   9.0329042
419  59.43625         1   79.37908     3.8106144  6.7511753   8.5465925
420  41.86886         2   89.74806     3.4380293  6.5072992   7.4185246
421  58.84467         2   91.39584     4.5202574  7.3004710   7.4515424
422  45.64815         5   89.28714     3.9480546  8.1912190   7.1479827
423  27.94084         5   80.07323     2.4875555  8.6868353   9.3888847
424  53.27594         5   85.92126     3.5844079  7.8992660   8.3196134
425  49.83120         5   75.96452     4.4270148  8.5700310   7.8885730
426  54.36819         1   81.68264     3.9810034  5.0297761  10.8774495
427  75.61114         5   82.81526     2.7531349  7.0625879   8.1854558
428  37.67218         4   89.60588     5.5294166  8.6746436   4.9705472
429  25.76139         2   80.43842     2.5690213  6.8544524   9.0508559
430  50.81679         3   81.82832     2.2921064  3.5974694   8.5921643
431  50.92835         2   73.69713     4.3888402  4.5370601   5.2969352
432  48.40122         1   84.32996     3.7757093  4.7890397   7.0958168
433  71.03991         4   84.07727     4.9296902  8.9936977  10.2301459
434  46.09190         3   80.61551     3.6629005  6.8282831   4.9758818
435  34.42113         1   80.67368     4.0369156  7.3692406   9.6097813
436  66.61072         3   82.20534     2.4474489 10.4010054   5.4510863
437  37.62241         2   84.40466     1.8756204  4.8352673   4.7669584
438  58.73803         2   81.52296     4.5282472  7.8440758  13.6443218
439  28.71284         3   79.37934     1.4501001  6.8935418   4.9880254
440  51.07494         4   87.41169     3.4486061  8.7865292   9.1325800
441  50.77665         5   81.27025     3.2510639  7.6503063  11.0074591
442  51.88535         3   89.60781     2.9563382  7.2674272  11.4030062
443  57.99570         5   83.86607     3.2421127  4.8759823   6.6364333
444  30.01724         1   77.05741     3.0658849 11.2640696   7.5886759
445  52.36040         2   83.65818     3.2590449 10.2478010   7.4483916
446  42.56553         4   83.91889     3.5384404  7.5681985   6.7366509
447  60.26956         1   75.48644     2.7984701  7.8858910   7.7447170
448  28.08152         5   87.67689     4.6487636  4.2307555   9.3257278
449  53.70944         1   82.26821     4.2833448  4.3376560  10.2428577
450  47.64489         5   83.81094     2.4288058  7.8005849   6.5854049
451  64.31701         3   80.62248     3.6177173 11.1853301   9.4185798
452  52.23081         2   85.10186     4.9214505  8.4853587   7.5489479
453  55.79934         1   83.30544     4.5575286  4.4039196   4.5368759
454  33.83519         5   90.99502     2.8017924  8.7866440   4.3792261
455  57.46759         4   87.23005     4.5143755  4.8623029   5.1122743
456  40.61292         4   83.67099     3.1010267  6.1470309   7.7220800
457  53.06542         4   86.95918     3.6052421  5.2528197   7.5857628
458  48.33262         3   86.80374     2.7788952  5.7950224  11.4303001
459  47.97352         1   82.38887     1.6569927  6.1709943   8.6407538
460  50.33682         4   83.85635     2.7405809  2.6013261  12.6088965
461  46.97443         2   84.27155     4.4486088 10.1053561  11.7593859
462  56.06210         3   86.03413     4.2188826  5.2084425   7.7168679
463  52.57244         4   87.81599     5.1068962  3.6587730   7.5959844
464  65.10080         4   83.13061     2.7862578  2.2633329   7.8685352
465  72.37252         5   87.04276     2.0510513  3.5681013   5.0868364
466  65.02852         2   85.83322     4.4811071  6.4603960   8.0315982
467  63.67134         4   82.87609     3.4781339  8.1675271   9.3993090
468  36.47778         1   72.88509     3.1198168  8.3442190   6.3540730
469  52.91818         4   80.20417     2.5769285 10.3902149   6.9009311
470  58.88325         1   84.53703     3.6643974  6.8225799   7.3424446
471  62.07536         1   84.31569     2.3648162  6.4087763   6.7623739
472  66.23407         3   77.92829     4.0982580  5.3428272   5.7989450
473  53.96391         1   79.79110     2.4361733  7.2884860   4.3534521
474  44.03932         2   86.49094     2.2398276  5.7379737   5.9469711
475  59.19257         2   79.96299     3.4212418  9.0132212  11.5879081
476  55.51789         2   78.63747     0.6580892  4.9777685   8.8897388
477  63.91326         2   88.80678     3.6610287  5.5669067   6.0751772
478  61.65283         3   78.09628     3.3993679  6.3939698   8.4275725
479  62.40064         5   84.10310     3.5794379  8.5402203   2.7080846
480  67.62994         1   80.19256     2.7176753  6.4979142   8.2877281
481  64.22269         5   89.16048     3.0162473  8.1349633   7.6374592
482  41.97650         1   84.00967     1.7941725 10.3523633   5.9647808
483  67.25984         3   76.11063     4.3788701  7.4171265   5.4670528
484  49.64369         3   79.81914     3.5013696  6.8865666   8.4182855
485  40.81853         5   85.83809     2.6694073  6.9554746   7.6236559
486  76.02496         5   87.01079     3.7963546  8.1923836   7.9827957
487  31.49478         4   83.71158     2.5819937  6.4950894   5.3096445
488  47.68288         5   86.58011     3.1369394  8.8406096   4.8129111
489  59.27699         5   85.41420     5.4077861  3.4992044   9.2587247
490  52.25568         4   80.35441     4.6162481  7.6840839   6.4660256
491  50.16813         4   86.54034     4.1373142  5.1495162   7.7722856
492  37.66873         3   84.97226     2.3932513  9.9705889   6.5456906
493  55.57407         1   81.15792     2.0494583 10.3446893   5.4421496
494  26.86275         4   82.55559     2.7073512  7.3012715   9.9477757
495  54.10947         3   81.07621     2.5824874  4.4681130  10.7783196
496  45.80306         4   79.57714     4.1161837  5.6668934   7.7914403
497  44.11791         4   83.89740     3.8785771  7.8828425  10.9373736
498  49.56608         2   85.99407     3.1808780  9.0448360   7.4959882
499  57.43336         5   89.05429     3.0752037  5.0010310   6.7722412
500  60.07486         4   78.71078     4.1638757  2.7672289   5.9875322
501  57.04303         5   85.41627     3.6232413  2.1505105   3.4909954
502  42.04666         3   74.00565     1.4539816  9.6902319   7.1208232
503  50.25151         5   74.93801     1.9635002  7.8925780   9.1481133
504  59.32957         3   88.04302     3.1918958  6.1396183   7.0234365
505  47.12832         4   91.80221     5.7855987  9.6505252   7.5281501
506  55.68824         2   78.71495     2.6112044  9.5823585   7.9795686
507  43.63686         4   80.80091     5.2994055  8.8069536   5.4684316
508  44.32639         1   78.64599     3.0682090 11.2144451   8.1766868
509  43.12086         4   76.50919     2.5513209  8.1238803   5.4167697
510  52.30435         5   82.75809     3.2621232  3.2584811  10.0533337
511  48.71147         4   76.86789     4.2075971  7.3643745   7.0909337
512  40.88391         3   77.90879     5.0841713  5.9557020   7.1025005
513  31.82474         5   90.70252     4.3234956  6.0517174   7.5515047
514  33.14716         5   83.79457     3.0708940 10.8378683  10.4479674
515  49.86958         4   91.42591     4.6873421  9.4851919   5.3658664
516  48.86873         5   82.85281     3.6895060  8.3483821   9.9003979
517  56.67458         5   89.49354     3.2277891 11.1387717   6.3958334
518  54.00904         2   77.59944     3.5661916  4.4981548   6.2140548
519  34.95430         5   85.45828     3.6623398  4.6749250   4.9304896
520  64.23085         4   78.10244     2.7421047  7.3771586  10.0177350
521  49.65736         3   76.91016     2.6611886  8.4608158   9.1525120
522  45.48062         1   83.29129     3.0337464  9.5114113   9.8309346
523  55.60467         5   84.23478     3.0060128  5.1471445   9.4701812
524  63.47086         4   85.57282     3.2774555 10.5283612   5.5441646
525  49.57453         5   78.30043     3.5841538  8.3812402  10.0105445
526  57.71945         4   81.88623     4.0524700  6.0070576   7.5594759
527  56.76738         1   79.07079     3.6264868  6.7274933  10.3278196
528  52.09467         5   81.27435     3.5261694  6.2488747   7.5657127
529  47.72315         2   76.17658     3.9329477  2.7886554   3.7230052
530  47.40208         5   80.23869     2.0748050  6.3574638  10.7981512
531  39.22100         2   83.00484     1.2128791  5.4401390   5.5422086
532  44.38729         4   84.09535     2.6110822  6.8459257   3.6241442
533  45.99099         3   83.72263     4.7886804  7.6908896   8.1167474
534  55.89217         1   90.47269     2.5488860  6.3098085   9.2871947
535  62.16898         2   82.86844     3.3343909  7.9924598   9.8645245
536  65.25365         4   81.97241     3.5200934  8.7992733   4.3745460
537  60.54359         4   83.99041     3.8514812  4.6903871   8.7498348
538  55.90686         3   85.14082     4.3771351  9.9818490   7.5908393
539  43.57607         1   76.83811     3.0777878  7.0948945  10.7421792
540  37.75153         3   69.33465     3.4096554  7.7015431   9.2719898
541  50.45283         3   78.89177     4.0093349  2.4317748  11.8884019
542  61.83155         3   82.94519     3.6665477  5.3832216   6.7612283
543  46.19009         4   81.21536     4.3779619  9.4712114   8.6189239
544  75.95150         5   84.58038     3.1374143  4.5495685   7.8016203
545  52.35136         2   81.20839     4.1243059  7.2369331   9.2291708
546  56.26182         1   71.96596     2.2553675  4.3256015  11.4303765
547  57.35270         3   82.73002     3.4156999  6.0585495   8.7033630
548  33.87351         3   73.99231     6.3483836  7.0548125   5.4483034
549  63.89855         5   84.96889     3.8469122  6.6548562  10.2391237
550  42.54814         4   80.88124     3.7461959  7.8111008   6.4865195
551  48.58558         4   82.94891     1.9640186  6.7871478   7.5423153
552  55.33482         2   84.96652     3.6207657  6.1622889   6.6921023
553  41.52486         2   78.89591     2.8743566  9.1856677   7.8087088
554  45.66093         1   82.32658     3.2446772  7.7621870   9.5469316
555  41.44816         5   81.76943     3.2118140  8.7623436   6.3402467
556  33.96084         1   83.69936     3.4116650  5.5851768   7.4819727
557  43.08712         5   83.41302     1.7143999  5.5639140   8.4254173
558  35.31462         2   80.27489     1.8104520  4.1328084   6.5538454
559  57.57896         2   80.61663     0.2596881  6.5156837   9.1886329
560  37.78099         5   86.43832     5.6050034  7.6163400   7.0579837
561  42.46397         5   85.88121     3.9875494  6.5929212   5.2365104
562  52.55278         2   78.70619     4.7786601  8.9402530   7.0955833
563  32.98590         5   88.38553     4.4603331  7.3585026   7.0280126
564  50.94436         2   86.24690     2.6629598  5.6481029  11.0141803
565  45.89907         4   85.80198     2.7337720 11.3963164   4.2229626
566  41.41838         1   90.46556     3.3454343  7.3392766   6.6661994
567  47.10857         2   76.34828     2.3641952  6.4717514   6.9264920
568  48.05796         1   76.97943     3.7257834  8.0062473   4.5831833
569  58.08115         1   85.73654     4.0064287  8.5681876   5.7621005
570  45.73928         4   86.97079     3.2162518  6.1237166   3.7238406
571  62.40737         1   80.60600     4.2364642  2.9893393   4.0725975
572  37.81015         2   81.16680     2.9294733  8.0076928   6.4783917
573  42.63581         5   84.19191     2.8775402  4.6594799   6.9878461
574  46.65739         4   82.09754     1.2411653  8.0038430  13.3684260
575  59.05073         5   84.09063     4.5364421  6.0314742   5.0524292
576  49.93150         3   86.73219     1.6055536  9.1274795   9.5320734
577  30.45346         2   81.55088     2.7130407  5.6559341   5.3517557
578  54.18768         5   81.79928     3.3913882  4.6020837   6.1722298
579  30.46336         4   74.84815     4.9827895  0.8994521  10.5680965
580  37.05176         2   80.63516     3.1644402  7.5289414   5.5792834
581  56.72717         2   77.07592     3.2902586  6.1159929   8.5802047
582  40.81033         4   86.31240     5.0022934  7.8152963   8.5934816
583  59.63141         4   74.71260     5.3243994  7.4353465   6.1695120
584  53.57180         1   86.27401     3.1177442  5.2861541   9.1605487
585  62.35322         3   82.38507     3.1229917  8.2059819  10.6541109
586  51.75556         2   86.35034     4.3988854  5.4341350   4.9528349
587  38.90721         1   86.33186     3.2354394  7.5803651   9.9776575
588  29.63742         2   79.31867     3.6801456 10.0126869   9.4174376
589  48.79223         5   79.48454     0.7842932  8.7072298   5.0454718
590  45.48511         5   82.77357     2.6645515  8.2453278   9.8107188
591  53.55329         5   82.03936     2.3117356  5.6073664   8.3383553
592  52.44154         4   81.85813     3.8702653 10.3426526   7.3137935
593  52.11548         4   75.95416     2.6132607  7.2900203   7.8050096
594  54.00836         4   84.44246     2.6123331  4.2384603   7.7343369
595  77.55420         3   84.80684     2.7679003  7.3597035   6.0770305
596  48.39641         4   84.88776     2.8314513  8.0285956   5.6758375
597  56.66807         5   82.98812     3.7036272  4.3032248   6.6418275
598  63.03855         3   76.47653     4.4091554  9.0446043   8.6287640
599  54.09483         1   90.99583     4.7409828  5.4121187  10.1093772
600  57.93973         4   83.64287     4.1328710  4.0392297   5.4011323
601  60.45372         3   82.33889     4.4098909  9.1299517   7.2021346
602  46.36589         3   82.98633     3.2723047 14.2657244   4.7623214
603  74.83412         4   80.74048     1.6675130  2.9976952   9.4494620
604  48.00362         2   84.40796     5.7627101  3.7334130   5.5880501
605  52.91244         3   82.99033     4.2983591 10.1130586   9.0919401
606  58.73080         5   72.64646     2.5841426  5.1582275   5.6165557
607  40.32385         1   72.51510     4.7732220 14.2712129   8.4746911
608  57.15276         2   81.81867     4.6099825  7.2052954   9.0797703
609  59.26803         4   81.51742     3.3681093  6.8976265   7.2314362
610  40.11361         2   92.63638     3.6409104  5.3790264  10.7501636
611  76.09194         1   79.93019     3.5427934  9.3961707  10.7590340
612  49.65173         1   84.55529     3.8131419  5.5066660  10.0901665
613  44.70795         3   91.18584     4.0700206  9.2696568   3.2653742
614  54.99754         2   85.29387     3.9474968  4.0762091   8.1569817
615  69.54686         2   84.08464     3.0727880  7.9687655   7.7296680
616  38.85055         4   76.48081     1.6690666  4.4198152   5.1086672
617  45.37981         1   83.68913     4.7223387  5.5218569   7.2404425
618  47.12620         1   79.01018     2.2444393  4.9852728   8.3925462
619  51.88259         3   76.60332     3.3820628  9.5226106  11.8575919
620  59.54208         1   85.50769     3.3913392  4.9916864   8.3898705
621  52.95995         2   87.16660     3.8069263  9.0284635   7.1811110
622  69.35729         4   85.09402     4.9999717  5.0966668   5.8895920
623  54.92037         1   84.38585     3.2286249  4.0281683   9.0077313
624  32.15020         3   80.23145     1.4110268  6.8737408   6.3483016
625  61.20500         3   85.28657     4.9850133  5.1688843   5.3711196
626  52.19540         4   83.16910     3.3634952  7.6668448   3.9169988
627  61.55707         5   75.77009     5.9814422  7.9937878   9.4067769
628  36.45332         4   81.44227     3.0027402  8.0615670   6.5042551
629  43.91359         3   91.53597     3.2052186  9.7488598   5.0988180
630  46.88628         5   83.02614     4.3253508  5.1586691   7.3477577
631  53.32781         4   78.50010     2.5015610  7.4605141   8.9196767
632  59.95771         2   86.03011     2.9161620  5.9893698   6.4119968
633  55.90069         3   81.12839     3.7139554  4.6337785   7.2128942
634  47.91551         4   78.10472     1.9743997  3.3542517   9.4975309
635  50.13553         1   81.48953     3.6776313  6.9203659   7.4335577
636  67.31135         2   81.58370     4.2690136  6.2293799   6.7453797
637  48.73183         4   89.62199     4.1038797  2.9856666   9.8191192
638  47.70865         3   79.57884     3.8105824  7.6167578  10.5110925
639  53.92132         2   87.48532     3.0061747  7.8314239   6.9227578
640  40.94553         2   76.07135     3.2405269  8.1515002  10.0562012
641  64.55679         2   79.85281     5.0324924  9.2698417   8.6383511
642  72.41617         3   82.71265     3.2275364  5.1729341   9.1237142
643  41.42846         2   78.94758     4.0103363  4.6749944   6.8284175
644  57.26084         2   81.28054     5.7415128 10.1589891   9.7362271
645  52.26153         4   86.13739     3.9573923  9.4191188   6.9959723
646  43.72801         4   76.09071     4.1973401  5.6529756   9.4843379
647  52.11620         5   84.48414     2.4904077  5.1023934   5.2857135
648  36.05032         2   79.86941     2.4040620  6.6499787  10.3930537
649  50.16953         5   83.19768     3.9767186  7.8016819   6.8563787
650  56.05656         2   82.42455     3.3414508  6.4014938   7.8577059
651  57.19968         2   78.65008     4.5328883  6.9362278   7.0025888
652  61.74547         2   83.89864     4.4338542  8.2744921   9.5454023
653  44.09657         1   81.12503     2.3896876  8.0202892   7.3113760
654  61.43785         4   87.20598     3.6088510 11.5115599   7.2914940
655  57.43139         1   82.07545     4.0971899  7.4043411   7.7800303
656  45.08888         5   80.59953     3.7406271  6.9207011   5.3526044
657  43.51898         1   83.24849     4.1183227  7.9730769  10.0151939
658  59.75340         5   86.04466     4.4341284  6.1276698   7.9556343
659  44.69738         3   83.17983     3.8854912  8.7736740   7.0120068
660  38.56905         1   78.34546     3.3755285  7.5742513   5.6408015
661  58.31035         4   77.30653     4.1751864  7.5984242   4.9680496
662  62.74704         5   79.85760     3.1479367  8.0071950   8.4334452
663  59.87735         5   82.28768     3.8291819  6.2640531   9.9285475
664  50.32396         3   82.63808     3.7402907  5.8396591   9.0710694
665  48.84730         1   94.09411     3.0200407  5.9889019   0.1878578
666  56.25316         2   80.34285     3.0123548  7.7937224   5.3519790
667  33.99065         2   80.94987     4.1055041  7.4495973   8.2786713
668  55.39626         5   87.84723     3.3938575  7.2082447   7.3372017
669  59.54607         5   81.71093     3.0920523  6.4756617  10.2585890
670  39.24223         4   77.95325     4.3175261  4.8580942   9.4076983
671  61.64949         4   82.85432     4.0989316  3.9807586  10.7391489
672  25.29788         5   91.60745     2.5143505  8.9119114   5.5982659
673  43.29613         3   92.88842     2.8443558  8.5209775   6.3971761
674  70.89989         5   83.19869     2.2069506  5.9131019   4.0424014
675  33.40955         2   89.28700     3.9653937  7.9486114   6.1090922
676  46.43118         1   91.47729     3.0779006  7.7771366   8.1192847
677  52.92636         5   83.92199     3.0249443  6.6336874   8.0508785
678  40.54482         5   84.76667     1.4990395  7.7868695  10.2699835
679  40.68009         2   87.22228     1.6236748  8.0189672   6.8026139
680  53.81469         1   86.99651     5.6609763  7.7143857   1.2190186
681  45.39155         2   81.74059     4.8355115  8.2150951   6.0615519
682  35.11540         5   76.98794     4.2326865 10.7903596   7.7909829
683  40.48404         5   83.06286     2.3901888  9.3635682   8.6298166
684  44.63281         2   81.21067     2.9363055  4.1661417   7.3183952
685  51.32330         4   86.70213     2.5233106  7.4203428   6.4102831
686  45.70598         1   84.28030     3.7553787  8.2170943   8.5918949
687  57.16061         5   88.79670     1.9822143  4.5618642   7.1752123
688  28.43121         2   78.08530     3.6118463  5.6195741   9.4715933
689  42.86838         2   74.33993     4.4317416  6.2635239   8.8537750
690  36.80256         4   74.14793     2.1324729  4.4000404  11.0278339
691  41.18611         1   80.35012     5.1951467  4.9177421   9.4497460
692  65.34327         5   82.26077     2.5140044  7.3365422   9.6208471
693  35.21741         2   87.12162     3.9696058  7.7529592   5.5917637
694  31.97761         5   86.84730     4.5364307  5.7995599  10.3813012
695  51.02413         1   77.57863     3.2485914  2.2955241   5.9309454
696  48.61956         4   81.86457     3.8687918  8.9603520   8.0358163
697  55.98726         1   77.02111     3.3429007  7.8171877  11.6807972
698  40.60172         3   83.19576     3.1898269  8.7607578  10.3964264
699  46.06958         2   83.63239     3.8535965  5.2972436   5.7944520
700  44.02785         5   82.16258     4.5944469 10.0723095   6.7532583
701  39.37010         2   87.61284     5.4532666  5.8986463   8.3960198
702  55.96806         1   82.90955     4.1554635  6.9838297   8.1626940
703  39.33574         4   73.78189     4.3890153  9.9381344   8.3262968
704  42.64917         1   78.35130     1.7528701  6.9345029   5.4615917
705  74.14214         5   76.51042     3.9407707 10.1047651   6.4267019
706  63.70505         2   86.27697     1.8587435  7.0936459   5.0934380
707  55.70518         4   76.61849     3.2781425  5.5228833   4.9666243
708  90.08043         2   79.49151     2.5415448  8.9295241   5.4821513
709  47.34475         1   84.90095     2.0760350  6.9242302   6.5337831
710  41.94383         4   88.30177     2.4772054  9.2108265   4.9992891
711  47.96936         2   82.35766     3.8623042 10.0203804   9.6524685
712  50.59073         3   87.22206     3.9562445  6.1049343   8.2717349
713  43.05201         5   81.42536     2.9384807  9.5100574  10.6961010
714  49.44794         2   93.14069     4.0516470  6.1947208   6.4970789
715  52.73344         3   93.20930     3.1695320  8.8872288   5.7016554
716  65.07171         4   86.28006     2.6409457  4.5644891   6.2652956
717  46.54395         5   81.34329     3.4437148  5.8276768   5.5129036
718  34.49758         1   82.01289     4.5144983 12.4373223   8.1430056
719  44.08286         1   75.97405     5.7949685  5.2529329   7.1120675
720  43.94360         2   92.33965     2.3456327  5.6445888   8.9999592
721  50.26785         3   88.13071     3.0757056  5.3166044   6.7742995
722  32.59828         2   91.75681     2.0870342  4.5404611   7.8516697
723  46.07944         4   85.60149     3.5673354  4.0374032   7.0581284
724  60.69333         2   87.06940     3.7900729  2.2838459  10.6879408
725  49.25044         4   84.81174     4.4463709  5.3168106  12.9302499
726  50.97240         5   82.61611     2.4043292  8.8453799   5.7048697
727  65.22491         1   80.78268     3.8659031  8.4682061   6.4416410
728  65.78504         1   79.91519     3.5513184  4.4783488   7.8271466
729  50.17182         1   82.45606     1.5632605  7.8583715   7.9683714
730  63.21278         1   77.35893     3.9567796  7.6771107   8.4959245
731  32.62314         3   85.40224     3.1647658  6.9638975   8.3230864
732  64.73693         1   80.68344     3.5456484  4.4222526   7.8642309
733  50.89795         4   88.65238     2.8761105  5.8940713   5.6905454
734  25.47995         2   86.59899     3.5659515  8.8053234   8.4484843
735  54.40845         1   76.99936     3.4464620  7.8320404  10.2589464
736  54.09298         5   84.57081     1.5663112  8.4134969   9.6816936
737  60.73950         3   87.57271     3.4597686  6.6600951   5.1929241
738  44.47861         3   82.08502     2.9181055  9.7687849   3.8967770
739  45.19552         4   88.66030     3.8379190  6.8134061   8.0033180
740  37.04460         4   84.39172     4.5746865 11.2333250   8.6493592
741  56.18911         2   77.68447     4.2642996  9.2170980   7.7292155
742  50.67542         3   82.15142     3.9380157  4.9859330   6.2809477
743  34.29563         4   81.25437     4.7685746  6.2944836   9.1960128
744  47.88801         3   87.31304     4.3581250  5.3510036  10.1214074
745  59.24915         2   83.16427     4.3350811 12.2032734   7.7411542
746  20.75134         5   75.40548     3.0465630  9.5264552   8.7142898
747  62.98501         3   76.08018     3.5693859  4.4678555  10.0826632
748  44.24001         3   85.23026     2.4417233  3.8538647   6.5616571
749  55.61397         3   85.54668     4.2699260  6.6489440  10.1044397
750  44.71681         2   85.10742     1.9468484  7.1970510  11.9016005
751  70.64367         4   84.68186     2.8307887  1.9243617  10.0912841
752  52.72134         5   84.45393     2.8929482  6.1982043  10.3626428
753  65.18793         3   78.70169     3.8465153  6.2278357   7.8798070
754  62.04000         4   82.04876     4.0679926  7.0349095   6.8335785
755  50.86110         3   81.88454     1.4522502 10.4041509   8.8299139
756  52.73742         2   89.77552     3.6376951  6.8935547   6.1145513
757  53.61833         1   81.33366     2.3676570  6.9537268   8.9734903
758  59.89684         4   89.99472     4.0153488  8.0190747   9.0502451
759  58.48055         5   84.84911     3.5592489 11.9862660   5.4597833
760  47.73746         2   82.88912     4.4664920  8.8652190  10.1587237
761  43.66617         2   83.49523     2.2300783  5.0733948  10.8265326
762  38.27060         3   79.65840     3.8925638  7.8799741   8.0552349
763  61.21116         1   81.00006     2.1027763  6.8796733   9.7077494
764  42.42030         3   80.98257     3.5292297  5.9087461   7.3573900
765  36.08515         5   94.01727     5.7998623  6.4707066   9.0610278
766  52.40435         5   88.44769     5.3590110  7.1959443   7.3514204
767  51.66869         4   73.30600     3.1830626  5.5863659   8.6874720
768  45.23087         1   84.33613     4.0072142  9.1840020   9.1085377
769  55.65344         5   78.66033     3.1533128  6.3783738   5.8311733
770  50.03411         1   73.41500     3.7198724  5.9247987   7.2163101
771  57.91626         3   77.34221     4.6529368  9.1452971   5.4441597
772  58.40468         2   88.12346     2.4612160  6.4769388   9.2628362
773  73.91532         2   77.92220     3.0994166  5.5245769  10.4515870
774  46.57411         5   93.89597     4.8192483  7.3441660   9.5572361
775  51.92469         4   85.43387     3.1465014  7.0492578   8.7615508
776  41.60323         1   80.37690     2.1501914  9.8183406   8.3918343
777  51.40265         3   81.45653     2.8369498  7.6106662   8.6793028
778  37.38972         3   88.29393     2.7012986  4.6523041  10.1244977
779  37.41341         2   83.44498     3.2114747  5.0782593  11.1983550
780  61.42069         1   85.58679     4.4948575  8.8967837   5.2261687
781  50.16955         1   84.07693     3.1386537  8.6955014   5.6222877
782  50.43100         2   81.92363     4.0655850  8.9829994   7.4847198
783  58.64329         2   79.68183     3.6878355  8.3359419  10.0452189
784  48.39705         4   80.40349     3.2989893  7.0586417   9.1741936
785  50.39780         1   83.16439     4.0497150  7.7374050  10.5423820
786  48.17520         1   88.48357     1.9821100  3.7640294   6.6171112
787  62.99596         3   86.28066     4.0717588  7.3295449   8.3015094
788  48.86042         2   81.51755     3.2850929  6.0868765   7.1492487
789  46.81069         4   85.12362     2.0869850  8.4411712   4.2378172
790  66.53805         3   78.76660     2.5688037  8.3566307  10.4819696
791  61.02936         3   82.59278     4.8912749  9.1893754   6.5894673
792  37.81042         5   83.46904     4.1556547  7.9079132   6.1285453
793  56.17780         4   88.26446     3.9636559  7.5851135  10.1363804
794  43.38625         1   83.87638     3.0462080  9.1131231   9.8671972
795  48.57625         4   83.88143     4.5577875 10.4568453   8.6756187
796  31.49869         2   80.13540     4.4379396  6.1419195   7.5633897
797  36.74002         4   85.09404     4.0699359  6.7275581   7.5658409
798  32.26888         4   81.25910     3.7181000  5.4007945   8.3507108
799  56.50578         1   80.68340     2.8089539  8.9535805   7.4957284
800  46.00207         1   76.08027     3.8294192  6.8301415   8.0787654
801  24.09705         1   74.59470     4.5796036  7.9788885  10.3468833
802  62.84461         4   84.68244     4.6560256  6.1409409   6.8399670
803  52.54119         3   88.08810     3.5512324  7.5818474  11.7595535
804  64.29926         3   78.35983     4.1667109  9.7990290   9.4847448
805  63.02696         5   93.56264     2.8893487  5.6860630   4.7376649
806  59.41136         4   86.16197     4.0759362 10.2651412   8.5968988
807  49.66132         5   75.80199     3.7603395  3.6997032   6.8747659
808  59.42226         1   79.50517     3.0200457  4.6965538   8.4090531
809  50.63253         1   81.22482     2.7207720  8.7325176   7.0967640
810  36.99466         2   99.13644     3.6901914  8.4494450   4.7530348
811  54.36698         4   85.29118     3.1378129  6.3573546   5.7891887
812  37.86854         4   84.90163     2.2734756  6.7302119   9.5394570
813  57.01332         5   91.13771     1.8300012  4.9063889   6.7459378
814  52.13753         4   83.24398     3.2740412  9.0640112   7.2376723
815  50.49214         2   81.47064     3.5093746  5.2208898   8.7406644
816  53.64805         1   86.66312     5.1491243  5.8994236   7.5857817
817  39.30045         4   86.34056     4.1750668  8.1597203  11.2410338
818  55.73454         3   82.79265     2.0814697  4.6313756   6.9126507
819  51.70868         2   79.15520     5.6201846  6.7158165   5.9660886
820  28.88835         4   90.51107     3.4271623  6.9809464   8.3527573
821  41.56666         4   78.83549     2.9205790  7.8506337   8.8429747
822  40.56889         5   80.05365     3.2621186  5.2909840   5.1571462
823  48.61522         4   80.78418     2.3022550  8.5282570   3.6321527
824  57.48973         1   78.53602     4.0959173 10.1866473   6.7097307
825  50.88262         1   85.47545     3.7715980  7.6368104   8.5997587
826  53.35357         1   82.49196     2.8109327  8.2513244   7.1903995
827  67.82154         5   73.72378     2.1994805  4.0274525   7.6283505
828  46.36597         1   78.58179     3.5246132  8.5494856   6.6781361
829  30.12299         4   80.35792     3.9912934  9.1230361   8.4558908
830  36.94867         1   77.37396     3.7168543  8.6903247   9.1491964
831  52.46420         3   86.93238     4.3412014  6.5611029   6.1274362
832  47.35781         1   85.03857     3.5286385  4.5459938   7.5105484
833  47.72897         4   75.66089     2.4853443  5.4621099  10.7768376
834  44.51930         4   84.58341     4.1880193  5.2854201   6.6134402
835  45.83105         2   82.81928     2.5580206  8.4847461  10.1569378
836  56.60199         5   86.47507     2.5220218  4.3970110   6.2417303
837  38.75980         5   79.12448     3.0347530  6.9590018   6.7098083
838  40.58359         3   79.32814     3.5638576  6.3222471   6.4448223
839  46.21958         1   75.29343     5.5419530  5.7392876   7.4563093
840  46.06002         4   85.51186     3.8171626  7.1735558   6.9396512
841  48.08034         5   84.01266     3.9789697  3.6268687   6.8262671
842  50.36410         3   89.57091     3.8735575  7.5587530  10.0306682
843  43.22491         3   87.38916     3.5780853  5.4514496  10.7363496
844  59.73636         5   83.90393     2.7026998  8.8441782   7.3362851
845  51.87804         2   79.44165     3.0342331  6.6507147   8.2430373
846  56.01128         5   79.68232     2.9056953  7.7130708   7.7974064
847  35.81715         1   81.80988     4.2210657 10.9363214   4.9764755
848  34.36998         2   83.45001     2.4876363  8.4381913   8.7228042
849  65.35055         3   74.78861     3.8270080  8.5190805   8.3953374
850  31.57856         2   74.82708     3.6802858  7.9551623   7.9011528
851  38.27854         5   84.42956     3.7769530  6.4552692   8.8719467
852  46.08814         5   82.01531     3.3572988  6.0691545   7.2440425
853  46.70045         2   82.25607     2.1644203  7.2211337   6.5312999
854  44.05429         2   79.72151     1.7292381  5.0124607   8.9950683
855  63.67365         1   84.51337     4.2124023 10.0828104   3.4225783
856  46.83899         3   81.90218     3.9353354  7.2664768   6.5294237
857  42.78063         1   86.18957     2.8095993  4.8431207   4.9668913
858  43.82553         2   82.82398     3.3734713  4.8114481   8.3275706
859  37.03305         3   81.30657     4.2412724  7.3015803   4.6083727
860  48.97691         3   79.70748     3.8515016  7.0214537   7.1973668
861  32.52138         5   87.16318     2.7835305  3.2845765   9.3121909
862  62.42894         3   83.74602     3.4751541  8.4102825   9.2011955
863  47.62711         1   89.65040     3.9762071  8.5190831   7.2998522
864  46.21580         2   75.17034     3.1070990  4.3972145   9.7652539
865  49.65903         4   83.00631     4.8965212  1.9701069  10.2614664
866  51.38825         1   84.65356     4.4010311  4.1259944   8.7486762
867  62.67017         2   73.68117     2.2989099  7.7903104   5.6935531
868  44.86136         3   81.27302     3.4389930 10.8666565   6.1603279
869  54.33556         4   74.07786     5.3216570  6.6430293   5.3829531
870  45.90466         2   85.50937     3.4799697  6.7097053   6.9435382
871  32.04848         3   77.39970     4.4802003  7.9353779   5.6402786
872  62.07288         5   80.87858     3.9762932  9.8448580   7.4994080
873  46.90102         2   86.14010     2.4920660  3.1986482   8.9998734
874  30.09508         5   83.67576     2.7043361  5.8459248   3.9082560
875  35.38084         1   76.62036     3.1533290  8.1961712   8.1870519
876  53.37289         4   83.75200     4.5998833  2.7256106   7.1710916
877  38.35111         1   84.28433     4.8258569  5.5980549   6.0097177
878  42.75532         4   79.61146     2.7455071  7.3371589   4.8624701
879  43.09331         3   85.88327     3.5083576  4.3746887   5.6123550
880  45.76035         5   89.66381     4.4890205  8.0264109   7.0109095
881  53.22559         4   82.70453     3.8532235  9.8567915  11.1713260
882  47.64294         2   84.08604     5.8420612  8.4992031   3.1005357
883  47.49803         3   84.53564     3.8609141  7.2675700   9.0304412
884  55.81104         5   82.72908     1.7640216  9.4086321   7.0741981
885  69.69223         4   82.56185     4.2274504  6.7575702   4.5984155
886  62.65121         2   77.99084     3.1966232  7.8179837   4.0763752
887  54.87173         2   77.27867     3.1802325  5.1414055   8.0630741
888  46.94968         1   86.21446     3.4978946  4.6238857   6.3460691
889  37.08350         1   83.93710     3.3676946  5.6057085   1.9289990
890  43.50548         2   86.11216     3.3415863  4.7433863   8.2020842
891  35.07728         4   79.49790     2.3509760  6.5699699   7.1903897
892  45.16981         2   75.68860     1.9092795  3.8519226   8.7554919
893  51.14135         2   88.38969     3.0565006  8.8511052   6.7961403
894  60.80142         4   75.58417     2.2420473  5.7287455   6.2176785
895  67.86677         4   78.44132     4.1711878  6.3926819   8.6482492
896  56.31859         3   80.66235     3.1157836  5.9350462   8.5452692
897  42.67337         1   79.91019     5.0319376 10.6794622   4.9243227
898  50.26849         5   77.93701     3.6173388  8.7016745   7.5540058
899  52.52599         2   84.65485     3.4674623  6.9353666   8.5157885
900  48.54980         3   88.45476     3.5465518  7.6149050   8.3721847
901  45.04135         1   82.04073     2.8703604  9.0668959   6.3645244
902  37.31211         3   82.57317     6.1761879  5.7222295   5.8116536
903  37.24525         4   74.09907     1.8316259  7.6505339   3.3990340
904  41.88259         5   84.28052     1.2771862  9.8771885   6.8660283
905  34.26564         3   79.99068     4.5074074  4.0034435   7.3316296
906  51.58419         3   82.26332     3.7881135  5.6449636   6.6670338
907  39.10686         2   81.19952     3.8753869  6.7371362   5.7529264
908  52.96814         4   81.68678     3.1744769  5.9145205   8.0376032
909  36.75481         3   81.04477     4.5112690  6.3762107   4.0405591
910  54.16626         2   84.77422     4.7686916  9.4859967  11.7437538
911  43.04000         5   76.38265     3.6194614  5.7593551   7.9200098
912  44.14754         1   77.34155     2.6158456  7.0166790  10.8257829
913  58.26376         5   73.52607     3.4148959  9.7871241   7.2586781
914  48.01278         2   82.86455     3.1732078  9.0678946   9.1058638
915  37.21135         3   75.77306     3.0219179  6.0494375   9.7776645
916  54.41807         4   81.55087     1.7977286  6.6709418   6.7177688
917  34.97244         3   80.38919     2.9440550  8.0249080   4.2029653
918  53.64001         5   84.39454     3.2077970  6.5533790   8.0268145
919  54.04060         3   75.87546     5.4716404  8.5173027   6.0124135
920  45.81960         5   85.78882     2.7904062  3.5577122  10.6682326
921  47.24746         2   86.07414     3.4762205 10.0985178   8.6855351
922  44.99092         2   87.08245     3.7147155  7.7655026   9.4617549
923  40.61041         4   86.00455     3.3443504  8.3586723   7.5122590
924  37.17581         1   86.86298     2.9562517  6.4769322   5.6448540
925  51.73030         5   78.47274     5.4058100  6.5347137   5.4324609
926  44.88209         5   84.73280     2.7540215  7.5240467   7.9881548
927  57.43417         3   88.65652     4.8268341  9.5796498   7.0029853
928  60.62569         2   73.59535     5.7792625  7.3672608   4.5724606
929  61.75756         1   84.31774     3.9226029  7.7727728   7.5184768
930  66.00446         2   90.00654     3.6260785  4.2500173  12.3372083
931  62.63145         2   80.10395     4.2070231  8.3940390  10.9672302
932  37.55719         3   85.34575     4.3420998  5.4461186   7.9687117
933  34.53511         2   88.10750     3.1904654  9.3804650   8.5965917
934  45.32571         1   74.68889     2.9971185  8.3677744   8.0427739
935  57.06290         1   80.36196     3.3385507  3.2785233   5.4754809
936  51.91125         3   86.36567     2.5668651  5.8496256   7.4970177
937  66.24627         2   82.94648     1.1137272  9.0913870   8.3199318
938  43.67610         5   85.43291     4.2975788  2.8907164  10.9582920
939  52.94562         4   80.70573     3.8504856  5.8034419   7.1857857
940  44.60522         2   80.48953     3.1278931  7.9522387   9.1945797
941  40.21895         2   85.95312     3.1120259  6.3778117   6.2181331
942  51.75441         5   81.27515     4.1742145  3.6696279   8.0271773
943  42.97734         3   83.42390     4.4264543 10.8006808   7.4127568
944  46.55055         4   81.10484     2.5453244  6.1241233   4.7573405
945  58.90048         3   85.53059     2.1876224  9.2037463   8.9037418
946  41.37386         1   76.60557     3.4202223  6.9920946   7.5288747
947  78.54108         3   86.94004     3.7277430  5.9205333   9.8656261
948  44.08628         2   80.24320     2.1456971  5.6008434   7.3776144
949  47.45327         3   90.45309     4.8425451  9.0370475   9.7495545
950  44.80431         4   83.42090     1.7182934  5.9516839   4.3721490
951  63.17391         4   84.82738     2.3860679  3.7880679   6.9170430
952  54.58319         4   84.52427     5.1495628  3.2126832  13.0700417
953  57.51127         1   76.43699     2.8000532  9.9090197   7.6513594
954  35.26754         2   83.47296     3.8225864  6.0943352   7.6840807
955  41.64071         2   81.61953     3.7820900 10.0410446   8.5863396
956  54.89231         2   82.03873     3.0097630  3.0155825   6.2543986
957  42.57216         4   87.07736     3.5230847  5.4924684   9.8532358
958  42.99622         4   73.61639     5.2190390  6.6229651   8.8685580
959  47.51265         2   74.64338     5.6348201  7.6395124   7.7537400
960  57.94479         1   76.92654     3.6901346  9.4580291   6.0860599
961  58.51823         2   71.22621     4.2821240  9.6775231   6.9123008
962  47.78565         2   75.16418     5.7770230  8.6510312   4.3552889
963  51.46027         1   86.78604     4.5568494  6.7308955   8.5280445
964  60.81779         2   87.60268     2.5930284  9.6683395   5.8158079
965  53.53323         1   89.39363     3.8605466  6.8221087  10.1119708
966  42.44806         4   82.48384     4.7661699 10.5392162   9.0531318
967  37.69803         5   79.42302     2.1477750  7.6402663   8.1991105
968  48.73752         3   80.87094     3.3554594 10.2080562   4.4359537
969  35.35059         1   84.89105     4.0765857  5.4459593   8.4447857
970  42.70194         5   79.98984     3.3755448  6.3454174   7.3343930
971  55.35773         1   76.52426     3.6224508 10.7877865  10.1760038
972  55.43045         5   88.83108     4.2899530  9.1189734   6.6470060
973  26.62772         5   83.04717     2.5708000  8.1028985   7.1153128
974  45.73366         2   68.79073     3.5351618  6.7516497   7.3622686
975  52.13506         1   94.65064     3.1395501  9.2760745   8.2182821
976  43.08257         1   88.40774     3.3191175  5.6290908   9.1289169
977  54.77944         2   81.75406     4.0964773  7.7261348  10.3349274
978  45.62512         1   84.02543     2.4975274  4.4066274   7.1074949
979  43.00853         1   79.01122     4.5991437  4.1160013   7.8926685
980  44.31285         1   77.10130     3.8122232  7.3110954   6.4186801
981  42.95927         1   88.25933     3.8326659  6.7063206   7.2824503
982  42.04893         4   78.59499     3.8781282  7.6183948   8.9088929
983  56.05578         5   75.05215     3.4026211  4.1808148  12.6099407
984  32.97431         2   82.41467     3.3814376  5.9865169   7.6989604
985  58.07549         1   85.44135     4.2998937  9.8993175   6.1461521
986  49.02327         5   84.57059     2.8374304  9.8111112   8.4892711
987  50.17082         2   85.39825     5.4112459  8.7806603   9.6680561
988  38.84675         4   86.78064     1.1301344  5.1270591   8.4907934
989  43.90190         1   83.91684     4.4341594  5.8800995   4.0036274
990  55.34405         4   81.10982     3.8905430  8.2155127   8.5192075
991  58.95242         5   81.03267     3.1844040  3.7671304   4.7316305
992  58.17359         4   80.89988     5.2389952 10.2475409   7.1252860
993  48.35171         3   83.93170     3.2579357  6.6012317   9.4940495
994  47.49903         2   83.25690     6.0102385  9.0187501   8.8587211
995  44.70014         1   87.54552     4.1113977  7.8183328   5.6744143
996  63.39559         1   84.20453     5.8448813  8.1387720   9.1982448
997  46.42234         2   77.73116     2.6131429  7.4868229  12.0925232
998  52.36226         3   86.86936     3.8167712  5.0658870   7.8746262
999  57.25032         5   81.79634     4.8805877 10.0530263   4.2717627
1000 43.86843         5   81.06175     5.1306116  5.4683743   6.3317187
     TestAnxiety ExtraCurricular MathSelfEfficacy Dropout
1     7.91338288              11        8.3972667       0
2     3.77536586               3        5.1780416       0
3     4.92243798               6        6.6849651       0
4     7.33046731               6        6.1152394       0
5     5.25460618               6        8.0659612       0
6     6.79555709               9        8.7530208       0
7     7.70115541              10        6.0773721       0
8     7.24658122              12        8.1404577       0
9     6.87165843              13        9.2059115       0
10    9.58208793               7        6.8522319       0
11    6.73197361               1        5.0029227       1
12    8.16052624               9        8.9018375       0
13    9.36549101               4        7.5416236       0
14    5.08389690              11        4.8952751       1
15    9.63861114               1        7.9362788       0
16    7.08138092               4        3.7260852       0
17    4.13200135              12        5.0386727       0
18    6.65082487               4        6.7819011       1
19    4.36132337              11        6.0474270       0
20   10.22835542               8        5.8132823       0
21    5.64138873              13        7.0401239       0
22    8.87367547              15        9.1460261       0
23    2.97810216               9        9.4499768       0
24    7.69554247              12        5.0568948       0
25    7.77668544               1       10.3291219       0
26    8.82240385               9        7.3719825       0
27    7.76392495              14        5.5231006       0
28    5.35217295              13        5.6648584       0
29    6.17956804              11        3.4618155       0
30    8.83714278              15        9.5280641       0
31    6.16442273              12        7.2467399       0
32   10.95242535              12        7.2774674       0
33    7.64340782               9        2.0529581       0
34   11.26574665               7        3.6158632       0
35    7.44534351               1        3.6012407       0
36    9.08676607               1        7.1973278       0
37    5.01139545               1        6.5943279       0
38    8.29866872              15        6.5349906       0
39    6.15375286              14        6.0318905       0
40    5.48538633               2        7.1181898       0
41    9.20190249               8        5.7869429       0
42    5.99745861              13        4.2654163       0
43    6.92871834              10        7.3981999       0
44    7.10809561              11        5.0248592       0
45    9.77940155              11        5.8655596       0
46    6.96367803               8        8.0182385       0
47    6.10036438              13        5.8578707       0
48    9.32678988               8       12.7784240       0
49    6.03359415               9        6.6064724       0
50    8.08119425               6        4.8136820       0
51    5.53229157               9        7.9646258       0
52    8.62294329               7        6.7814756       0
53    9.33765237               7        6.6078645       0
54    8.74271282              15       10.0840572       0
55    8.57397255               9        6.4385291       0
56    4.63543155               1        8.0035813       0
57    5.97917805              14        5.9771976       0
58    5.94604986              13        4.8635897       0
59    5.57186961              10        5.5484857       0
60   10.73280839              15        7.5437135       0
61    6.89551832               6        9.7212697       0
62    6.29716286              12        4.8687452       0
63    5.82448078              11        9.7326279       0
64    7.33587577              10        7.6609526       0
65    5.79633395               9        8.3636903       0
66   10.59478133               3        8.7767231       0
67    3.92865611              13        6.9028586       1
68    4.25860662              12       10.4831658       0
69    5.07845900              12        8.2862801       0
70    5.18033370               6        4.9425415       0
71    6.26671505               1        2.8907442       0
72    5.61402489              14        6.5161805       0
73    6.52729198               1        6.8347687       0
74    5.18932517               8        4.7160473       0
75    7.28906622              11        7.5487647       0
76   13.32923081              11        8.1818099       0
77    5.92149601               9        5.8290162       1
78    8.00001950               4        8.1851330       0
79    8.45836537               3        7.1491385       0
80    6.93038294              14        8.7846512       0
81    2.97951911               9        7.3809835       0
82    7.84872503              14        9.8549231       0
83    7.13471669               9        3.4831897       0
84    9.52392935               8        6.3279760       0
85    6.37438698              10        5.0172786       0
86    4.55440166              11        7.4225010       0
87    7.24185148              15        5.2817994       0
88    9.35927070               5        6.8496725       0
89    8.22697135               3        6.0875112       0
90    5.91961611              11       10.9275901       0
91    6.64930665              14        9.7977212       0
92    5.33379838               3        3.1997376       0
93    7.87805640              14        9.0842574       0
94    2.76845867               1        6.2474112       0
95    5.31063900              14        7.5181515       0
96    9.04821598               2        6.7618464       0
97    8.99431019               7        6.5893756       0
98    4.29247306               5        5.0021902       0
99    4.96602973              14        3.1915604       0
100   6.35305532               5        8.2493327       0
101   8.74407419               6        8.9393135       0
102   9.42850872              13        5.5902629       0
103   7.30633210               4        6.6178605       0
104   9.70243209               2        8.8801135       0
105   7.86873461               4        6.4054766       0
106   9.76598046               8        6.4347158       0
107   5.81039762               7        6.2162937       0
108   8.75889685              15        9.3550554       0
109   6.54532191               1        6.9392895       0
110   8.06614555               3        7.8417465       0
111   5.90530348               4        5.7922693       1
112   8.52554471               6        7.6626267       1
113   6.26040133              12       10.5027923       0
114   6.00195218               4       11.0029230       0
115   5.24478748              15        9.4119215       0
116   9.41522952               2        9.6731960       0
117   2.59516656               5        6.8919274       0
118   8.36358440              14        6.6902181       0
119   5.87249614               1        5.5280996       0
120   9.14129249               9        5.5806341       1
121   7.42474363              11        6.7538161       0
122   7.08590364               1        7.6567443       0
123   8.38952546               6        5.6000214       0
124   8.57790452               4        8.2445028       1
125   3.03326226               1        4.7568559       0
126   8.66118083               2        6.4042337       0
127   8.46931826               9        4.7449021       1
128   4.92411616               3        8.5348787       0
129   5.82020041              10        9.9251703       0
130   5.70917296              13        7.8662415       0
131   8.54779881              11        6.2921477       0
132   5.83731390               5        6.6829479       0
133   7.85790091               8        8.1658779       1
134   7.06427473               4        5.3349479       0
135   6.28584747              14        7.5005887       0
136   8.49260424              11        6.2478566       0
137   6.34040805               3        6.5676580       0
138   8.35134857              10        5.3418832       1
139   8.02333375              13       10.3857957       0
140   5.42719436               3        8.3031007       0
141   7.12345194              13        2.4602898       1
142   8.91261525               7        7.3280262       0
143   4.26268758               6        7.7095810       1
144   9.22597674               4        3.9431966       0
145   5.66955745               3        8.8156944       0
146   3.62831692               6       12.5566694       0
147   8.65155043               9        8.9549559       0
148  11.73492517               3        5.3729600       0
149   5.86066216               6        7.9529061       0
150   6.87969975               1        7.4718195       0
151   8.59922782               6       10.3770762       0
152   8.34849103              15        4.1437295       0
153   6.53190040               2        5.1995878       0
154   6.26542285              12        8.3395182       0
155   9.03166695              15        7.7449582       0
156   7.76843347              10        8.6865106       0
157   5.30465998              11        6.1699887       0
158   9.46329145              14        5.9790425       0
159   6.12524004              15        8.1231793       0
160   6.96795486               3        3.2138523       0
161   8.65214705              11        5.6513849       0
162   6.12052055               7        8.0014200       0
163   6.10449228               2       12.1517678       0
164   7.64773771              12        8.6791786       0
165   6.83492279              12        7.3217960       0
166   8.73520746              13        4.6128375       0
167   6.89388717               7        6.5143618       0
168   7.05522737               5        6.2675235       0
169   7.51797645              14       11.0448462       0
170   6.09405374              13        8.1233421       0
171  10.63292465              10        7.1000613       0
172   5.51206380              10        6.1490492       0
173   9.76955744               6        6.3484507       0
174   7.12643771              13        5.5621876       0
175   7.04986718               8        6.0082325       0
176   7.87004211               5        4.8051858       0
177   7.95408816              13        7.2485377       0
178   7.19132971               1        5.9734223       0
179   6.93652068               6        8.1899177       0
180   6.24501235               3        7.7681187       0
181   6.01129070              14        6.0243635       0
182   6.30277502              15        6.0842536       0
183   7.81087915               9       12.3195837       1
184   6.22125549               8        8.7154398       0
185   4.85447274              12        6.5527578       0
186   8.40233629               9        7.5278667       0
187   7.00973654               7        8.7697048       0
188   6.24020345               2        4.1597509       0
189   3.84361591               8        9.8499728       0
190   8.39915204              13        4.0307188       0
191   6.43321735              11        8.7126130       0
192   4.33606029              12        7.6498942       0
193   5.07896531               9        4.5606704       0
194   6.28292467              11        7.7415520       0
195   8.31940432               2        6.3766619       1
196   4.39595375              13        5.8459147       0
197   7.48589820              15        7.7621159       1
198   8.25935894               2        5.7003999       1
199   4.80960758               2        6.8776428       0
200   7.23714732               7        7.8662863       0
201   6.40828663              11        5.5052846       0
202   6.85353579              14        9.3777536       0
203   4.90967849               9        9.4036327       0
204   6.40399385               4        4.4573193       0
205   5.45589738               2        8.3981226       0
206  10.16723535              10        9.2757188       0
207   6.15631697               1        6.1578030       0
208   4.24120258               4        9.5797810       0
209   4.41410598               4        7.7039760       0
210   7.92982290              12        5.4837887       0
211   6.19808822              14        4.7868287       0
212   4.46724015               8        8.6061847       0
213   4.62003345               7        9.4342619       0
214   7.75397977              14        4.3700565       0
215   7.29699741              14        8.7362421       0
216   8.75961525               2        6.9574693       1
217   4.49121723               6        6.7291165       0
218   9.49634609               6        3.7926841       0
219   7.53711483              13       10.5559295       0
220   8.61222322               1        7.6151914       0
221   8.46187538              14        5.9767580       0
222   5.57655900              13        4.9208497       1
223   9.22367949              13        6.9998418       0
224   6.21696663              11        3.2105414       1
225   5.03225504               7        5.9594609       0
226  10.00151251               5        7.1601597       0
227   6.13726740              13       10.9448441       0
228  10.00533224               8        7.5491811       1
229   6.73774085              14        8.5401090       1
230   6.52304276               3       11.3070546       0
231   3.80358335               4        5.7440940       0
232   5.46796410              10        5.9943706       0
233   4.26382867               7        9.0583183       0
234   4.17329995              12        6.5012150       0
235   8.65603972               5        5.2130009       0
236   4.52396232              13        9.1544562       0
237   3.52311078               3        8.6103762       0
238   9.43199415               6        7.7620625       0
239   5.11341718               4        6.8362936       0
240   7.81523866              10        5.0495509       0
241   7.59576891               7        9.1028266       0
242   7.17782360               1        4.7466194       0
243   6.90523361              15        7.7859606       0
244   4.87062993               5        5.9110906       0
245  10.60991998               5        9.5233964       0
246   7.63572030               8        8.0699887       0
247   7.66983816              13        7.5084791       1
248   9.36792365              13        7.2794065       0
249   7.39080602              15        9.1672085       1
250   4.38453121               5        4.3125593       0
251   4.73545191              12       10.0733067       0
252   6.13991957              15        5.1351067       0
253   5.52339937               1        9.8927088       1
254  11.39930861              14        3.2351602       0
255   8.86505071               2        9.5434618       0
256   7.43348134              15        6.7835573       0
257   6.31869658              15        7.5726980       0
258   5.56756710              14        5.5793045       1
259   5.71936770              13        7.9456408       0
260   9.86922268               3        4.2943662       0
261  10.71314564               3        5.7854746       0
262   7.79170682              12        6.0532514       0
263   7.90855323              12       10.8491305       0
264   9.57138262               5        7.6350701       1
265   7.48772053              12        7.2590996       0
266   6.13763755              15        5.6789035       0
267   9.12812538               4        7.9278314       0
268   7.62006233               3        5.7605665       0
269   6.92084328              13        6.5901131       0
270   8.52692772               8        9.3761036       0
271   6.02105537              10        7.8562985       0
272   9.74715345              14        8.1398130       0
273   4.28583050               2        3.5868826       0
274   5.12535281              12        7.4386711       0
275   7.04244317              15        7.1173680       0
276   5.62691147              14        8.0060130       0
277   7.51347198               7       13.8950730       0
278   6.75909113               2        4.3574190       0
279   6.81830695              12        7.2970141       0
280   8.49514037              14        8.3787228       0
281   5.53936518               7        7.1573967       0
282   6.32855564               6        5.7787642       1
283   4.63174239              12        7.4511241       0
284   6.02694042              10        6.9599203       0
285   7.72472791              12        4.3121927       0
286   8.29198458               2        8.7372651       1
287   6.19097023              12        7.0689001       0
288   6.07641835               6       11.8466860       0
289   7.52292462              10        4.5235331       0
290   8.10835879               2        5.5392402       0
291   8.41777490               7       10.6451242       1
292   7.78805602              11        7.1203820       0
293   5.17914764               3        6.0438583       0
294   6.59885918              15        6.0681588       0
295   8.77916595               4        7.3530980       0
296   6.27077828              12       10.7343875       0
297   8.31701094              14        8.7550255       0
298   6.52085902               2        4.4765576       0
299   7.39581145               7        5.0594925       0
300   4.67058612               8        8.8844535       1
301   5.62262272               8        5.3198519       0
302   7.90786032               4        5.4945553       0
303   6.69691644              12        8.8273466       0
304   6.37738052              12        9.9169787       0
305   5.32683834              12        6.7986646       0
306   7.68435762              12        7.4726438       0
307   8.38842632              11        7.6482221       1
308   9.86822360               9        8.6588929       0
309   3.94463567               1        7.9989445       0
310   8.47162388              13        5.9089396       0
311   8.43990815               4        5.6424762       0
312   4.57458947               6        4.1101501       0
313   7.90143398              11        4.8579729       0
314   7.74970084               1        8.0354374       0
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730   8.07267221               7        7.6803124       0
731   7.68698643              10        6.8784852       0
732   5.46948650              12        4.0373652       0
733   5.51743491              10        5.1054828       0
734   8.84663010               4        8.8829147       0
735   8.24975564               3        7.2593506       1
736   5.70599507              14        9.0714357       0
737  12.18358773              10        6.3742681       0
738   9.32187120               3        9.4522819       0
739  11.00327023               6        6.9622606       0
740  10.18231134              15       11.4493678       0
741  10.35879093               6        9.5750702       0
742   9.06334034              15        4.5447343       0
743   8.66263854               9        6.9573853       1
744   7.30390589              11        4.9391019       0
745   8.73514127               4       11.8784748       0
746  10.33452514              12        8.9571463       1
747   6.99316252               5        5.0897741       0
748   7.29623779               6        3.3216048       0
749   6.84828180              15        6.3127800       0
750   7.00422460               5        8.2839152       0
751   8.08590180               3        2.3048738       0
752   8.30343006               4        5.8300879       0
753   4.52596408               7        5.8410177       0
754   6.37384870               8        6.1999410       0
755   5.78800542              12       10.0064287       0
756   6.35502859               6        6.8695869       0
757   6.96799274              11        7.3869152       0
758   9.46295810               5        7.6493051       0
759   7.17045248              13       11.6918056       0
760   9.08750683              13        8.6111736       0
761   4.80959381              12        5.6311641       0
762   7.10050384               7        7.1512068       1
763   7.02855755               1        6.2619683       0
764   7.62927682               9        6.1244462       0
765   7.87895979               1        6.1206549       0
766   4.78806492               5        7.7831494       0
767   5.32053725              14        4.4645930       0
768   6.29002562              12        9.9010575       0
769   7.31843129               5        6.7128831       0
770   9.07812283              13        6.1510583       0
771   4.36052202               3        9.3353680       0
772   8.86107115              13        6.7480352       1
773   8.50225481              14        6.7190570       0
774   7.21247736               9        7.0165174       0
775   9.80307955               1        6.4413171       0
776   7.41106298              10        9.5642620       0
777   6.90571053              14        7.6899048       0
778   7.66603466               3        5.0322828       0
779   7.86736817              12        4.9470897       0
780   9.77441212               8        9.0046610       0
781   5.09758344              13        9.0302590       0
782   6.77729625               4        8.8842512       0
783   8.24436893              11        8.5489468       0
784   4.67824303              15        7.0120843       0
785   3.53564557               5        7.2064588       0
786   6.10231463               2        4.1097441       0
787   6.69689169              13        5.6397694       0
788   6.97488222               3        5.4088488       1
789   9.13716840               4        8.4528001       0
790   5.68278363               4        8.3758136       0
791   5.20340151               7       10.0004249       0
792   2.62364615               9        7.8596399       0
793  10.43591657               9        7.1684867       0
794   7.61630958               8        8.4913438       0
795   8.31786290               9       10.1418603       0
796   8.39209355               3        6.3923881       0
797   3.59666298               3        6.4588087       0
798   6.05805843               8        5.5601066       1
799   9.63962209               6        9.3863150       0
800  10.03508352               4        7.0203144       1
801   8.88547844               7        7.5575176       0
802   6.54437128               8        6.0844610       0
803   6.17826038               8        7.2574481       0
804   6.99952683               7        9.3357316       0
805   6.74363383               4        4.9504612       0
806   6.87804456               1       10.6364849       0
807   5.47658079               4        4.5931479       1
808   2.42297742               7        4.9804235       0
809   4.69318685               4        8.5922230       0
810   7.72794879               9        8.8950564       0
811   5.05748989              11        5.9176210       0
812  13.77218568              12        6.6335219       0
813   8.41958367               8        5.6199814       0
814   8.53258864              14        9.3267234       1
815   5.62703323               6        5.4386989       0
816   9.13127778              14        5.4712085       0
817   6.01593120               7        8.5892651       0
818   7.50138251               8        3.6427914       0
819   6.39959368              12        7.0742717       0
820   6.12880933               7        6.1868147       0
821   6.74507697               2        8.0360602       1
822  11.42296620               8        5.4586150       0
823   8.69948255              13        8.0608086       0
824   8.01308402              13       10.3134643       0
825   7.73730118              15        7.4770088       0
826   6.99878277               3        8.3996879       0
827  11.06613002               6        4.0559478       0
828   7.91084673              10        8.7776905       0
829   6.51160396               2        9.0437706       0
830   7.04936396               2        8.5029676       1
831   4.78092254               5        6.5333955       0
832   5.25571295              10        5.5815118       1
833   5.96186022               9        6.1872884       0
834   6.98659250               3        5.5706815       1
835   9.47872991               4        8.3891147       0
836   9.04018652               8        4.4326306       0
837   7.08180136               2        7.8663687       0
838   5.51418763              14        5.6818695       0
839   7.63057693               1        5.6285598       0
840   7.60317064               6        7.4971318       0
841   9.71093288               9        4.3992459       0
842   5.96892568              13        6.7612045       0
843   4.09208127              12        4.9950366       0
844   6.94807611               6        9.0214478       0
845   5.71329215              11        6.4391059       0
846   6.87226490               5        8.1679609       0
847   5.87422261              14       11.5106570       0
848   9.39077501               3        9.5787688       1
849  11.63051878               9        8.4915949       0
850   9.33048483               3        7.7401615       0
851   6.82686600              15        6.3737534       0
852   5.55997005               4        6.0349505       0
853  10.96316187              14        7.9885641       0
854   3.86124238              10        4.9795246       0
855  10.34289525               2       11.1024463       0
856   7.40425888               4        6.7403062       0
857   6.99596676               1        4.8244555       0
858   6.11278339               8        5.0007785       0
859   8.23492412               4        8.4948753       0
860   3.85009994              10        6.2745954       0
861   7.42963242              14        3.1056591       0
862   8.24968596               1        8.2338722       0
863  11.69752058               2        7.9047406       0
864   5.44577242               7        5.3243324       0
865   5.65007936               1        2.7222140       0
866   6.22815540              15        3.3637297       0
867   7.01588857              10        7.7225407       0
868   2.96960415               8       11.0827446       0
869   3.64044310               1        6.1630477       0
870   8.33585309               5        6.9750627       0
871   6.40498910               3        8.1664992       0
872   9.37399537               7       10.1086529       0
873   7.68109757              14        2.6587841       0
874   6.14415246              12        5.1751420       0
875   6.63440758              10        7.7487725       0
876   7.17993757              11        2.8488472       0
877   6.35444959               4        5.8100608       1
878   6.41748957               2        7.7531541       0
879   8.54901418               6        5.0452267       0
880   8.92855394               5        7.1600617       0
881   8.96315913               7       10.1642480       0
882   5.70629620               4        8.7518388       0
883   9.53497670               6        7.5774787       0
884   6.72816243               2        9.6938492       0
885   5.05082037               9        7.1119020       1
886   8.25799346               8        8.3833051       0
887   8.87213138              12        4.7476183       0
888   9.22980611              11        4.5450253       0
889   5.89710064               3        6.7050647       0
890   5.58706885              11        4.8800819       0
891   9.95427261               4        7.0572455       1
892   9.10126713               9        3.9583646       0
893   7.27834188               8        8.7901062       0
894   7.91823507               7        4.8307203       0
895   5.51592333               5        6.5357555       0
896   5.59703227               2        6.2292575       0
897   9.69353969               9       10.9830157       0
898   9.16183559              12        9.0986534       0
899   7.27647925               8        6.6941889       0
900  11.71903008              12        8.5119714       0
901  11.37301280              14        8.8008508       0
902   8.96514318               4        5.0600168       1
903   5.93086708              15        8.0392195       0
904   6.60273077              15        9.0730709       0
905   6.66859180              11        4.5497459       1
906   8.77214323               6        4.9120284       0
907   5.40908207              14        6.4759576       0
908   5.37695528               1        6.0434770       0
909   7.52567255               5        6.7089510       0
910   6.75808324               8        8.9154587       0
911   9.48636542               5        6.1421251       0
912   7.84513264               3        7.1681764       0
913   8.46483794               3       10.0656899       0
914   5.15382206               8        9.2346435       0
915   5.01726674              15        5.8164282       0
916   5.04045571               6        6.5336413       0
917   7.19910360               5        8.2555371       0
918   6.44184247               3        5.3927453       0
919  12.67715688               1        8.5190910       0
920   4.78953650               2        4.1475499       0
921   5.64912939              10        9.4310212       0
922   2.18301311               4        7.2860177       0
923   6.48442071               8        8.0457831       0
924   7.07830767               9        6.3672810       0
925   5.17511628              12        6.7417660       0
926   5.14557882               6        7.1904634       0
927  10.35627026               5        9.6663003       0
928   6.10186595              14        6.3679857       0
929   6.56637533              15        8.4360394       0
930   8.80011065              14        4.5355983       0
931   3.44682038              11        9.2047202       0
932   4.49209225              11        5.5503604       0
933   7.52463008               6        9.9821209       0
934   6.17532457               5        7.6925253       0
935   7.47232413               5        3.3106046       0
936   9.07777665              13        5.6808335       0
937  10.66938592               2        9.2308705       0
938   6.77493691              15        2.8383142       0
939   8.26520036              11        4.6182888       0
940   6.48678842              11        8.7783642       0
941   5.89604463               1        6.5230287       0
942   8.19140614               8        3.4117302       0
943   8.10429519              11       10.4391025       0
944  10.65266366               6        7.1759631       0
945   9.18853699              12        9.5390855       0
946   9.05908666               6        6.6109226       0
947   9.67636375              14        6.3328061       0
948   7.15098173               1        5.2211738       0
949   9.23319923              13        9.0061618       0
950   8.46383160               8        6.4091989       0
951   6.22377187              13        4.0782851       0
952   7.04187296               5        3.1517804       0
953  10.04179627               9        9.5793555       0
954   4.46179120               4        6.2718563       1
955   5.47598866               2       10.3787692       0
956   5.79493619               1        3.1351805       0
957   6.00804646              10        6.2088713       0
958   4.33590865               7        5.4279465       0
959   6.01692175               1        7.2429580       1
960   7.05079481               7        9.2110865       0
961   6.35961354               7        9.6164193       0
962   9.84425660               7        7.8987694       0
963   8.53417419              11        6.4456385       0
964   7.90404872              11       10.0605159       0
965   7.25568916               5        7.5455813       1
966   7.88228245               4       10.6712719       0
967   4.35763484               5        7.6365686       0
968   8.38831459              10        9.6262420       0
969   7.10020409               8        5.9565316       0
970   7.99547059               9        6.6000136       0
971   7.73398512               2       10.9461425       0
972   8.05439768               6        8.3139269       0
973   6.33618076               9        7.5026714       0
974   8.60245885              12        6.5798378       0
975   5.89716813              15        9.4079148       0
976   8.27970095               7        5.0939625       0
977   4.17642782              11        7.5896588       0
978   9.63435558               6        4.7359940       0
979   9.37628384              15        4.4261299       0
980   4.93306339               3        8.0556718       0
981   5.39413809               6        6.4164723       0
982   5.15028197               7        7.3709867       0
983   6.21762263               4        4.9069408       0
984   7.55328460               2        5.6613804       0
985   8.57186739               3        9.6540860       0
986   7.48639183              13       10.1941338       0
987   5.06472229               4        8.4962835       0
988   8.92408668              15        4.6705280       0
989   8.39064197               7        6.3984964       0
990   8.46601164              13        8.8285250       0
991   4.52927384              12        3.6792858       0
992   8.11495887               8       10.3784899       0
993  10.71226124              14        5.9683000       0
994   7.24380902               7        9.7606527       0
995   6.46908889               9        6.3540172       0
996   9.00445751               3        9.1219823       0
997   7.90712600               1        8.3223347       0
998   5.59374259              14        5.6034202       0
999   7.62303860               5        9.4213477       0
1000  7.35095551               4        5.3921849       0

★ Convert DV to a Factor

# Convert Dropout to a Factor

dropout_data_new$Dropout <- as.factor(dropout_data_new$Dropout)

# Provide a description of what the values 0 and 1 represent.

attr(dropout_data_new$Dropout, "label") <- "Dropout (1=Dropout; 0=NotDropout)"

# Check the structure of variables in this dataset

str(dropout_data_new)

'data.frame':   1000 obs. of  10 variables:
 $ SES             : num  37.3 58.9 46.9 58.2 60.2 ...
  ..- attr(*, "label")= chr "Socioeconomic Status (1-100)"
 $ ParentEdu       : int  3 5 4 1 3 2 4 2 1 2 ...
  ..- attr(*, "label")= chr "Parental Education Level (1-5)"
 $ Attendance      : num  82 80.2 87.6 86.3 86.5 ...
  ..- attr(*, "label")= chr "Attendance Rate (percent)"
 $ HomeworkHours   : num  4.9 2.02 2.32 3.58 3.28 ...
  ..- attr(*, "label")= chr "Hours Spent on Homework (per week)"
 $ Motivation      : num  8.33 5.53 6.66 5.8 7.9 ...
  ..- attr(*, "label")= chr "Student Motivation (1-15)"
 $ PeerSupport     : num  7.05 7.79 8.35 6.36 11.73 ...
  ..- attr(*, "label")= chr "Peer Support (0-15)"
 $ TestAnxiety     : num  7.91 3.78 4.92 7.33 5.25 ...
  ..- attr(*, "label")= chr "Test Anxiety (0-15)"
 $ ExtraCurricular : int  11 3 6 6 6 9 10 12 13 7 ...
  ..- attr(*, "label")= chr "Extracurricular Activities (number)"
 $ MathSelfEfficacy: num  8.4 5.18 6.68 6.12 8.07 ...
  ..- attr(*, "label")= chr "Math Self-Efficacy (0-15)"
 $ Dropout         : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
  ..- attr(*, "label")= chr "Dropout (1=Dropout; 0=NotDropout)"

# View Levels: In R, when performing logistic regression with a factor variable, the first level of the factor is treated as the reference category. This means that R will treat "NotDropout" (0) as the reference category and will model the log-odds of being a dropout (1) compared to not being a dropout (0).

levels(dropout_data_new$Dropout)

[1] "0" "1"

★ When calculating performance measures like Receiver Operating Characteristic (ROC) and Area Under the Curve (AUC), R has trouble using numbers like 0 and 1 as category labels, even if they are already factors, because they don’t work well as variable names in its system. To fix this, we can rename them with clearer labels like “NotDropout” and “Dropout.”

levels(dropout_data_new$Dropout) <- c("NotDropout", "Dropout")
levels(dropout_data_new$Dropout)

[1] "NotDropout" "Dropout"   

This sets the levels of the factor Dropout as follows:

• First level (NotDropout): Treated as the negative class (reference group).

• Second level (Dropout): Treated as the positive class.

★ Normalization / Standardization

In K-Nearest Neighbors (KNN), normalization or standardization is important because KNN is a distance-based algorithm. It calculates the distance between data points to determine which neighbors are closest, and those distances heavily influence the model’s predictions. Normalization or Standardization in KNN ensures that all features (predictors) contribute equally to the distance calculations, preventing features with larger scales from dominating the model’s predictions, and ultimately leading to more accurate results.

We can use the preProcess() function from the caret package in R to perform both normalization and standardization.

• method = “range” is used for normalization (Min-Max scaling).

• method = c(“center”, “scale”) is used for standardization (mean = 0, standard deviation = 1).

For this demonstration, we “normalized” all the predictors.

library(caret)

Loading required package: ggplot2

Loading required package: lattice

# Normalization using preProcess() in caret

normalizationknn <- preProcess(dropout_data_new[, -c(10)], method = "range")  # The -c(10) tells R to exclude column 11, Dropout.

# Apply the transformation

normalized_predictorsknn <- predict(normalizationknn, dropout_data_new[, -c(10)])

# Combine the normalized predictors with the rest of the data (untransformed column: Dropout)

dropout_data_normalizedknn <- dropout_data_new #Recreate new data
dropout_data_normalizedknn[, 1:9]<- normalized_predictorsknn

Normalize data for Naive Bayes Evaluation

library(caret)

# Normalization using preProcess() in caret

normalizationnb <- preProcess(dropout_data_new[, -c(10)], method = "range")  # The -c(10) tells R to exclude column 10, Dropout.

# Apply the transformation

normalized_predictorsnb <- predict(normalizationnb, dropout_data_new[, -c(10)])

# Combine the normalized predictors with the rest of the data (untransformed column: Dropout)

dropout_data_normalizednb <- dropout_data_new #Recreate new data
dropout_data_normalizednb[, 1:9]<- normalized_predictorsnb

Split the Data into Training and Test sets

The purpose of this split is to train a model on one part of the data (training set) and then test how well it performs on unseen data (test set). The caret package is used to split the dataset into training and test sets.

• createDataPartition() is a function from the caret package that splits data based on the distribution of a target variable (in this case, the Dropout variable).

• The p = 0.8 argument specifies that 80% of the data will be used for training. Note. Both 70/30 and 80/20 splits are common practices, and the choice depends on the size of the dataset, model complexity, and your evaluation needs. p = 0.8 is generally more popular, but p = 0.7 may be more appropriate if you have a large dataset and want a more reliable test set for evaluation.

• The list = FALSE argument ensures that the output is returned as a vector of row indices rather than a list.

# Load caret library

library(caret)

# Set a seed for reproducibility

set.seed(668)

# Split the data

split <- createDataPartition(dropout_data_normalizedknn$Dropout, p = 0.8, list = FALSE)
split <- createDataPartition(dropout_data_normalizednb$Dropout, p = 0.8, list = FALSE)

# Create Training and Test Sets

train_dataknn <- dropout_data_normalizedknn[split, ]
test_dataknn <- dropout_data_normalizedknn[-split, ]

train_datanb <- dropout_data_normalizednb[split, ]
test_datanb <- dropout_data_normalizednb[-split, ]

# Check the dimensions of the training and test sets

dim(train_dataknn)  # Should be around 800 rows

[1] 800  10

dim(test_dataknn)   # Should be around 200 rows

[1] 200  10

dim(train_datanb)  # Should be around 800 rows

[1] 800  10

dim(test_datanb)   # Should be around 200 rows

[1] 200  10

# Ensure the Dropout variable is a factor (Double Check!)

str(train_dataknn)

'data.frame':   800 obs. of  10 variables:
 $ SES             : num  0.239 0.551 0.377 0.544 0.468 ...
 $ ParentEdu       : num  0.5 1 0.75 0.25 0.25 0.25 0 0.75 1 0.75 ...
 $ Attendance      : num  0.436 0.375 0.618 0.563 0.313 ...
 $ HomeworkHours   : num  0.762 0.29 0.338 0.246 0.671 ...
 $ Motivation      : num  0.555 0.346 0.431 0.594 0.52 ...
 $ PeerSupport     : num  0.491 0.544 0.584 0.652 0.635 ...
 $ TestAnxiety     : num  0.574 0.272 0.356 0.492 0.525 ...
 $ ExtraCurricular : num  0.714 0.143 0.357 0.571 0.786 ...
 $ MathSelfEfficacy: num  0.559 0.337 0.44 0.583 0.541 ...
 $ Dropout         : Factor w/ 2 levels "NotDropout","Dropout": 1 1 1 1 1 1 2 1 2 1 ...

str(test_dataknn)

'data.frame':   200 obs. of  10 variables:
 $ SES             : num  0.541 0.569 0.278 0.406 0.509 ...
 $ ParentEdu       : num  0 0.5 0.75 0 0.75 0.5 0.5 0.75 0.75 0 ...
 $ Attendance      : num  0.577 0.582 0.569 0.199 0.374 ...
 $ HomeworkHours   : num  0.545 0.496 0.538 0.467 0.628 ...
 $ Motivation      : num  0.366 0.524 0.423 0.612 0.505 ...
 $ PeerSupport     : num  0.441 0.825 0.495 0.577 0.71 ...
 $ TestAnxiety     : num  0.531 0.38 0.558 0.498 0.679 ...
 $ ExtraCurricular : num  0.357 0.357 0.643 0.857 0.214 ...
 $ MathSelfEfficacy: num  0.401 0.536 0.399 0.614 0.5 ...
 $ Dropout         : Factor w/ 2 levels "NotDropout","Dropout": 1 1 1 1 1 1 1 1 1 1 ...

str(train_datanb)

'data.frame':   800 obs. of  10 variables:
 $ SES             : num  0.239 0.551 0.377 0.544 0.468 ...
 $ ParentEdu       : num  0.5 1 0.75 0.25 0.25 0.25 0 0.75 1 0.75 ...
 $ Attendance      : num  0.436 0.375 0.618 0.563 0.313 ...
 $ HomeworkHours   : num  0.762 0.29 0.338 0.246 0.671 ...
 $ Motivation      : num  0.555 0.346 0.431 0.594 0.52 ...
 $ PeerSupport     : num  0.491 0.544 0.584 0.652 0.635 ...
 $ TestAnxiety     : num  0.574 0.272 0.356 0.492 0.525 ...
 $ ExtraCurricular : num  0.714 0.143 0.357 0.571 0.786 ...
 $ MathSelfEfficacy: num  0.559 0.337 0.44 0.583 0.541 ...
 $ Dropout         : Factor w/ 2 levels "NotDropout","Dropout": 1 1 1 1 1 1 2 1 2 1 ...

str(test_datanb)

'data.frame':   200 obs. of  10 variables:
 $ SES             : num  0.541 0.569 0.278 0.406 0.509 ...
 $ ParentEdu       : num  0 0.5 0.75 0 0.75 0.5 0.5 0.75 0.75 0 ...
 $ Attendance      : num  0.577 0.582 0.569 0.199 0.374 ...
 $ HomeworkHours   : num  0.545 0.496 0.538 0.467 0.628 ...
 $ Motivation      : num  0.366 0.524 0.423 0.612 0.505 ...
 $ PeerSupport     : num  0.441 0.825 0.495 0.577 0.71 ...
 $ TestAnxiety     : num  0.531 0.38 0.558 0.498 0.679 ...
 $ ExtraCurricular : num  0.357 0.357 0.643 0.857 0.214 ...
 $ MathSelfEfficacy: num  0.401 0.536 0.399 0.614 0.5 ...
 $ Dropout         : Factor w/ 2 levels "NotDropout","Dropout": 1 1 1 1 1 1 1 1 1 1 ...

# (Convert it if needed)
# train_data$Dropout <- as.factor(train_data$Dropout)
# test_data$Dropout <- as.factor(test_data$Dropout)

Dealing with Class Imbalance using SMOTE

Before we train our model using the training data, we need to address a common issue in classification tasks: class imbalance. When one class is significantly underrepresented compared to others (for example, very few students drop out compared to those who do not), it can cause predictive models to perform poorly on the minority class. Synthetic Minority Over-sampling Technique (SMOTE) is one method used to deal with this imbalance by generating synthetic (fake) samples for the minority class.

themis is a package in R that contains functions for handling imbalanced datasets using various resampling techniques, including SMOTE.

smotenc(): This function applies SMOTE to the train_data to balance the Dropout variable (the dependent variable).

• train_data: The training dataset.

• var = “Dropout”: Specifies the Dropout variable as the target variable to balance.

• k = 5: Refers to the number of nearest neighbors SMOTE uses to generate new samples for the minority class. In this case, it uses 5 nearest neighbors.

• over_ratio = 1: Controls the degree of oversampling. A value of 1 means that after applying SMOTE, the minority class (Dropout) will have the same number of samples as the majority class (NotDropout), achieving a 1:1 ratio.

(Image Source: Link)

# Check Class Distribution

table(train_dataknn$Dropout)

NotDropout    Dropout 
       720         80 

table(train_datanb$Dropout)

NotDropout    Dropout 
       720         80 

# Install and Load themis Package

#install.packages("themis")
library(themis)

Loading required package: recipes

Attaching package: 'recipes'

The following object is masked from 'package:stats':

    step

# Apply SMOTE

set.seed(668)

train_dataknn_smote <- smotenc(train_dataknn, var = "Dropout", k = 5, over_ratio = 1)
train_datanb_smote <- smotenc(train_datanb, var = "Dropout", k = 5, over_ratio = 1)

# Check Class Distribution After SMOTE

table(train_dataknn_smote$Dropout)

NotDropout    Dropout 
       720        720 

table(train_datanb_smote$Dropout)

NotDropout    Dropout 
       720        720 

SMOTE creates new dropout cases by taking each of the 80 original ones and finding 5 similar cases (nearest neighbors) based on their characteristics (like grades, attendance, etc.). Instead of just copying them, SMOTE mixes features from the original case with one of the 5 similar ones to create new, realistic dropout cases. This process is repeated enough times to bring the total number of dropout cases to 720, helping balance the data so that the model can learn better and make fair predictions for both dropout and non-dropout students.

★ 10-fold cross-validation

In this analysis, we start by focusing on finding the best value for k in our K-Nearest Neighbors (KNN) model for predicting student dropout. The value of k represents the number of neighbors the model considers when making a prediction. Choosing the right k is crucial because too small a value can make the model overly sensitive to individual data points (overfitting), while too large a value can make the model too generalized (underfitting). By testing multiple values of k through 10-fold cross-validation, we can identify the best k that balances accuracy and generalization.

We use 10-fold cross-validation to split the dataset into different training and validation sets repeatedly, which helps ensure the model performs well on new, unseen data. The caret package is used to enable class probabilities (classProbs = TRUE), allowing the model to estimate how likely a student is to drop out, rather than giving a simple yes/no prediction. This is important because it lets us calculate performance metrics like ROC (Receiver Operating Characteristic) and AUC (Area Under the Curve), which show how well the model distinguishes between correct and incorrect predictions. Additionally, the summaryFunction = twoClassSummary function computes three key metrics for evaluating the performance of a binary classifier: ROC/AUC, Sensitivity, and Specificity.

# Install and load the MLmetrics package to calculate additional performance metrics

# install.packages("MLmetrics") # Uncomment to install the package if not installed
library(MLmetrics)

Attaching package: 'MLmetrics'

The following objects are masked from 'package:caret':

    MAE, RMSE

The following object is masked from 'package:base':

    Recall

# Set up 10-fold cross-validation with class probabilities enabled

cv10 <- trainControl(
  method = "cv",            # Perform cross-validation
  number = 10,              # Use 10-folds
  classProbs = TRUE,        # Enable class probabilities (needed for ROC/AUC)
  summaryFunction = multiClassSummary  # Evaluate performance using multiple metrics
)


# Define the control method for cross-validation with class probabilities

#cv10 <- trainControl(
 # method = "cv", # Cross-validation
 # number = 10,   # 10-fold
  #classProbs = TRUE, # Enable class probabilities for ROC/AUC
 # summaryFunction = twoClassSummary  # Use two-class metrics for evaluation 

Now, we can start exploring the best k in our KNN model.

train(Dropout ~ ., data = train_data_smote): This specifies that the model should predict the Dropout variable using all the other variables in the dataset train_data_smote. The tilde (~) means “based on” and . means “all other predictors.”

• method = “knn”: This specifies that we are training a KNN model.

• tuneLength = 20: This means the model will test 20 different values of k to determine the best number of neighbors to consider when making predictions. It automatically selects a reasonable range of k values to test.

• trControl = cv10: This is where we define the cross-validation strategy. Here, 10-fold cross-validation is being used to evaluate the model’s performance, as previously set up.

• metric = “ROC”: The model is being optimized based on the ROC curve. This metric balances the trade-off between sensitivity (true positive rate) and specificity (false positive rate), ensuring the model performs well in distinguishing between the classes (“Dropout” and “NotDropout”).

# Explore the best k in our KNN model

set.seed(668)

knn_fit <- train(
  Dropout ~ ., 
  data = train_dataknn_smote,
  method = "knn", 
  tuneLength = 20, # Try 20 different values of 'k'
  trControl = cv10, # Use cross-validation with classProbs enabled
  metric = "ROC"  # Optimize model based on ROC (AUC)
)

Warning in train.default(x, y, weights = w, ...): The metric "ROC" was not in
the result set. logLoss will be used instead.

# Print the results

print(knn_fit)

k-Nearest Neighbors 

1440 samples
   9 predictor
   2 classes: 'NotDropout', 'Dropout' 

No pre-processing
Resampling: Cross-Validated (10 fold) 
Summary of sample sizes: 1296, 1296, 1296, 1296, 1296, 1296, ... 
Resampling results across tuning parameters:

  k   logLoss    AUC        prAUC      Accuracy   Kappa      F1       
   5  2.0511027  0.9284626  0.3471770  0.8187500  0.6375000  0.7784715
   7  1.5578931  0.9293596  0.4473966  0.7986111  0.5972222  0.7493409
   9  1.2552981  0.9227141  0.5355766  0.7756944  0.5513889  0.7171599
  11  0.9933345  0.9103299  0.6072639  0.7659722  0.5319444  0.7016604
  13  0.7881977  0.9013503  0.6628825  0.7513889  0.5027778  0.6783738
  15  0.6662486  0.8936439  0.7004141  0.7486111  0.4972222  0.6753364
  17  0.6334393  0.8835359  0.7392521  0.7375000  0.4750000  0.6611721
  19  0.5951142  0.8786265  0.7644648  0.7326389  0.4652778  0.6528592
  21  0.5752688  0.8749325  0.7785447  0.7291667  0.4583333  0.6496713
  23  0.5571150  0.8711709  0.8002087  0.7215278  0.4430556  0.6428288
  25  0.5602957  0.8682388  0.8094094  0.7187500  0.4375000  0.6412721
  27  0.5622138  0.8650656  0.8116371  0.7187500  0.4375000  0.6399365
  29  0.5675365  0.8613137  0.8162862  0.7180556  0.4361111  0.6387349
  31  0.5735834  0.8560571  0.8130884  0.7166667  0.4333333  0.6356465
  33  0.5791082  0.8511767  0.8127176  0.7131944  0.4263889  0.6325555
  35  0.5842478  0.8461516  0.8108429  0.7118056  0.4236111  0.6330387
  37  0.5878642  0.8431713  0.8116918  0.7090278  0.4180556  0.6308566
  39  0.5692086  0.8405671  0.8103413  0.7069444  0.4138889  0.6288869
  41  0.5515329  0.8360629  0.8082102  0.6986111  0.3972222  0.6152230
  43  0.5527387  0.8332562  0.8075362  0.7006944  0.4013889  0.6220450
  Sensitivity  Specificity  Pos_Pred_Value  Neg_Pred_Value  Precision
  0.6444444    0.9930556    0.9899331       0.7381781       0.9899331
  0.6083333    0.9888889    0.9826610       0.7178025       0.9826610
  0.5722222    0.9791667    0.9650181       0.6968243       0.9650181
  0.5541667    0.9777778    0.9618417       0.6878385       0.9618417
  0.5291667    0.9736111    0.9536887       0.6752899       0.9536887
  0.5263889    0.9708333    0.9482815       0.6730094       0.9482815
  0.5152778    0.9597222    0.9287371       0.6652192       0.9287371
  0.5069444    0.9583333    0.9269042       0.6613798       0.9269042
  0.5055556    0.9527778    0.9147893       0.6592496       0.9147893
  0.5041667    0.9388889    0.8920462       0.6552588       0.8920462
  0.5055556    0.9319444    0.8810991       0.6541489       0.8810991
  0.5027778    0.9347222    0.8856865       0.6535656       0.8856865
  0.5013889    0.9347222    0.8851265       0.6529292       0.8851265
  0.4972222    0.9361111    0.8863614       0.6513847       0.8863614
  0.4958333    0.9305556    0.8774384       0.6491756       0.8774384
  0.5000000    0.9236111    0.8688269       0.6495849       0.8688269
  0.5000000    0.9180556    0.8607381       0.6481752       0.8607381
  0.5000000    0.9138889    0.8536280       0.6473392       0.8536280
  0.4847222    0.9125000    0.8474388       0.6399043       0.8474388
  0.4958333    0.9055556    0.8395489       0.6433450       0.8395489
  Recall     Detection_Rate  Balanced_Accuracy
  0.6444444  0.3222222       0.8187500        
  0.6083333  0.3041667       0.7986111        
  0.5722222  0.2861111       0.7756944        
  0.5541667  0.2770833       0.7659722        
  0.5291667  0.2645833       0.7513889        
  0.5263889  0.2631944       0.7486111        
  0.5152778  0.2576389       0.7375000        
  0.5069444  0.2534722       0.7326389        
  0.5055556  0.2527778       0.7291667        
  0.5041667  0.2520833       0.7215278        
  0.5055556  0.2527778       0.7187500        
  0.5027778  0.2513889       0.7187500        
  0.5013889  0.2506944       0.7180556        
  0.4972222  0.2486111       0.7166667        
  0.4958333  0.2479167       0.7131944        
  0.5000000  0.2500000       0.7118056        
  0.5000000  0.2500000       0.7090278        
  0.5000000  0.2500000       0.7069444        
  0.4847222  0.2423611       0.6986111        
  0.4958333  0.2479167       0.7006944        

logLoss was used to select the optimal model using the smallest value.
The final value used for the model was k = 41.

plot(knn_fit)

★ Train a KNN model with the best k

Why Avoid Starting with k = 1?

• k = 1: The model simply assigns the class of the nearest neighbor, making it very sensitive to noise. This can result in overfitting, where the model fits the training data very well but performs poorly on unseen data.

• k = 5: A common starting point that balances underfitting (if k is too large, the model becomes too generalized) and overfitting (if k is too small, the model fits the noise).

ROC was used to select the optimal model using the largest value. The final value used for the model was k = 7. Now, we need to train our final KNN model with K=7.

# Define the tuning grid with k = 41

tune_grid <- expand.grid(k = 41) # This creates a custom grid for tuning where the value of k is fixed at 41. This step forces the model to use exactly k = 41.

# Train the KNN model with k = 41

set.seed(668)

knn_final <- train(
  Dropout ~ ., 
  data = train_dataknn_smote,
  method = "knn", 
  tuneGrid = tune_grid, # Use custom grid with k = 41
  trControl = cv10, # Use cross-validation with classProbs enabled
  metric = "ROC"  # Optimize model based on ROC (AUC)
)

Warning in train.default(x, y, weights = w, ...): The metric "ROC" was not in
the result set. logLoss will be used instead.

# Print the results

print(knn_final)

k-Nearest Neighbors 

1440 samples
   9 predictor
   2 classes: 'NotDropout', 'Dropout' 

No pre-processing
Resampling: Cross-Validated (10 fold) 
Summary of sample sizes: 1296, 1296, 1296, 1296, 1296, 1296, ... 
Resampling results:

  logLoss    AUC        prAUC      Accuracy   Kappa      F1        Sensitivity
  0.5515329  0.8360629  0.8082102  0.6986111  0.3972222  0.615223  0.4847222  
  Specificity  Pos_Pred_Value  Neg_Pred_Value  Precision  Recall   
  0.9125       0.8474388       0.6399043       0.8474388  0.4847222
  Detection_Rate  Balanced_Accuracy
  0.2423611       0.6986111        

Tuning parameter 'k' was held constant at a value of 41

# Variable importance

varImp(knn_final) # This function returns the importance of each predictor variable in the KNN model. While KNN is a distance-based algorithm and doesn’t typically assign direct "importance" to variables (unlike models like decision trees), this function evaluates the model’s performance and how much each variable contributes to the prediction accuracy.

ROC curve variable importance

                 Importance
Attendance          100.000
ExtraCurricular      67.174
SES                  62.196
ParentEdu            16.897
PeerSupport          14.965
HomeworkHours         5.915
TestAnxiety           5.047
Motivation            3.562
MathSelfEfficacy      0.000

Evaluate Model Performance on the Test Set

# Predict Outcome Using Model on Test Data

predictionsknn <- predict(knn_final, newdata=test_dataknn)

# Create Confusion Matrix to Assess Model Performance

confusionMatrix(data=predictionsknn, test_dataknn$Dropout, positive = "Dropout", mode = "everything") # MUST specify positive = "Dropout"; otherwise, the default setting treats "NotDropout" as the positive class.

Confusion Matrix and Statistics

            Reference
Prediction   NotDropout Dropout
  NotDropout        101       8
  Dropout            79      12
                                          
               Accuracy : 0.565           
                 95% CI : (0.4933, 0.6348)
    No Information Rate : 0.9             
    P-Value [Acc > NIR] : 1               
                                          
                  Kappa : 0.0625          
                                          
 Mcnemar's Test P-Value : 6.153e-14       
                                          
            Sensitivity : 0.6000          
            Specificity : 0.5611          
         Pos Pred Value : 0.1319          
         Neg Pred Value : 0.9266          
              Precision : 0.1319          
                 Recall : 0.6000          
                     F1 : 0.2162          
             Prevalence : 0.1000          
         Detection Rate : 0.0600          
   Detection Prevalence : 0.4550          
      Balanced Accuracy : 0.5806          
                                          
       'Positive' Class : Dropout         
                                          

Here’s a guide to the key metrics in the confusion matrix and what they mean:

Accuracy (0.64)

• Definition: The proportion of correct predictions (both dropouts and non-dropouts) out of the total predictions.

• When to Report: Accuracy is a common metric, but it can be misleading with imbalanced datasets (like this one, where 90% are non-dropouts). Because the data is skewed, this doesn’t reflect how well the model handles the minority class (students who drop out).

Sensitivity (Recall or True Positive Rate) (0.40)

• Definition: The proportion of actual dropouts (possitive class) that were correctly predicted as dropouts.

• When to Report: When we want to correctly identify as many dropouts as possible.

Specificity (True Negative Rate) (0.67)

• Definition: The proportion of actual non-dropouts (negative class) that were correctly identified as non-dropouts.

• When to Report: Specificity is crucial if we are interested in correctly identifying non-dropouts.

Kappa (0.03)

• Definition: A metric that adjusts accuracy for the possibility of random chance. It measures how much better your model is compared to random guessing.

• When to Report: Kappa is useful for understanding how well your model performs above random chance, especially in imbalanced datasets. A Kappa value close to 0 suggests very poor agreement between the prediction and true values.

Positive Predictive Value (PPV; a.k.a. Precision) (0.12)

• Definition: The proportion of predicted dropouts (positive class) that are actually dropouts.

• When to Report: PPV is crucial when we want to be sure that when the model predicts a student will drop out, it is correct. A low PPV indicates that when the model predicts a dropout, it is often wrong.

Negative Predictive Value (NPV) (0.91)

• Definition: The proportion of predicted non-dropouts (negative class) that are actual non-dropouts.

• When to Report: NPV is critical when we want to know if the model predicts a student will not drop out, how often that is correct. The high NPV means the model is mostly correct when predicting non-dropouts. High NPV is good, but since dropout prediction focuses on identifying students who will drop out, this isn’t our primary focus.

Balanced Accuracy (0.53)

• Definition: The average of sensitivity and specificity. It provides a better metric when dealing with imbalanced data, as it accounts for performance on both classes equally.

• When to Report: Balanced accuracy is useful because it weighs performance on both classes (dropouts and non-dropouts) equally. This metric is helpful for evaluating how well your model balances predicting both dropout and non-dropout students.

AUC (Area Under the Curve) (see the next section)

• Definition: AUC summarizes how well the model distinguishes between the two classes (dropout and non-dropout) over all possible thresholds. An AUC closer to 1 is desirable.

• When to Report: Report AUC if we’ve plotted the ROC curve, as it gives a single value to represent model performance across thresholds. This is a great metric to summarize overall model performance.

Please revisit our Week 2 slides and review our textbook for each performance metric.

# Generate Predicted Probabilities for the Test Data

predicted_probsknn <- predict(knn_final, newdata = test_dataknn, type = "prob")[, 2] # Selects the second column, which contains the predicted probabilities for the "Dropout" class (class 1).

# The ROCR package is used to generate performance curves such as the ROC curve.

#install.packages("ROCR")
library(ROCR)

# Create the ROC Curve

predknn <- prediction(predicted_probsknn, test_dataknn$Dropout, label.ordering = c("NotDropout", "Dropout")) # This creates an object that stores the predicted probabilities (predicted_probs) and the true labels (test_data$Dropout). It’s required for generating performance metrics.label.ordering = c("NotDropout", "Dropout") tells R to treat "NotDropout" as the negative class (coded as 0) and "Dropout" as the positive class (coded as 1).

perfknn <- performance(predknn, "tpr", "fpr") # This function generates the ROC curve, plotting the true positive rate (tpr) against the false positive rate (fpr).

ATTENTION!

I spent a few hours trying to figure out why I had an inverted ROC curve and discovered that if we run pred <- prediction(predicted_probs, test_data$Dropout) without specifying label.ordering, R treats “NotDropout” as the positive class. You can confirm this by checking the levels using levels(pred@labels[[1]]). To avoid this unexpected situation, be sure to include label.ordering = c(“NotDropout”, “Dropout”). This will ensure that when you run pred <- prediction(predicted_probs, test_data$Dropout, label.ordering = c(“NotDropout”, “Dropout”)), R continues to treat “NotDropout” as the negative class (first level, reference group) and “Dropout” as the positive class (second level, focal group).

# Plot the ROC Curve
plot(perfknn, col = "blue", main = "ROC Curve")
abline(a = 0, b = 1, col = "red", lty = 2) # Adds a red diagonal line to represent random guessing (where the true positive rate equals the false positive rate).

# Calculate AUC (Area Under the Curve)
aucknn <- performance(predknn, "auc") # Calculates the AUC
auc_valueknn <- aucknn@y.values[[1]] # Extracts the AUC value.
print(paste("AUC =", auc_valueknn)) # Prints the AUC value

[1] "AUC = 0.6175"

AUC = 0.5: A model with an AUC of 0.5 performs no better than random chance. It has no discriminatory power.

AUC = 1.0: A perfect model that distinguishes perfectly between the positive and negative classes.

AUC < 0.5: The model is performing worse than random guessing.

Naive Bayes Evaluation

# Install the naivebayes package

# install.packages("naivebayes") #Remove # to install it

# Load the package

library(naivebayes)

naivebayes 1.0.0 loaded

For more information please visit: 

https://majkamichal.github.io/naivebayes/

# Naive Bayes (NB) with 10-fold cross-validation

set.seed(668)

NB_fit <- train(
  Dropout ~ ., 
  data = train_datanb_smote,
  method = "naive_bayes", # NB
  trControl = cv10, 
  metric = "ROC", 
  tuneGrid = expand.grid(laplace = 1, usekernel = TRUE, adjust = 1)
)

Warning in train.default(x, y, weights = w, ...): The metric "ROC" was not in
the result set. logLoss will be used instead.

# Print the results

print(NB_fit)

Naive Bayes 

1440 samples
   9 predictor
   2 classes: 'NotDropout', 'Dropout' 

No pre-processing
Resampling: Cross-Validated (10 fold) 
Summary of sample sizes: 1296, 1296, 1296, 1296, 1296, 1296, ... 
Resampling results:

  logLoss    AUC        prAUC      Accuracy   Kappa      F1         Sensitivity
  0.5345795  0.8081211  0.7888365  0.7333333  0.4666667  0.7154964  0.6722222  
  Specificity  Pos_Pred_Value  Neg_Pred_Value  Precision  Recall   
  0.7944444    0.7670972       0.7088643       0.7670972  0.6722222
  Detection_Rate  Balanced_Accuracy
  0.3361111       0.7333333        

Tuning parameter 'laplace' was held constant at a value of 1
Tuning
 parameter 'usekernel' was held constant at a value of TRUE
Tuning
 parameter 'adjust' was held constant at a value of 1

# Shows the results of each fold of the cross-validation, providing a more detailed look at model performance on different training/validation splits.

print(NB_fit$resample)

     logLoss       AUC     prAUC  Accuracy     Kappa        F1 Sensitivity
1  0.4636564 0.8684414 0.8544818 0.7847222 0.5694444 0.7633588   0.6944444
2  0.5489119 0.8009259 0.7798498 0.7430556 0.4861111 0.7448276   0.7500000
3  0.5035520 0.8215664 0.7996806 0.7222222 0.4444444 0.7142857   0.6944444
4  0.5567209 0.7712191 0.7657937 0.6736111 0.3472222 0.6356589   0.5694444
5  0.5570521 0.8011188 0.7731237 0.7291667 0.4583333 0.7067669   0.6527778
6  0.5497886 0.8109568 0.7870581 0.7430556 0.4861111 0.7218045   0.6666667
7  0.6040886 0.7463349 0.7177115 0.6736111 0.3472222 0.6569343   0.6250000
8  0.5458845 0.8059414 0.7872964 0.7638889 0.5277778 0.7536232   0.7222222
9  0.5092954 0.8344907 0.8105641 0.7569444 0.5138889 0.7445255   0.7083333
10 0.5068444 0.8202160 0.8128051 0.7430556 0.4861111 0.7131783   0.6388889
   Specificity Pos_Pred_Value Neg_Pred_Value Precision    Recall Detection_Rate
1    0.8750000      0.8474576      0.7411765 0.8474576 0.6944444      0.3472222
2    0.7361111      0.7397260      0.7464789 0.7397260 0.7500000      0.3750000
3    0.7500000      0.7352941      0.7105263 0.7352941 0.6944444      0.3472222
4    0.7777778      0.7192982      0.6436782 0.7192982 0.5694444      0.2847222
5    0.8055556      0.7704918      0.6987952 0.7704918 0.6527778      0.3263889
6    0.8194444      0.7868852      0.7108434 0.7868852 0.6666667      0.3333333
7    0.7222222      0.6923077      0.6582278 0.6923077 0.6250000      0.3125000
8    0.8055556      0.7878788      0.7435897 0.7878788 0.7222222      0.3611111
9    0.8055556      0.7846154      0.7341772 0.7846154 0.7083333      0.3541667
10   0.8472222      0.8070175      0.7011494 0.8070175 0.6388889      0.3194444
   Balanced_Accuracy Resample
1          0.7847222   Fold01
2          0.7430556   Fold02
3          0.7222222   Fold03
4          0.6736111   Fold04
5          0.7291667   Fold05
6          0.7430556   Fold06
7          0.6736111   Fold07
8          0.7638889   Fold08
9          0.7569444   Fold09
10         0.7430556   Fold10

# Variable importance

varImp(NB_fit) 

ROC curve variable importance

                 Importance
Attendance          100.000
ExtraCurricular      71.554
SES                  63.371
ParentEdu            17.822
PeerSupport          13.858
HomeworkHours         6.136
MathSelfEfficacy      6.133
TestAnxiety           3.366
Motivation            0.000

plot(varImp(NB_fit))

# Predict Outcome Using Model on Test Data

predictionsnb <- predict(NB_fit, newdata=test_datanb)

# Create Confusion Matrix to Assess Model Performance

confusionMatrix(data=predictionsnb, test_datanb$Dropout, positive = "Dropout", mode = "everything") # MUST specify positive = "Dropout"; otherwise, the default setting treats "NotDropout" as the positive class.

Confusion Matrix and Statistics

            Reference
Prediction   NotDropout Dropout
  NotDropout        118       9
  Dropout            62      11
                                          
               Accuracy : 0.645           
                 95% CI : (0.5744, 0.7112)
    No Information Rate : 0.9             
    P-Value [Acc > NIR] : 1               
                                          
                  Kappa : 0.0944          
                                          
 Mcnemar's Test P-Value : 6.775e-10       
                                          
            Sensitivity : 0.5500          
            Specificity : 0.6556          
         Pos Pred Value : 0.1507          
         Neg Pred Value : 0.9291          
              Precision : 0.1507          
                 Recall : 0.5500          
                     F1 : 0.2366          
             Prevalence : 0.1000          
         Detection Rate : 0.0550          
   Detection Prevalence : 0.3650          
      Balanced Accuracy : 0.6028          
                                          
       'Positive' Class : Dropout         
                                          

# Generate Predicted Probabilities for the Test Data

predicted_probsnb <- predict(NB_fit, newdata = test_datanb, type = "prob")[, 2] # Selects the second column, which contains the predicted probabilities for the "Dropout" class (class 1).

# The ROCR package is used to generate performance curves such as the ROC curve.

#install.packages("ROCR")
library(ROCR)

# Create the ROC Curve

prednb <- prediction(predicted_probsnb, test_datanb$Dropout, label.ordering = c("NotDropout", "Dropout")) # This creates an object that stores the predicted probabilities (predicted_probs) and the true labels (test_data$Dropout). It’s required for generating performance metrics.label.ordering = c("NotDropout", "Dropout") tells R to treat "NotDropout" as the negative class (coded as 0) and "Dropout" as the positive class (coded as 1).

perfnb <- performance(prednb, "tpr", "fpr") # This function generates the ROC curve, plotting the true positive rate (tpr) against the false positive rate (fpr).

# Plot the ROC Curve

plot(perfnb, col = "blue", main = "ROC Curve")
abline(a = 0, b = 1, col = "red", lty = 2) # Adds a red diagonal line to represent random guessing (where the true positive rate equals the false positive rate).

# Add the ROC curve for knn (Add another plot for knn)

plot(perfknn, col = "purple", add = TRUE) #add = True is to add another plot.

# Add a legend

legend("bottomright", legend = c("NB", "KNN"),
       col = c("blue", "purple"), lwd = 1)

# Calculate AUC (Area Under the Curve)

aucnb <- performance(prednb, "auc") # Calculates the AUC
auc_valuenb <- aucnb@y.values[[1]] # Extracts the AUC value.

aucknn <- performance(predknn, "auc") # Calculates the AUC
auc_valueknn <- aucknn@y.values[[1]] # Extracts the AUC value.

print(paste("AUCnb =", auc_valuenb)) # Prints the AUC value

[1] "AUCnb = 0.645833333333333"

print(paste("AUCknn =", auc_valueknn)) # Prints the AUC value

[1] "AUCknn = 0.6175"

Acknowledgement

This document was created by the author with assistance from ChatGPT in clarifying aspects of the R code. Students are encouraged to learn R programming and explore machine learning concepts with the help of AI tools, as long as these tools contribute positively to their learning experience.