Week5_textlytics
Raka
10/26/2020
Assignment 1: Detecting vandalism on Wikipedia
Wikipedia is a free online encyclopedia that anyone can edit and contribute to. It is available in many languages and is growing all the time. On the English language version of Wikipedia:
There are currently 4.7 million pages.
There have been a total over 760 million edits (also called revisions) over its lifetime.
There are approximately 130,000 edits per day.One of the consequences of being editable by anyone is that some people vandalize pages. This can take the form of removing content, adding promotional or inappropriate content, or more subtle shifts that change the meaning of the article. With this many articles and edits per day it is difficult for humans to detect all instances of vandalism and revert (undo) them. As a result, Wikipedia uses bots - computer programs that automatically revert edits that look like vandalism. In this assignment we will attempt to develop a vandalism detector that uses machine learning to distinguish between a valid edit and vandalism.
The data for this problem is based on the revision history of the page Language. Wikipedia provides a history for each page that consists of the state of the page at each revision. Rather than manually considering each revision, a script was run that checked whether edits stayed or were reverted. If a change was eventually reverted then that revision is marked as vandalism. This may result in some misclassifications, but the script performs well enough for our needs.
As a result of this preprocessing, some common processing tasks have already been done, including lower-casing and punctuation removal. The columns in the dataset are:
Vandal = 1 if this edit was vandalism, 0 if not.
Minor = 1 if the user marked this edit as a "minor edit", 0 if not.
Loggedin = 1 if the user made this edit while using a Wikipedia account, 0 if they did not.
Added = The unique words added.
Removed = The unique words removed.Notice the repeated use of unique. The data we have available is not the traditional bag of words - rather it is the set of words that were removed or added. For example, if a word was removed multiple times in a revision it will only appear one time in the “Removed” column.
wiki <- read.csv("wiki.csv", stringsAsFactors = FALSE)
str(wiki)## 'data.frame': 3876 obs. of 7 variables:
## $ X.1 : int 1 2 3 4 5 6 7 8 9 10 ...
## $ X : int 1 2 3 4 5 6 7 8 9 10 ...
## $ Vandal : int 0 0 0 0 0 0 0 0 0 0 ...
## $ Minor : int 1 1 0 1 1 0 0 0 1 0 ...
## $ Loggedin: int 1 1 1 0 1 1 1 1 1 0 ...
## $ Added : chr " represent psycholinguisticspsycholinguistics orthographyorthography help text all actions through human ethno"| __truncated__ " website external links" " " " afghanistan used iran mostly that farsiis is countries some xmlspacepreservepersian parts tajikestan region" ...
## $ Removed : chr " " " talklanguagetalk" " regarded as technologytechnologies human first" " represent psycholinguisticspsycholinguistics orthographyorthography help all actions through ethnologue relat"| __truncated__ ...table(wiki$Vandal)##
## 0 1
## 2061 1815Bags of words
We will now use the bag of words approach to build a model. We have two columns of textual data, with different meanings. For example, adding rude words has a different meaning to removing rude words. We’ll start like we did in class by building a document term matrix from the Added column. The text already is lowercase and stripped of punctuation. So to pre-process the data, just complete the following four steps:
Create the corpus for the Added column, and call it “corpusAdded”.
Remove the English-language stopwords.
Stem the words.
Build the DocumentTermMatrix, and call it dtmAdded.
If the code length(stopwords(“english”)) does not return 174 for you, then please run the line of code in this file, which will store the standard stop words in a variable called sw. When removing stop words, use tm_map(corpusAdded, removeWords, sw) instead of tm_map(corpusAdded, removeWords, stopwords(“english”)).
How many terms appear in dtmAdded?
library(tm)## Warning: package 'tm' was built under R version 4.0.3## Loading required package: NLP## Warning: package 'NLP' was built under R version 4.0.3corpusAdded <- Corpus(VectorSource(wiki$Added))
strwrap(corpusAdded[[1]])## [1] "represent psycholinguisticspsycholinguistics orthographyorthography"
## [2] "help text all actions through human ethnologue relationships"
## [3] "linguistics regarded writing languages to other listing"
## [4] "xmlspacepreservelanguages metaverse formal term philology common each"
## [5] "including phonologyphonology often ten list humans affiliation see"
## [6] "computer are speechpathologyspeech our what for ways dialects please"
## [7] "artificial written body be of quite hypothesis found alone refers by"
## [8] "about language profanity study programming priorities rosenfelders"
## [9] "technologytechnologies makes or first among useful languagephilosophy"
## [10] "one sounds use area create phrases mark their genetic basic families"
## [11] "complete but sapirwhorfhypothesissapirwhorf with talklanguagetalk"
## [12] "population animals this science up vocal can concepts called at and"
## [13] "topics locations as numbers have in pathology different develop 4000"
## [14] "things ideas grouped complex animal mathematics fairly literature"
## [15] "httpwwwzompistcom philosophy most important meaningful a"
## [16] "historicallinguisticsorphilologyhistorical semanticssemantics patterns"
## [17] "the oral"corpusAdded <- tm_map(corpusAdded, removeWords, stopwords("english"))## Warning in tm_map.SimpleCorpus(corpusAdded, removeWords, stopwords("english")):
## transformation drops documentscorpusAdded <- tm_map(corpusAdded, stemDocument)## Warning in tm_map.SimpleCorpus(corpusAdded, stemDocument): transformation drops
## documentsfrequencies <- DocumentTermMatrix(corpusAdded)
frequencies## <<DocumentTermMatrix (documents: 3876, terms: 6675)>>
## Non-/sparse entries: 15368/25856932
## Sparsity : 100%
## Maximal term length: 784
## Weighting : term frequency (tf)sparse <- removeSparseTerms(frequencies, 0.997)
sparse## <<DocumentTermMatrix (documents: 3876, terms: 166)>>
## Non-/sparse entries: 2681/640735
## Sparsity : 100%
## Maximal term length: 28
## Weighting : term frequency (tf)Bags of Words 2
Convert sparseAdded to a data frame called wordsAdded, and then prepend all the words with the letter A, by using the command:
colnames(wordsAdded) = paste(“A”, colnames(wordsAdded))
Now repeat all of the steps we’ve done so far (create a corpus, remove stop words, stem the document, create a sparse document term matrix, and convert it to a data frame) to create a Removed bag-of-words dataframe, called wordsRemoved, except this time, prepend all of the words with the letter R:
colnames(wordsRemoved) = paste(“R”, colnames(wordsRemoved))
How many words are in the wordsRemoved data frame?
wordsAdded <- as.data.frame(as.matrix(sparse))
colnames(wordsAdded) <- paste("A", colnames(wordsAdded))
removedWords <-Corpus(VectorSource(wiki$Removed))
strwrap(removedWords[[1]])## [1] ""removedWords <- tm_map(removedWords, removeWords, stopwords("english"))## Warning in tm_map.SimpleCorpus(removedWords, removeWords, stopwords("english")):
## transformation drops documentsremovedWords <- tm_map(removedWords, stemDocument)## Warning in tm_map.SimpleCorpus(removedWords, stemDocument): transformation drops
## documentsfrequencies_rm <- DocumentTermMatrix(removedWords)
frequencies_rm## <<DocumentTermMatrix (documents: 3876, terms: 5403)>>
## Non-/sparse entries: 13293/20928735
## Sparsity : 100%
## Maximal term length: 784
## Weighting : term frequency (tf)sparse2 <- removeSparseTerms(frequencies_rm, 0.997)
sparse2## <<DocumentTermMatrix (documents: 3876, terms: 162)>>
## Non-/sparse entries: 2552/625360
## Sparsity : 100%
## Maximal term length: 28
## Weighting : term frequency (tf)wordsRemoved <- as.data.frame(as.matrix(sparse2))
colnames(wordsRemoved) <- paste("R", colnames(wordsRemoved))Bags of Words 3
Combine the two data frames into a data frame called wikiWords with the following line of code:
wikiWords = cbind(wordsAdded, wordsRemoved)
The cbind function combines two sets of variables for the same observations into one data frame. Then add the Vandal column (HINT: remember how we added the dependent variable back into our data frame in the Twitter lecture). Set the random seed to 123 and then split the data set using sample.split from the “caTools” package to put 70% in the training set.
What is the accuracy on the test set of a baseline method that always predicts “not vandalism” (the most frequent outcome)?
library(caTools)
wikiWords <- cbind(wordsAdded, wordsRemoved)
wikiWords$Vandal <- wiki$Vandal
set.seed(123)split <- sample.split(wikiWords$Vandal, SplitRatio = 0.7)
train <- subset(wikiWords, split == TRUE)
test <- subset(wikiWords, split == FALSE)
table(test$Vandal)##
## 0 1
## 618 545(618)/(618+545)## [1] 0.5313844Bags of words 4
Build a CART model to predict Vandal, using all of the other variables as independent variables. Use the training set to build the model and the default parameters (don’t set values for minbucket or cp).
What is the accuracy of the model on the test set, using a threshold of 0.5? (Remember that if you add the argument type=“class” when making predictions, the output of predict will automatically use a threshold of 0.5.)
library(rpart)
library(rpart.plot)
wikiCART <- rpart(Vandal ~ ., data = train, method = 'class')
prp(wikiCART)
predCART <- predict(wikiCART, newdata = test, type = 'class')
table(test$Vandal, predCART)## predCART
## 0 1
## 0 614 4
## 1 526 19(614+19)/(614+19+4+526)## [1] 0.544282Part 2.1 Problem-specific knowledge
The key class of words we will use are website addresses. “Website addresses” (also known as URLs - Uniform Resource Locators) are comprised of two main parts. An example would be “http://www.google.com”. The first part is the protocol, which is usually “http” (HyperText Transfer Protocol). The second part is the address of the site, e.g. “www.google.com”. We have stripped all punctuation so links to websites appear in the data as one word, e.g. “httpwwwgooglecom”. We hypothesize that given that a lot of vandalism seems to be adding links to promotional or irrelevant websites, the presence of a web address is a sign of vandalism.
wikiWords2 <- wikiWords
wikiWords2$http <- ifelse(grepl("http", wiki$Added, fixed = TRUE), 1, 0)
table(wikiWords2$http)##
## 0 1
## 3659 217Prob-specific knowledge 2
In problem 1.5, you computed a vector called “spl” that identified the observations to put in the training and testing sets. Use that variable (do not recompute it with sample.split) to make new training and testing sets:
wikiTrain2 = subset(wikiWords2, spl==TRUE)
wikiTest2 = subset(wikiWords2, spl==FALSE)
Then create a new CART model using this new variable as one of the independent variables.
What is the new accuracy of the CART model on the test set, using a threshold of 0.5?
split <- sample.split(wikiWords2$Vandal, SplitRatio = 0.7)
wikiTrain2 <- subset(wikiWords2, split == TRUE)
wikiTest2 <- subset(wikiWords2, split == FALSE)
wikiCART2 <- rpart(Vandal ~ ., data = wikiTrain2, method = 'class')
predCART2 <- predict(wikiCART2, newdata = wikiTest2, type = "class")
table(wikiTest2$Vandal, predCART2)## predCART2
## 0 1
## 0 606 12
## 1 481 64(605+70)/(605+70+13+475)## [1] 0.5803955Problem-specific knowledge 3
Another possibility is that the number of words added and removed is predictive, perhaps more so than the actual words themselves. We already have a word count available in the form of the document-term matrices (DTMs).
Sum the rows of dtmAdded and dtmRemoved and add them as new variables in your data frame wikiWords2 (called NumWordsAdded and NumWordsRemoved) by using the following commands:
wikiWords2$NumWordsAdded = rowSums(as.matrix(dtmAdded))
wikiWords2$NumWordsRemoved = rowSums(as.matrix(dtmRemoved))
What is the average number of words added?
wikiWords2$NumWordsAdded <- rowSums(as.matrix(frequencies))
wikiWords2$NumWordsRemoved <- rowSums(as.matrix(frequencies_rm))
mean(wikiWords2$NumWordsAdded)## [1] 4.050052Problem-specific knowledge 5
In problem 1.5, you computed a vector called “spl” that identified the observations to put in the training and testing sets. Use that variable (do not recompute it with sample.split) to make new training and testing sets with wikiWords2. Create the CART model again (using the training set and the default parameters).
What is the new accuracy of the CART model on the test set?
train_new <- subset(wikiWords2, split == TRUE)
test_new <- subset(wikiWords2, split == FALSE)
CART3 <- rpart(Vandal ~ ., data = train_new, method = "class")
predCART3 <- predict(CART3, newdata = test_new, type = "class")
table(test_new$Vandal, predCART3)## predCART3
## 0 1
## 0 495 123
## 1 269 276(514+248)/(514+248+104+297)## [1] 0.6552021Using non-textual data
We have two pieces of “metadata” (data about data) that we haven’t yet used. Make a copy of wikiWords2, and call it wikiWords3:
wikiWords3 = wikiWords2
Then add the two original variables Minor and Loggedin to this new data frame:
wikiWords3\(Minor = wiki\)Minor
wikiWords3\(Loggedin = wiki\)Loggedin
In problem 1.5, you computed a vector called “spl” that identified the observations to put in the training and testing sets. Use that variable (do not recompute it with sample.split) to make new training and testing sets with wikiWords3.
Build a CART model using all the training data. What is the accuracy of the model on the test set?
wikiWords3 <- wikiWords2
wikiWords3$Minor <- wiki$Minor
wikiWords3$Loggedin <- wiki$Loggedin
train_new2 <- subset(wikiWords3, split == TRUE)
test_new2 <- subset(wikiWords3, split == FALSE)
CART4 <- rpart(Vandal ~ ., data = train_new2, method = "class")
predCART4 <- predict(CART4, newdata = test_new2, type = "class")
table(test_new2$Vandal, predCART4)## predCART4
## 0 1
## 0 566 52
## 1 263 282(595+241)/(595+241+23+304)## [1] 0.7188306prp(CART4)
## Assignment 2: Automating Reviews in Medicine
The medical literature is enormous. Pubmed, a database of medical publications maintained by the U.S. National Library of Medicine, has indexed over 23 million medical publications. Further, the rate of medical publication has increased over time, and now there are nearly 1 million new publications in the field each year, or more than one per minute.
The large size and fast-changing nature of the medical literature has increased the need for reviews, which search databases like Pubmed for papers on a particular topic and then report results from the papers found. While such reviews are often performed manually, with multiple people reviewing each search result, this is tedious and time consuming. In this problem, we will see how text analytics can be used to automate the process of information retrieval.
trials <- read.csv("clinical_trial.csv", stringsAsFactors = FALSE)
str(trials)## 'data.frame': 1860 obs. of 3 variables:
## $ title : chr "Treatment of Hodgkin's disease and other cancers with 1,3-bis(2-chloroethyl)-1-nitrosourea (BCNU; NSC-409962)." "Cell mediated immune status in malignancy--pretherapy and post-therapy assessment." "Neoadjuvant vinorelbine-capecitabine versus docetaxel-doxorubicin-cyclophosphamide in early nonresponsive breas"| __truncated__ "Randomized phase 3 trial of fluorouracil, epirubicin, and cyclophosphamide alone or followed by Paclitaxel for "| __truncated__ ...
## $ abstract: chr "" "Twenty-eight cases of malignancies of different kinds were studied to assess T-cell activity and population bef"| __truncated__ "BACKGROUND: Among breast cancer patients, nonresponse to initial neoadjuvant chemotherapy is associated with un"| __truncated__ "BACKGROUND: Taxanes are among the most active drugs for the treatment of metastatic breast cancer, and, as a co"| __truncated__ ...
## $ trial : int 1 0 1 1 1 0 1 0 0 0 ...max(nchar(trials$abstract))## [1] 3708table(nchar(trials$abstract))##
## 0 243 273 282 288 290 332 337 345 363 378 420 434 444 447 454
## 112 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 463 464 465 468 469 477 482 483 489 491 492 501 507 511 514 519
## 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1
## 528 541 543 548 559 563 566 567 576 584 585 588 591 593 600 601
## 1 1 1 2 1 1 2 1 1 1 1 1 1 1 1 1
## 604 610 615 617 620 627 628 631 634 639 644 645 647 655 656 660
## 1 1 1 2 1 1 2 1 1 1 2 1 1 1 2 2
## 666 671 673 675 681 685 688 695 700 701 713 717 720 721 722 723
## 1 1 1 1 1 1 1 3 1 1 1 2 1 1 1 1
## 725 730 733 735 739 740 741 765 773 775 777 781 782 783 788 795
## 1 1 1 1 1 1 1 2 1 2 1 3 1 1 1 1
## 798 802 805 806 808 811 820 823 825 829 832 834 836 837 838 840
## 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1
## 842 846 851 852 857 860 861 865 868 871 874 878 882 885 888 891
## 1 1 1 1 1 1 1 1 1 1 1 1 1 3 2 1
## 892 900 902 904 906 909 910 913 919 920 921 922 924 925 926 927
## 2 1 1 1 1 3 1 1 2 1 2 1 1 1 1 3
## 930 932 933 937 939 940 942 948 953 957 958 959 960 962 964 965
## 2 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2
## 968 969 973 974 980 981 984 987 989 990 991 993 994 996 1000 1005
## 3 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1
## 1006 1007 1009 1016 1018 1020 1021 1022 1024 1025 1026 1028 1029 1030 1031 1033
## 1 2 2 1 1 2 1 2 1 1 1 1 2 1 1 1
## 1034 1035 1037 1038 1041 1045 1047 1049 1050 1052 1054 1063 1064 1065 1066 1067
## 3 2 1 1 1 2 3 2 1 2 1 1 1 2 1 1
## 1069 1070 1071 1073 1077 1078 1079 1081 1082 1083 1085 1088 1089 1093 1094 1097
## 2 2 1 1 1 3 1 1 2 2 1 1 1 1 2 1
## 1098 1101 1103 1105 1107 1108 1111 1112 1115 1116 1121 1122 1123 1124 1125 1126
## 2 2 1 1 1 1 1 3 2 2 2 1 1 1 1 2
## 1127 1128 1133 1134 1136 1137 1138 1140 1145 1148 1149 1159 1161 1165 1167 1169
## 2 1 1 2 1 2 1 1 1 1 1 1 1 1 2 3
## 1171 1173 1175 1176 1177 1178 1179 1181 1182 1184 1185 1188 1189 1191 1192 1193
## 2 1 1 1 1 1 1 2 2 4 1 1 1 1 3 3
## 1194 1196 1197 1198 1199 1200 1201 1202 1207 1208 1209 1210 1211 1212 1214 1215
## 2 2 1 1 1 1 2 1 2 1 2 2 1 2 2 2
## 1216 1217 1221 1222 1223 1225 1229 1231 1234 1235 1236 1239 1240 1241 1242 1243
## 3 2 2 2 1 2 1 1 1 1 1 2 1 1 1 2
## 1245 1250 1254 1255 1256 1258 1259 1261 1262 1265 1267 1268 1269 1270 1271 1272
## 1 1 1 2 2 1 1 1 1 1 1 1 2 2 1 1
## 1273 1274 1276 1277 1278 1279 1281 1284 1288 1289 1290 1291 1292 1293 1294 1295
## 1 1 1 1 2 1 3 1 1 2 1 2 1 1 3 1
## 1296 1298 1300 1302 1303 1305 1306 1307 1308 1309 1310 1312 1313 1316 1317 1318
## 1 1 1 1 1 3 3 1 3 2 1 1 2 1 1 1
## 1321 1323 1324 1325 1326 1329 1330 1331 1335 1336 1337 1339 1340 1341 1342 1343
## 2 2 2 1 2 1 1 4 1 1 2 2 3 1 1 1
## 1344 1346 1347 1348 1349 1350 1351 1352 1354 1355 1356 1358 1359 1360 1361 1362
## 1 2 2 2 2 1 3 1 3 1 1 2 2 1 2 1
## 1363 1364 1367 1368 1369 1370 1371 1372 1373 1375 1376 1377 1380 1381 1383 1386
## 1 2 1 3 4 3 1 3 2 2 1 4 2 1 1 1
## 1387 1389 1390 1391 1392 1393 1394 1396 1397 1399 1400 1401 1403 1404 1405 1407
## 1 2 2 1 1 2 2 2 1 2 1 2 1 2 3 2
## 1408 1409 1410 1412 1413 1415 1416 1418 1419 1421 1422 1423 1424 1425 1426 1428
## 1 2 1 2 4 3 4 1 3 3 1 2 3 2 1 1
## 1432 1433 1434 1437 1438 1441 1442 1445 1446 1447 1448 1449 1450 1451 1452 1453
## 2 1 2 1 1 2 1 1 1 2 2 2 3 2 1 2
## 1455 1456 1459 1460 1461 1463 1467 1468 1470 1472 1474 1475 1476 1477 1478 1479
## 2 1 2 1 3 2 2 4 1 1 2 1 2 3 3 3
## 1480 1481 1485 1487 1489 1490 1491 1492 1493 1494 1495 1496 1497 1499 1500 1501
## 1 3 2 1 2 1 1 1 1 1 1 1 1 1 5 2
## 1503 1504 1505 1506 1508 1509 1510 1512 1514 1515 1516 1517 1518 1519 1521 1522
## 2 1 1 3 3 5 1 1 1 1 3 3 2 1 2 1
## 1523 1524 1525 1526 1528 1529 1530 1532 1533 1534 1535 1536 1537 1539 1540 1541
## 1 1 3 3 1 1 1 2 2 1 4 2 3 1 1 2
## 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1555 1556 1558 1563
## 2 2 4 1 1 1 2 2 3 1 3 1 4 1 1 3
## 1566 1569 1570 1572 1574 1575 1577 1578 1580 1581 1582 1583 1584 1585 1586 1588
## 4 5 2 3 1 3 3 1 1 2 2 3 2 1 2 1
## 1589 1592 1593 1594 1596 1597 1598 1600 1601 1602 1603 1604 1605 1606 1609 1610
## 2 1 1 2 1 4 1 1 4 3 2 2 1 3 3 2
## 1613 1614 1615 1616 1617 1618 1620 1621 1623 1624 1625 1626 1627 1628 1630 1631
## 1 2 4 2 1 1 1 1 4 3 2 3 1 2 2 1
## 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1643 1644 1645 1646 1647 1648
## 3 1 3 1 2 2 2 2 3 1 3 2 2 1 1 1
## 1649 1650 1651 1652 1654 1655 1656 1658 1659 1660 1662 1663 1665 1666 1667 1668
## 5 3 3 1 1 4 2 4 3 2 4 1 1 1 3 2
## 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 1681 1682 1683 1684
## 2 1 2 5 1 5 1 1 1 1 1 3 1 4 4 3
## 1685 1686 1687 1689 1690 1692 1694 1696 1697 1698 1699 1700 1702 1703 1704 1705
## 2 1 2 1 2 3 1 2 3 3 2 2 2 1 1 2
## 1706 1707 1708 1709 1710 1711 1712 1713 1714 1715 1716 1717 1718 1719 1720 1721
## 3 3 2 2 2 2 1 2 5 1 1 3 2 2 1 1
## 1722 1724 1725 1726 1727 1728 1729 1730 1731 1733 1734 1735 1736 1737 1738 1739
## 1 3 2 1 2 4 5 3 1 2 2 2 4 2 5 3
## 1740 1741 1742 1743 1744 1745 1747 1748 1749 1750 1751 1753 1754 1755 1756 1757
## 4 3 3 5 3 2 1 1 1 1 4 3 3 5 3 1
## 1759 1760 1761 1762 1763 1764 1765 1766 1768 1769 1770 1771 1772 1773 1774 1775
## 3 4 2 4 3 2 1 2 2 2 2 1 5 2 3 4
## 1776 1777 1779 1780 1781 1782 1783 1784 1786 1787 1788 1789 1790 1791 1792 1793
## 2 3 2 2 1 2 2 2 3 3 1 2 1 4 1 2
## 1794 1795 1796 1797 1798 1799 1800 1801 1802 1803 1804 1805 1806 1807 1808 1809
## 1 1 3 1 2 1 4 1 1 4 4 3 2 3 1 2
## 1810 1811 1812 1813 1814 1815 1816 1817 1818 1819 1820 1821 1822 1823 1824 1825
## 1 1 4 4 3 3 1 3 3 2 3 2 3 1 3 2
## 1827 1828 1829 1830 1832 1833 1834 1837 1838 1839 1840 1841 1843 1844 1845 1846
## 2 3 1 2 2 4 1 4 2 3 2 1 1 2 1 2
## 1848 1850 1852 1854 1855 1856 1857 1858 1859 1861 1862 1863 1865 1867 1869 1870
## 2 3 3 1 1 2 1 2 2 3 2 2 1 2 3 1
## 1871 1872 1873 1875 1882 1883 1884 1885 1887 1888 1890 1891 1892 1893 1895 1896
## 1 2 2 2 2 1 1 1 3 2 1 3 3 1 1 1
## 1897 1898 1899 1901 1902 1903 1904 1906 1908 1909 1910 1911 1912 1914 1916 1917
## 3 2 1 2 2 1 1 1 1 3 2 1 1 2 2 1
## 1918 1919 1920 1921 1922 1923 1924 1925 1927 1928 1929 1933 1934 1935 1936 1937
## 1 2 2 1 3 1 1 3 2 2 3 1 1 1 1 2
## 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1951 1952 1953 1954 1955
## 3 1 3 1 2 1 5 1 2 1 2 2 1 1 2 1
## 1956 1957 1958 1959 1960 1962 1965 1970 1971 1973 1974 1975 1976 1980 1981 1982
## 1 2 1 1 1 2 1 1 1 1 2 1 3 2 2 1
## 1986 1987 1989 1990 1992 1993 1995 1996 1998 1999 2001 2002 2004 2005 2008 2011
## 1 2 1 2 3 1 1 1 2 3 1 1 1 1 1 2
## 2012 2013 2015 2016 2018 2019 2020 2024 2025 2028 2030 2031 2036 2037 2039 2040
## 2 2 2 1 1 1 1 1 2 1 1 1 1 1 1 1
## 2041 2043 2044 2046 2050 2051 2053 2056 2057 2059 2061 2062 2069 2071 2072 2075
## 2 1 1 1 2 1 1 1 1 4 1 1 1 1 1 2
## 2076 2078 2080 2081 2082 2089 2093 2095 2097 2101 2105 2106 2108 2110 2117 2120
## 1 2 1 1 2 1 1 1 1 2 1 1 1 1 1 1
## 2125 2126 2127 2131 2133 2134 2137 2138 2141 2142 2143 2146 2151 2153 2154 2172
## 1 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1
## 2173 2175 2177 2182 2183 2190 2191 2193 2194 2195 2196 2206 2207 2208 2214 2216
## 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 2217 2219 2221 2223 2228 2229 2232 2235 2236 2238 2240 2241 2242 2247 2248 2250
## 1 1 1 2 1 2 1 1 1 1 2 1 2 1 1 1
## 2252 2254 2257 2259 2262 2263 2267 2270 2271 2276 2282 2287 2290 2292 2293 2299
## 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 2
## 2300 2302 2303 2311 2325 2329 2331 2334 2336 2345 2348 2349 2358 2360 2367 2376
## 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1
## 2380 2382 2387 2389 2394 2404 2410 2412 2422 2428 2430 2431 2436 2439 2441 2450
## 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 2
## 2474 2479 2481 2482 2483 2489 2494 2496 2497 2504 2511 2516 2523 2528 2530 2531
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 2532 2533 2534 2539 2547 2550 2556 2584 2602 2606 2607 2633 2636 2682 2685 2700
## 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1
## 2709 2712 2722 2723 2746 2751 2752 2779 2790 2791 2796 2797 2798 2816 2838 2891
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 2903 2905 2910 2942 2961 2965 3050 3104 3138 3178 3214 3298 3465 3642 3708
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1which.min(nchar(trials$title))## [1] 1258trials$title[which.min(nchar(trials$title))]## [1] "A decade of letrozole: FACE."Preparing two Corpora
Because we have both title and abstract information for trials, we need to build two corpora instead of one. Name them corpusTitle and corpusAbstract.
Following the commands from lecture, perform the following tasks (you might need to load the “tm” package first if it isn’t already loaded). Make sure to perform them in this order.
corpusTitle <- Corpus(VectorSource(trials$title))
corpusAbstract <- Corpus(VectorSource(trials$abstract))
corpusTitle <- tm_map(corpusTitle, tolower)## Warning in tm_map.SimpleCorpus(corpusTitle, tolower): transformation drops
## documentscorpusAbstract <- tm_map(corpusAbstract, tolower)## Warning in tm_map.SimpleCorpus(corpusAbstract, tolower): transformation drops
## documentscorpusTitle <- tm_map(corpusTitle, removePunctuation)## Warning in tm_map.SimpleCorpus(corpusTitle, removePunctuation): transformation
## drops documentscorpusAbstract <- tm_map(corpusAbstract, removePunctuation)## Warning in tm_map.SimpleCorpus(corpusAbstract, removePunctuation):
## transformation drops documentscorpusTitle <- tm_map(corpusTitle, removeWords, stopwords("english"))## Warning in tm_map.SimpleCorpus(corpusTitle, removeWords, stopwords("english")):
## transformation drops documentscorpusAbstract <- tm_map(corpusAbstract, removeWords, stopwords("english"))## Warning in tm_map.SimpleCorpus(corpusAbstract, removeWords,
## stopwords("english")): transformation drops documentscorpusTitle <- tm_map(corpusTitle, stemDocument)## Warning in tm_map.SimpleCorpus(corpusTitle, stemDocument): transformation drops
## documentscorpusAbstract <- tm_map(corpusAbstract, stemDocument)## Warning in tm_map.SimpleCorpus(corpusAbstract, stemDocument): transformation
## drops documentsdtmTitle <- DocumentTermMatrix(corpusTitle)
dtmTitle## <<DocumentTermMatrix (documents: 1860, terms: 2837)>>
## Non-/sparse entries: 23417/5253403
## Sparsity : 100%
## Maximal term length: 49
## Weighting : term frequency (tf)dtmAbstract <- DocumentTermMatrix(corpusAbstract)
dtmAbstract## <<DocumentTermMatrix (documents: 1860, terms: 12457)>>
## Non-/sparse entries: 153302/23016718
## Sparsity : 99%
## Maximal term length: 67
## Weighting : term frequency (tf)dtmTitle <- removeSparseTerms(dtmTitle, 0.95)
dtmAbstract <- removeSparseTerms(dtmAbstract, 0.95)
dtmTitle <- as.data.frame(as.matrix(dtmTitle))
dtmAbstract <- as.data.frame(as.matrix(dtmAbstract))
max(colSums(dtmAbstract))## [1] 8381Building the model
We want to combine dtmTitle and dtmAbstract into a single data frame to make predictions. However, some of the variables in these data frames have the same names. To fix this issue, run the following commands:
colnames(dtmTitle) = paste0(“T”, colnames(dtmTitle))
colnames(dtmAbstract) = paste0(“A”, colnames(dtmAbstract))
What was the effect of these functions?
colnames(dtmTitle) <- paste0("T", colnames(dtmTitle))
colnames(dtmAbstract) <- paste0("A", colnames(dtmAbstract))
dtm <- cbind(dtmTitle, dtmAbstract)
dtm$trial <- trials$trial
ncol(dtm)## [1] 367Building the model 2
Now that we have prepared our data frame, it’s time to split it into a training and testing set and to build regression models. Set the random seed to 144 and use the sample.split function from the caTools package to split dtm into data frames named “train” and “test”, putting 70% of the data in the training set.
What is the accuracy of the baseline model on the training set? (Remember that the baseline model predicts the most frequent outcome in the training set for all observations.)
set.seed(144)
spl <- sample.split(dtm$trial, SplitRatio = 0.7)
train <- subset(dtm, spl == TRUE)
test <- subset(dtm, spl == FALSE)
table(test$trial)##
## 0 1
## 313 245(313)/(313+245)## [1] 0.5609319Building the CART model
Build a CART model called trialCART, using all the independent variables in the training set to train the model, and then plot the CART model. Just use the default parameters to build the model (don’t add a minbucket or cp value). Remember to add the method=“class” argument, since this is a classification problem.
What is the name of the first variable the model split on?
trialCART <- rpart(trial ~ ., data = train, method = "class")
prp(trialCART)
pred <- predict(trialCART, newdata = test)
pred.prob <- pred[,2]
max(pred.prob)## [1] 0.8718861length(pred)## [1] 1116pred2 <- predict(trialCART, newdata = train, type = "class")
table(train$trial, pred2)## pred2
## 0 1
## 0 631 99
## 1 131 441(631+441)/(631+441+99+131) # accuracy## [1] 0.8233487(441)/(441+131) # sensitivity## [1] 0.770979631/(631+99) # specificity## [1] 0.8643836library(ROCR)
predROCR <- prediction(pred.prob, test$trial)
perfROCR <- performance(predROCR, "tpr", "fpr")
plot(perfROCR, colorize = TRUE)
performance(predROCR, "auc")@y.values## [[1]]
## [1] 0.8371063Assignment 3: Separating Span from Ham
Nearly every email user has at some point encountered a “spam” email, which is an unsolicited message often advertising a product, containing links to malware, or attempting to scam the recipient. Roughly 80-90% of more than 100 billion emails sent each day are spam emails, most being sent from botnets of malware-infected computers. The remainder of emails are called “ham” emails.
As a result of the huge number of spam emails being sent across the Internet each day, most email providers offer a spam filter that automatically flags likely spam messages and separates them from the ham. Though these filters use a number of techniques (e.g. looking up the sender in a so-called “Blackhole List” that contains IP addresses of likely spammers), most rely heavily on the analysis of the contents of an email via text analytics.
Begin by loading the dataset emails.csv into a data frame called emails. Remember to pass the stringsAsFactors=FALSE option when loading the data.
How many emails are in the dataset?
emails <- read.csv("emails.csv")
table(emails$spam)##
## 0 1
## 4360 1368max(nchar(emails$text))## [1] 43952which.min(nchar(emails$text))## [1] 1992Preparing the Corpus
Follow the standard steps to build and pre-process the corpus:
Build a new corpus variable called corpus.
Using tm_map, convert the text to lowercase.
Using tm_map, remove all punctuation from the corpus.
Using tm_map, remove all English stopwords from the corpus.
Using tm_map, stem the words in the corpus.
Build a document term matrix from the corpus, called dtm.
corpus_mail <- Corpus(VectorSource(emails$text))
corpus_mail <- tm_map(corpus_mail, tolower)## Warning in tm_map.SimpleCorpus(corpus_mail, tolower): transformation drops
## documentscorpus_mail <- tm_map(corpus_mail, removePunctuation)## Warning in tm_map.SimpleCorpus(corpus_mail, removePunctuation): transformation
## drops documentscorpus_mail <- tm_map(corpus_mail, removePunctuation)## Warning in tm_map.SimpleCorpus(corpus_mail, removePunctuation): transformation
## drops documentscorpus_mail <- tm_map(corpus_mail, removeWords, stopwords("english"))## Warning in tm_map.SimpleCorpus(corpus_mail, removeWords, stopwords("english")):
## transformation drops documentscorpus_mail <- tm_map(corpus_mail, stemDocument)## Warning in tm_map.SimpleCorpus(corpus_mail, stemDocument): transformation drops
## documentsdtm <- DocumentTermMatrix(corpus_mail)
dtm## <<DocumentTermMatrix (documents: 5728, terms: 28687)>>
## Non-/sparse entries: 481719/163837417
## Sparsity : 100%
## Maximal term length: 24
## Weighting : term frequency (tf)#limited dm
spdtm <- removeSparseTerms(dtm, 0.95)
spdtm## <<DocumentTermMatrix (documents: 5728, terms: 330)>>
## Non-/sparse entries: 213551/1676689
## Sparsity : 89%
## Maximal term length: 10
## Weighting : term frequency (tf)emailsSparse <- as.data.frame(as.matrix(spdtm))
colnames(emailsSparse) <- make.names(colnames(emailsSparse)) #approproiating names
colSums(emailsSparse)## busi chang compani corpor day done effect
## 2313 1035 2290 565 1860 337 471
## effort even full good inform interest list
## 473 622 469 1097 2701 1814 1410
## look made make manag market much order
## 2003 622 1884 2600 2750 861 1210
## origin product provid realli result see special
## 892 1197 1405 417 655 1567 451
## subject system use websit will within without
## 10202 1118 2330 700 8252 732 389
## continu group like trade tri approv ask
## 552 2604 2352 1366 661 648 871
## complet credit form hear home new offer
## 707 960 664 469 660 2281 1171
## opportun rate take time visit want way
## 918 717 1361 3145 1126 1488 864
## addit click com fax mail messag now
## 774 769 5443 1038 2269 1983 1300
## phone request version best end get great
## 1001 1344 564 1291 635 2462 837
## money softwar custom hello one onlin pleas
## 776 739 796 534 2108 518 5113
## access account allow alreadi also applic area
## 789 829 450 446 1864 567 489
## assist base believ buy can cost creat
## 598 837 456 442 4257 821 413
## current design develop differ director discuss due
## 1044 457 1882 598 705 1326 445
## email event expect file forward futur gas
## 2066 552 554 770 3161 722 1070
## give given high import includ increas industri
## 1055 453 624 530 1238 491 970
## invest involv just know locat mani may
## 867 405 1354 2614 485 758 2465
## mean mention might month need note number
## 390 355 577 958 2328 688 1182
## offic oper person posit possibl present price
## 1068 820 767 1104 796 1543 2694
## problem process project read relat report requir
## 666 975 1522 413 694 1279 736
## research resourc return review risk secur servic
## 2820 556 509 976 2267 857 1337
## set short specif state term thing today
## 727 439 407 1086 786 535 828
## two understand unit well work hour lot
## 911 521 554 1125 2708 548 348
## real right start X000 X2001 follow name
## 648 639 880 1007 3089 1552 1089
## sent last avail first http join line
## 1126 998 1152 929 1609 469 448
## next. remov repli wish www year back
## 1145 460 397 414 1323 1890 864
## internet member receiv site anoth associ comment
## 623 545 1557 913 435 777 531
## corp date find free issu long move
## 1692 1187 867 1141 944 534 612
## particip recent respons say week dear regard
## 782 451 824 423 1758 838 2045
## thank address contact engin etc immedi net
## 3730 1154 1543 571 434 385 548
## per place respond sincer type come confirm
## 642 516 430 441 466 903 532
## analysi bring call data detail happi idea
## 495 374 1687 955 661 396 378
## info send success sure team web don
## 438 1379 519 495 926 668 676
## copi help part life meet sever question
## 797 1430 571 400 2623 430 1152
## write think point let link communic contract
## 390 1216 536 1963 421 1343 629
## either final howev peopl power put run
## 318 490 545 958 2117 458 437
## shall soon support attach abl program sorri
## 884 492 854 1176 590 1438 343
## valu check feel better plan experi hope
## 721 488 543 383 904 405 858
## begin X2000 case depart financi houston intern
## 317 4967 561 621 909 1582 606
## john juli mark open public sinc still
## 1042 701 613 416 468 521 523
## thought univers appreci keep cours direct togeth
## 367 1059 541 431 626 657 438
## energi london updat suggest option monday kevin
## 2179 843 606 554 1488 649 656
## book deal invit tuesday interview schedul school
## 756 498 647 474 1333 1071 655
## model financ morn attend robert student april
## 2199 1073 586 573 482 726 682
## talk arrang deriv thursday resum doc confer
## 981 410 676 575 933 675 1297
## wednesday edu friday ect hou vinc X853
## 464 1627 854 11427 5577 8532 462
## shirley enron kaminski X713 crenshaw vkamin gibner
## 1689 13388 4801 1097 1115 301 633
## stinson
## 1051colSums(emailsSparse)[324]## enron
## 13388which.max(colSums(emailsSparse))## enron
## 324emailsSparse$spam <- emails$spam
#only ham
ham_mails <- subset(emailsSparse, spam == 0)
length(colSums(ham_mails))## [1] 331sort(colSums(subset(emailsSparse, spam == 0)))## spam life remov money onlin without websit
## 0 80 103 114 173 191 194
## click special wish repli buy net link
## 217 226 229 239 243 243 247
## immedi done mean design lot effect info
## 249 254 259 261 268 270 273
## read either write line begin success sorri
## 279 279 286 289 291 293 293
## involv softwar creat better vkamin say keep
## 294 299 299 301 301 305 306
## bring believ full increas realli mention thought
## 311 313 317 320 324 325 325
## invest idea secur specif sever experi thing
## 327 327 337 338 340 346 347
## allow due check type happi return expect
## 348 351 351 352 354 355 356
## short effort open internet sincer public recent
## 357 358 360 361 361 364 368
## anoth alreadi home made respond given etc
## 369 372 375 380 382 383 385
## put within place version right hello sure
## 385 386 388 390 390 395 396
## area run arrang account join hour locat
## 397 398 399 401 403 404 406
## togeth import engin per corpor high result
## 406 411 411 412 414 416 418
## hear final deal applic even web custom
## 420 422 423 428 429 430 433
## soon long sinc futur member event X000
## 435 436 439 440 446 447 447
## don part feel tuesday wednesday unit still
## 450 450 453 454 456 457 457
## site X853 continu understand resourc robert form
## 458 461 464 464 466 466 468
## analysi point assist confirm differ intern might
## 468 474 475 485 489 489 490
## real case howev comment complet abl rate
## 490 492 496 505 515 515 516
## appreci tri move updat approv suggest free
## 518 521 526 527 533 533 535
## contract detail morn end mani attend thursday
## 544 546 546 550 550 558 558
## direct requir cours person relat depart today
## 561 562 567 569 573 575 577
## start way mark valu problem peopl note
## 580 586 588 590 593 599 600
## school invit access term juli monday gibner
## 607 614 617 625 630 630 633
## base director offer cost addit kevin great
## 635 640 643 646 648 654 655
## set file find much order oper deriv
## 658 659 665 669 669 669 673
## doc april book address copi financi month
## 673 677 680 693 700 702 709
## student respons possibl associ particip now first
## 710 711 712 715 717 725 726
## industri dear support plan back name come
## 731 734 734 738 739 745 748
## opportun report product two origin ask credit
## 760 772 776 787 796 797 798
## state system process hope london just receiv
## 806 816 826 828 828 830 830
## chang review current shall friday team phone
## 831 834 841 844 847 850 858
## issu data avail last good give www
## 865 868 872 874 876 883 897
## gas list posit visit includ resum best
## 905 907 917 920 924 928 933
## offic servic talk number well fax provid
## 935 942 943 951 961 963 970
## sent next. send http john univers financ
## 971 975 986 1009 1022 1025 1038
## stinson schedul take date want question program
## 1051 1054 1057 1060 1068 1069 1080
## think X713 crenshaw attach trade help email
## 1084 1097 1115 1155 1167 1168 1201
## compani request see communic confer discuss make
## 1225 1227 1238 1251 1264 1270 1281
## contact follow interview project mail present busi
## 1301 1308 1320 1328 1352 1397 1416
## interest option day call one year week
## 1429 1432 1440 1497 1516 1523 1527
## messag houston also look edu corp shirley
## 1538 1577 1604 1607 1620 1643 1687
## develop get new use let regard inform
## 1691 1768 1777 1784 1856 1859 1883
## need power may like risk energi market
## 1890 1972 1976 1980 2097 2124 2150
## model price work manag know group meet
## 2170 2191 2293 2334 2345 2474 2544
## time research forward X2001 can thank com
## 2552 2752 2952 3060 3426 3558 4444
## pleas kaminski X2000 hou will vinc subject
## 4494 4801 4935 5569 6802 8531 8625
## ect enron
## 11417 13388length(sort(colSums(subset(emailsSparse, spam == 0))))## [1] 331length(sort(colSums(ham_mails)))## [1] 331length(which(colSums(ham_mails)>10000))## [1] 2length(which(colSums(ham_mails)>1000))## [1] 83length(which(colSums(ham_mails)>5000))## [1] 6length(which(colSums(emailsSparse)>1000))## [1] 119subset(emailsSparse, spam == 1)## busi chang compani corpor day done effect effort even full good inform
## 1 2 2 3 1 1 1 2 1 1 1 2 1
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## 7 3 1 16 0 0 0 0 1 1 0 0 11
## 8 0 0 0 0 0 0 1 0 1 0 0 0
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## 294 0 0 0 0 0 0 0 1
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## 297 0 0 0 0 0 0 0 1
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## 299 0 0 0 0 0 0 0 1
## 300 0 0 0 0 0 0 0 1
## 301 0 0 0 0 0 0 0 1
## 302 0 0 0 0 0 0 0 1
## [ reached 'max' / getOption("max.print") -- omitted 1066 rows ]sort(colSums(subset(emailsSparse, spam == 1)))## enron kaminski X713 crenshaw vkamin gibner stinson
## 0 0 0 0 0 0 0
## vinc X853 kevin doc shirley deriv houston
## 1 1 2 2 2 3 5
## april resum edu friday wednesday hou ect
## 5 5 7 7 8 8 10
## arrang interview london attend robert student schedul
## 11 13 15 15 16 16 17
## thursday monday john tuesday attach suggest appreci
## 17 19 20 20 21 21 23
## mark comment begin analysi X2001 model mention
## 25 26 26 27 29 29 30
## hope X2000 togeth invit confer univers financ
## 30 32 32 33 33 34 35
## talk either run shall morn happi thought
## 38 39 39 40 40 42 42
## depart confirm respond school hear corp etc
## 46 47 48 48 49 49 49
## howev sorri idea energi discuss open option
## 49 50 51 55 56 56 56
## understand soon experi cours associ point bring
## 57 57 59 59 62 62 63
## director particip join anoth still research final
## 65 65 66 66 66 68 68
## set specif case given juli problem put
## 69 69 69 70 71 73 73
## ask alreadi fax abl deal team book
## 74 74 75 75 75 76 76
## locat issu meet updat lot sincer short
## 79 79 79 79 80 80 82
## better sinc done recent question possibl end
## 82 82 83 83 83 84 85
## contract move might data continu note resourc
## 85 86 87 87 88 88 90
## sever feel area communic realli due origin
## 90 90 92 92 93 94 96
## direct unit copi long member sure allow
## 96 97 97 98 99 99 102
## dear write public event let differ file
## 104 104 104 105 107 109 111
## involv respons creat type effort approv detail
## 111 113 114 114 115 115 115
## request intern say import support relat part
## 117 117 118 119 120 121 121
## assist two last back keep addit date
## 123 124 124 125 125 126 127
## place group mean valu think offic read
## 128 130 131 131 132 133 134
## immedi check hello applic tri review phone
## 136 137 139 139 140 142 143
## believ hour power present process corpor oper
## 143 144 145 146 149 151 151
## full return sent come opportun real repli
## 152 154 155 155 158 158 158
## line engin term credit well gas info
## 159 160 161 162 164 165 165
## plan risk next. increas access give thank
## 166 170 170 171 172 172 172
## version requir link cost great wish regard
## 174 174 174 175 182 185 186
## posit thing call develop much complet even
## 187 188 190 191 192 192 193
## project form design without expect person trade
## 194 196 196 198 198 198 199
## buy effect rate base find current first
## 199 201 201 202 202 203 203
## chang visit financi high mani forward good
## 204 206 207 208 208 209 221
## special success don per number week result
## 225 226 226 230 231 231 237
## web industri made contact follow month right
## 238 239 242 242 244 249 249
## today also internet help manag know way
## 251 260 262 262 266 269 278
## state avail futur home start system take
## 280 280 282 285 300 302 304
## net includ life see name onlin within
## 305 314 320 329 344 345 346
## remov best program peopl custom year like
## 357 358 358 359 363 367 372
## interest send servic look work day want
## 385 393 395 396 415 420 420
## product www account provid need softwar messag
## 421 426 428 435 438 440 445
## site address may list price new websit
## 455 461 489 503 503 504 506
## report secur just offer invest order use
## 507 520 524 528 540 541 546
## click X000 now one time market http
## 552 560 575 592 593 600 600
## make free pleas money get receiv inform
## 603 606 619 662 694 727 818
## can email busi mail com compani spam
## 831 865 897 917 999 1065 1368
## will subject
## 1450 1577Machine learning models
First, convert the dependent variable to a factor with “emailsSparse\(spam = as.factor(emailsSparse\)spam)”.
Next, set the random seed to 123 and use the sample.split function to split emailsSparse 70/30 into a training set called “train” and a testing set called “test”. Make sure to perform this step on emailsSparse instead of emails.
Using the training set, train the following three machine learning models. The models should predict the dependent variable “spam”, using all other available variables as independent variables. Please be patient, as these models may take a few minutes to train.
A logistic regression model called spamLog. You may see a warning message here - we’ll discuss this more later.
A CART model called spamCART, using the default parameters to train the model (don’t worry about adding minbucket or cp). Remember to add the argument method=“class” since this is a binary classification problem.
A random forest model called spamRF, using the default parameters to train the model (don’t worry about specifying ntree or nodesize). Directly before training the random forest model, set the random seed to 123 (even though we’ve already done this earlier in the problem, it’s important to set the seed right before training the model so we all obtain the same results. Keep in mind though that on certain operating systems, your results might still be slightly different).
For each model, obtain the predicted spam probabilities for the training set. Be careful to obtain probabilities instead of predicted classes, because we will be using these values to compute training set AUC values. Recall that you can obtain probabilities for CART models by not passing any type parameter to the predict() function, and you can obtain probabilities from a random forest by adding the argument type=“prob”. For CART and random forest, you need to select the second column of the output of the predict() function, corresponding to the probability of a message being spam.
You may have noticed that training the logistic regression model yielded the messages “algorithm did not converge” and “fitted probabilities numerically 0 or 1 occurred”. Both of these messages often indicate overfitting and the first indicates particularly severe overfitting, often to the point that the training set observations are fit perfectly by the model. Let’s investigate the predicted probabilities from the logistic regression model.
How many of the training set predicted probabilities from spamLog are less than 0.00001?
emailsSparse$spam <- as.factor(emailsSparse$spam)
set.seed(123)
splt <- sample.split(emailsSparse$spam, SplitRatio = 0.7)
train <- subset(emailsSparse, splt == TRUE)
test <- subset(emailsSparse, splt == FALSE)
# 3 machine learning models
spamLog <- glm(spam ~ ., data = train, family = binomial)## Warning: glm.fit: algorithm did not converge## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurredspamCART <- rpart(spam ~., data = train, method = 'class')
set.seed(123)
library(randomForest)## randomForest 4.6-14## Type rfNews() to see new features/changes/bug fixes.spamRF <- randomForest(spam ~., data = train)
predLog <- predict(spamLog, newdata = train, type = "response")
predLog## 1 3 6 7 9 10
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 12 13 14 15 17 18
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 19 23 25 27 28 29
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 30 35 36 38 39 40
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 41 42 43 44 45 46
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 47 48 49 51 52 54
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 55 56 57 60 61 62
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 63 64 66 70 72 74
## 1.000000e+00 1.000000e+00 1.000000e+00 9.999999e-01 1.000000e+00 1.000000e+00
## 75 76 77 78 79 80
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 81 82 83 85 86 90
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 91 92 93 94 95 96
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 98 99 100 101 102 103
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 105 108 109 110 112 113
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 116 117 119 120 121 122
## 4.000000e-01 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 123 124 125 127 128 129
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 131 133 135 136 140 141
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 142 143 144 146 147 148
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 149 152 153 154 155 156
## 4.000000e-01 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 157 158 159 160 161 162
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 163 164 165 166 168 169
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 170 171 172 175 176 177
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 178 180 182 184 185 186
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 187 188 191 192 194 196
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 197 198 199 200 201 203
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 204 205 207 208 209 210
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 211 212 213 214 215 217
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 218 221 224 225 226 227
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 228 231 232 233 234 235
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 236 237 239 241 242 243
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 244 245 247 251 252 253
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 254 255 257 258 259 263
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 265 266 267 268 269 270
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 272 273 274 278 279 280
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 282 283 284 285 286 287
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 288 289 290 291 292 293
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 298 299 302 305 306 307
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 308 309 310 311 312 314
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 315 318 319 322 323 325
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 326 328 329 331 332 335
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 336 338 339 341 342 343
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 344 345 346 348 349 350
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 351 353 354 355 357 358
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 359 361 362 364 365 367
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 368 369 370 371 372 374
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 375 378 379 381 383 385
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 387 388 389 390 392 395
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 396 397 398 399 402 404
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 405 406 408 409 410 411
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 413 414 415 416 418 419
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 420 421 422 423 424 426
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 427 428 429 432 433 435
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 436 437 438 439 440 441
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 442 444 448 449 450 451
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 452 453 454 455 459 460
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 462 463 464 465 466 467
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 469 471 473 475 476 477
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 478 479 481 483 484 486
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 487 488 489 492 493 495
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 497 498 499 501 502 503
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 504 505 506 507 508 510
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 511 512 514 516 517 519
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 521 522 523 524 525 526
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 528 530 532 533 535 537
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 539 540 542 544 547 550
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 551 552 553 555 556 557
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 558 559 560 561 564 565
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 566 567 569 571 573 574
## 1.000000e+00 1.000000e+00 4.000000e-01 1.000000e+00 1.000000e+00 1.000000e+00
## 577 578 579 580 584 586
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 587 588 590 591 592 594
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 595 597 598 600 601 602
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 603 604 605 607 609 610
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 611 612 613 615 620 624
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 625 626 627 629 630 633
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 635 636 640 641 644 645
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 646 648 649 650 653 654
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 658 659 660 663 665 666
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 668 669 670 671 672 673
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 674 675 676 678 679 680
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 686 687 688 689 690 691
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 692 693 694 695 696 697
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 698 699 700 702 703 705
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 706 707 708 709 710 711
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 712 713 715 716 717 718
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 720 721 725 728 730 731
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 733 735 736 739 740 742
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 743 744 745 746 748 751
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 752 753 754 755 756 757
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 759 760 761 762 763 764
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 765 766 767 768 769 770
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 773 775 776 777 778 779
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 781 783 784 786 787 788
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 789 792 793 794 796 797
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 798 799 800 801 802 803
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 804 805 807 808 810 811
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 813 816 817 818 819 820
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 821 822 823 826 827 828
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 829 831 833 835 836 838
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 839 840 843 844 845 846
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 848 849 850 851 855 856
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 858 859 861 862 863 864
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 865 866 867 868 869 870
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 871 872 874 876 877 880
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 881 883 884 887 888 889
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 890 891 893 894 897 898
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 899 902 904 905 906 910
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 911 912 914 915 917 918
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 919 920 922 923 926 927
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 928 929 932 934 936 937
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 940 942 943 944 945 946
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 947 948 949 950 951 952
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 954 955 957 958 959 960
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 961 962 963 964 966 967
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 968 970 972 974 975 976
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 978 979 980 981 984 987
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 988 989 990 991 992 993
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 994 995 997 998 1000 1001
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1002 1003 1006 1008 1009 1010
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1011 1012 1013 1014 1015 1017
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1018 1019 1020 1021 1023 1024
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1026 1027 1028 1029 1030 1031
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1032 1033 1034 1035 1036 1037
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1038 1039 1040 1043 1044 1045
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1046 1047 1048 1054 1055 1056
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1057 1058 1059 1062 1063 1064
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1065 1067 1068 1070 1075 1076
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1077 1078 1079 1080 1081 1082
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1083 1084 1086 1087 1088 1090
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1092 1093 1094 1098 1099 1100
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1103 1106 1107 1110 1111 1113
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1114 1115 1116 1117 1119 1120
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1121 1122 1124 1125 1126 1128
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1129 1130 1131 1134 1137 1138
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1139 1140 1142 1143 1145 1146
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1147 1148 1149 1150 1152 1155
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1156 1157 1159 1160 1161 1162
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1163 1164 1165 1166 1168 1169
## 1.000000e+00 4.000000e-01 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1171 1172 1173 1175 1176 1178
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1179 1180 1181 1182 1183 1186
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1187 1190 1191 1192 1193 1195
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1196 1198 1200 1203 1205 1207
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1208 1210 1211 1213 1214 1215
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1217 1219 1221 1222 1223 1226
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1227 1228 1230 1231 1232 1233
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1234 1235 1236 1237 1240 1241
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1242 1243 1244 1246 1247 1248
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1249 1252 1253 1254 1255 1257
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1258 1260 1261 1262 1263 1264
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1266 1267 1269 1271 1273 1274
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1276 1278 1279 1280 1281 1283
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1285 1286 1288 1289 1290 1292
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1293 1295 1296 1300 1301 1302
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1303 1306 1307 1308 1309 1310
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1311 1312 1314 1316 1318 1319
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1320 1322 1324 1326 1327 1328
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1329 1330 1331 1332 1333 1334
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1335 1336 1340 1341 1342 1343
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1344 1345 1347 1348 1349 1350
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1351 1352 1353 1354 1355 1356
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1357 1359 1360 1361 1362 1364
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
## 1365 1366 1367 1368 1369 1370
## 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 2.220446e-16 2.220446e-16
## 1371 1372 1373 1374 1375 1377
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1379 1380 1381 1382 1384 1386
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1387 1389 1390 1392 1393 1394
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1395 1397 1398 1399 1400 1401
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1402 1403 1404 1405 1407 1409
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1413 1414 1415 1417 1418 1420
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1422 1423 1425 1426 1427 1430
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1432 1435 1436 1437 1439 1440
## 2.220446e-16 1.643287e-10 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1441 1442 1443 1444 1447 1448
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1449 1450 1451 1454 1455 1457
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 1.177981e-10
## 1460 1464 1465 1468 1469 1470
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1472 1474 1475 1477 1482 1486
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1488 1489 1491 1492 1495 1498
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1499 1500 1503 1504 1505 1506
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1507 1508 1509 1510 1511 1514
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1515 1516 1517 1518 1519 1520
## 1.231119e-11 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1522 1524 1526 1527 1528 1529
## 2.220446e-16 2.220446e-16 2.220446e-16 8.159955e-10 2.220446e-16 2.220446e-16
## 1530 1532 1534 1535 1536 1537
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1538 1540 1541 1543 1544 1545
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1546 1547 1548 1549 1552 1553
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 5.023578e-08
## 1554 1555 1556 1557 1558 1559
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1562 1564 1565 1566 1567 1569
## 2.220446e-16 2.220446e-16 2.220446e-16 4.572824e-09 2.220446e-16 2.220446e-16
## 1571 1572 1574 1575 1577 1578
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1579 1580 1581 1582 1583 1584
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1586 1587 1588 1589 1590 1593
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1594 1595 1596 1597 1598 1600
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1601 1602 1603 1606 1608 1609
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1610 1611 1613 1616 1617 1618
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1619 1620 1621 1622 1623 1625
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1627 1628 1629 1632 1633 1634
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1637 1638 1639 1641 1645 1649
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1650 1651 1653 1654 1655 1656
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1657 1659 1662 1663 1664 1666
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1668 1669 1670 1671 1672 1673
## 2.220446e-16 2.220446e-16 8.988169e-10 2.220446e-16 6.837331e-09 2.220446e-16
## 1675 1676 1677 1678 1679 1680
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1681 1682 1684 1685 1686 1687
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1688 1691 1692 1693 1698 1699
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1700 1702 1703 1707 1708 1710
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.755693e-09 3.892545e-09
## 1711 1712 1713 1715 1717 1718
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1720 1722 1723 1724 1725 1727
## 3.467147e-09 2.220446e-16 1.109652e-08 7.663650e-10 2.220446e-16 2.220446e-16
## 1728 1729 1730 1732 1733 1736
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1737 1741 1743 1744 1745 1746
## 2.220446e-16 2.220446e-16 3.560278e-10 2.220446e-16 2.220446e-16 2.220446e-16
## 1750 1754 1756 1758 1759 1761
## 2.220446e-16 2.220446e-16 2.220446e-16 3.976486e-10 2.220446e-16 2.220446e-16
## 1762 1763 1764 1765 1768 1771
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1772 1773 1774 1775 1776 1777
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 6.139323e-10 2.220446e-16
## 1778 1779 1780 1781 1782 1784
## 4.739024e-11 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1785 1786 1788 1789 1791 1792
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1793 1795 1796 1797 1799 1800
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1801 1803 1804 1805 1806 1808
## 2.220446e-16 2.220446e-16 2.220446e-16 1.439668e-11 2.220446e-16 2.220446e-16
## 1810 1811 1812 1814 1815 1816
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1817 1818 1819 1820 1822 1823
## 1.493482e-10 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1825 1827 1832 1834 1835 1836
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1837 1838 1841 1842 1843 1845
## 4.315969e-09 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1846 1847 1848 1850 1853 1854
## 2.220446e-16 2.220446e-16 6.676559e-09 2.220446e-16 2.220446e-16 2.220446e-16
## 1855 1856 1858 1859 1861 1862
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1863 1865 1866 1867 1869 1870
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1871 1873 1874 1875 1877 1878
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1880 1882 1883 1884 1885 1887
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1888 1889 1890 1891 1893 1896
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1897 1899 1900 1901 1902 1903
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 8.192911e-11 2.220446e-16
## 1905 1906 1907 1909 1910 1911
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1912 1913 1914 1915 1916 1917
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1918 1920 1922 1924 1925 1926
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1927 1928 1929 1931 1932 1933
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 3.710924e-12 2.220446e-16
## 1934 1935 1936 1937 1939 1941
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1942 1943 1944 1945 1947 1948
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1950 1951 1953 1954 1955 1956
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1957 1959 1960 1962 1963 1964
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1965 1966 1967 1968 1970 1971
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1973 1974 1976 1977 1978 1980
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 1982 1983 1984 1985 1986 1987
## 1.584644e-09 2.220446e-16 2.220446e-16 2.681811e-09 2.220446e-16 2.220446e-16
## 1988 1989 1990 1991 1992 1994
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 4.000000e-01 2.220446e-16
## 1995 1997 1999 2000 2001 2002
## 1.427825e-10 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2003 2004 2005 2006 2007 2008
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.905871e-10
## 2009 2010 2012 2013 2014 2016
## 2.220446e-16 1.493482e-10 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2018 2019 2020 2022 2024 2025
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2026 2027 2028 2029 2031 2032
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2033 2034 2035 2037 2041 2042
## 2.220446e-16 2.833888e-10 2.220446e-16 2.220446e-16 1.099640e-13 2.220446e-16
## 2043 2048 2049 2050 2051 2052
## 2.220446e-16 2.586225e-09 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2054 2056 2057 2060 2061 2063
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2065 2066 2067 2068 2071 2073
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2074 2075 2077 2078 2080 2081
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2082 2084 2085 2086 2087 2089
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 9.540720e-09
## 2090 2091 2092 2093 2094 2095
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2098 2099 2100 2101 2102 2103
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2105 2107 2108 2112 2113 2114
## 9.008423e-09 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 3.108793e-09
## 2115 2116 2118 2122 2123 2124
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2126 2128 2129 2131 2132 2133
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2134 2135 2136 2137 2140 2142
## 2.220446e-16 2.220446e-16 3.120743e-11 2.220446e-16 2.220446e-16 2.220446e-16
## 2143 2144 2145 2146 2147 2148
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 4.604890e-11
## 2149 2151 2153 2154 2155 2156
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2157 2159 2160 2162 2163 2165
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 6.214985e-09
## 2167 2170 2171 2172 2173 2174
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2176 2177 2179 2182 2183 2184
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2186 2189 2191 2192 2193 2197
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2198 2199 2200 2204 2205 2206
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2207 2209 2210 2211 2212 2213
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2214 2215 2216 2217 2218 2219
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2220 2221 2222 2224 2226 2227
## 2.220446e-16 2.220446e-16 1.373181e-10 2.220446e-16 1.106060e-09 2.220446e-16
## 2228 2230 2233 2234 2235 2236
## 2.220446e-16 3.889352e-10 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2238 2239 2241 2242 2243 2247
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2249 2250 2253 2255 2256 2257
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2258 2259 2261 2263 2264 2265
## 4.619710e-10 2.220446e-16 2.220446e-16 2.220446e-16 4.000000e-01 5.979689e-10
## 2266 2267 2269 2270 2271 2272
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2273 2274 2278 2279 2280 2281
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2283 2284 2285 2286 2287 2288
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2289 2290 2291 2293 2294 2296
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2297 2299 2301 2303 2304 2306
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2307 2308 2310 2311 2312 2313
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2314 2315 2317 2318 2319 2320
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2321 2322 2323 2325 2326 2327
## 1.618697e-10 2.220446e-16 3.733060e-10 2.220446e-16 2.220446e-16 2.220446e-16
## 2328 2329 2330 2331 2332 2333
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2336 2337 2341 2342 2345 2346
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 1.824753e-10 2.220446e-16
## 2347 2348 2349 2350 2353 2355
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2356 2357 2358 2359 2360 2361
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2363 2365 2366 2367 2368 2370
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2372 2373 2374 2375 2376 2378
## 2.220446e-16 2.220446e-16 2.501102e-10 2.220446e-16 2.220446e-16 2.220446e-16
## 2379 2381 2382 2384 2386 2387
## 3.604407e-10 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2389 2391 2392 2393 2394 2397
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2398 2399 2402 2403 2406 2407
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2408 2410 2412 2413 2414 2416
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2417 2418 2419 2420 2421 2423
## 2.220446e-16 2.220446e-16 2.220446e-16 2.348254e-11 2.220446e-16 2.220446e-16
## 2424 2425 2426 2427 2429 2432
## 2.659053e-09 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2433 2435 2436 2437 2438 2439
## 2.220446e-16 2.220446e-16 2.118330e-09 2.220446e-16 2.387414e-09 2.220446e-16
## 2441 2442 2443 2444 2445 2447
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2448 2449 2450 2452 2453 2457
## 6.884614e-09 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 3.505733e-12
## 2458 2459 2460 2461 2462 2464
## 2.220446e-16 2.220446e-16 3.486935e-09 2.220446e-16 2.220446e-16 2.220446e-16
## 2465 2466 2467 2468 2469 2470
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2471 2472 2473 2474 2475 2476
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2478 2480 2481 2482 2484 2486
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2487 2488 2489 2492 2493 2498
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2499 2500 2502 2504 2505 2506
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2507 2510 2511 2512 2513 2514
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2516 2517 2518 2519 2520 2522
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2524 2525 2527 2528 2529 2532
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2533 2534 2536 2537 2542 2545
## 2.220446e-16 5.466767e-10 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2547 2549 2550 2551 2552 2553
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 7.510289e-09 2.703253e-09
## 2554 2556 2557 2558 2559 2560
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2561 2563 2564 2565 2567 2568
## 2.220446e-16 2.220446e-16 2.813953e-09 2.220446e-16 2.220446e-16 4.000000e-01
## 2569 2571 2572 2573 2574 2575
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 1.949247e-10
## 2576 2577 2578 2579 2582 2584
## 2.220446e-16 2.220446e-16 7.624962e-09 2.220446e-16 1.813330e-09 2.220446e-16
## 2585 2586 2589 2590 2591 2593
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 4.524509e-10
## 2594 2595 2597 2600 2601 2602
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.039139e-09
## 2603 2605 2606 2607 2608 2609
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2610 2612 2613 2614 2615 2617
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2618 2619 2622 2623 2626 2627
## 2.220446e-16 1.879574e-08 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2628 2629 2630 2631 2633 2634
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2635 2636 2638 2639 2640 2641
## 2.220446e-16 2.220446e-16 1.486908e-09 2.220446e-16 2.220446e-16 2.924218e-09
## 2643 2644 2648 2649 2650 2654
## 9.851576e-10 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2655 2656 2657 2659 2660 2661
## 2.220446e-16 2.220446e-16 2.220446e-16 7.977920e-10 2.220446e-16 2.220446e-16
## 2662 2664 2665 2666 2667 2668
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2669 2670 2671 2672 2674 2675
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2676 2677 2679 2680 2681 2682
## 2.220446e-16 2.220446e-16 2.220446e-16 5.112585e-10 2.220446e-16 2.220446e-16
## 2685 2687 2689 2691 2692 2693
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2694 2695 2697 2699 2701 2703
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2704 2705 2710 2712 2713 2714
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2715 2717 2718 2719 2720 2722
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2723 2728 2729 2730 2731 2734
## 2.220446e-16 2.220446e-16 3.831589e-09 2.220446e-16 2.220446e-16 2.220446e-16
## 2736 2737 2739 2741 2742 2743
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2744 2747 2748 2749 2750 2752
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2753 2754 2755 2756 2757 2760
## 2.220446e-16 2.882849e-10 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2761 2762 2763 2764 2765 2766
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2768 2770 2771 2772 2773 2774
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2775 2778 2779 2780 2781 2783
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 1.325718e-12 2.220446e-16
## 2786 2788 2791 2792 2793 2794
## 2.220446e-16 2.220446e-16 2.220446e-16 5.249282e-11 2.220446e-16 2.220446e-16
## 2796 2797 2798 2799 2801 2802
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2803 2804 2806 2807 2809 2812
## 4.949000e-10 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2816 2817 2819 2821 2822 2825
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2826 2828 2829 2830 2831 2832
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2833 2835 2836 2838 2841 2842
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2845 2848 2849 2850 2852 2853
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2854 2856 2857 2859 2862 2863
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2864 2865 2867 2869 2870 2871
## 2.220446e-16 2.220446e-16 2.220446e-16 8.693163e-10 4.984183e-09 2.220446e-16
## 2872 2873 2874 2877 2878 2879
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2881 2882 2884 2885 2888 2889
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2891 2893 2894 2895 2896 2898
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2899 2900 2902 2904 2906 2908
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2909 2911 2912 2914 2916 2919
## 1.277026e-09 2.220446e-16 2.220446e-16 2.220446e-16 2.936904e-09 2.220446e-16
## 2921 2922 2924 2925 2926 2929
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2930 2931 2932 2933 2934 2936
## 2.220446e-16 2.220446e-16 2.220446e-16 3.210851e-10 2.220446e-16 2.220446e-16
## 2937 2938 2939 2940 2941 2943
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2944 2945 2947 2948 2949 2950
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2951 2952 2954 2955 2957 2959
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2960 2962 2964 2965 2966 2968
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 4.000000e-01 2.220446e-16
## 2969 2970 2972 2973 2974 2975
## 2.220446e-16 2.220446e-16 7.274467e-10 2.220446e-16 2.220446e-16 2.220446e-16
## 2976 2978 2980 2982 2983 2984
## 2.220446e-16 2.220446e-16 2.220446e-16 5.754560e-09 2.220446e-16 2.220446e-16
## 2985 2988 2989 2990 2991 2992
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 2994 2996 2998 2999 3000 3001
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3003 3004 3005 3006 3008 3012
## 2.220446e-16 2.220446e-16 1.221842e-10 2.220446e-16 2.220446e-16 2.220446e-16
## 3013 3014 3015 3016 3018 3020
## 3.012577e-10 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3021 3023 3024 3029 3032 3033
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3034 3036 3037 3038 3039 3041
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3042 3043 3044 3045 3047 3048
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3049 3051 3052 3054 3055 3057
## 2.220446e-16 2.220446e-16 1.667874e-11 2.220446e-16 2.220446e-16 3.967708e-09
## 3062 3063 3064 3065 3067 3069
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3070 3073 3074 3075 3077 3078
## 2.220446e-16 2.220446e-16 2.220446e-16 5.887196e-09 2.220446e-16 2.258905e-10
## 3080 3082 3083 3084 3085 3086
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3088 3089 3090 3093 3094 3096
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3097 3098 3099 3100 3101 3103
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3105 3106 3108 3110 3111 3112
## 2.220446e-16 2.220446e-16 2.220446e-16 5.139171e-10 2.220446e-16 2.220446e-16
## 3113 3114 3115 3117 3120 3121
## 7.308648e-10 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3122 3125 3128 3129 3131 3132
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3134 3135 3136 3137 3138 3139
## 3.127462e-10 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3140 3142 3143 3144 3145 3146
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3147 3149 3150 3153 3154 3155
## 2.220446e-16 2.220446e-16 8.608385e-09 2.220446e-16 2.220446e-16 2.220446e-16
## 3156 3157 3158 3159 3160 3161
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 9.543944e-11
## 3162 3164 3165 3167 3168 3169
## 2.220446e-16 9.543944e-11 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3170 3171 3172 3173 3175 3176
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 1.318287e-10
## 3178 3181 3183 3184 3185 3186
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3187 3188 3189 3191 3192 3193
## 2.220446e-16 9.131185e-10 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3197 3198 3200 3201 3202 3204
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3205 3206 3207 3208 3209 3210
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3211 3212 3214 3216 3218 3220
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3222 3224 3225 3227 3228 3229
## 2.220446e-16 2.220446e-16 1.931921e-09 2.220446e-16 2.220446e-16 2.220446e-16
## 3230 3231 3232 3233 3234 3236
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3238 3239 3240 3241 3242 3248
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 3.950263e-09 2.220446e-16
## 3249 3251 3252 3253 3254 3256
## 2.220446e-16 2.220446e-16 1.205250e-10 2.220446e-16 2.220446e-16 2.220446e-16
## 3257 3260 3261 3262 3263 3264
## 1.485003e-09 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3265 3268 3269 3270 3271 3272
## 1.213121e-09 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3274 3277 3278 3279 3280 3281
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3282 3283 3284 3286 3288 3290
## 5.068746e-10 2.220446e-16 4.180367e-09 2.220446e-16 2.220446e-16 2.220446e-16
## 3291 3292 3293 3294 3295 3296
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3298 3299 3301 3302 3303 3304
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 5.864350e-12 2.220446e-16
## 3306 3308 3309 3310 3311 3313
## 2.220446e-16 2.220446e-16 3.747406e-09 2.220446e-16 2.220446e-16 2.220446e-16
## 3315 3316 3318 3319 3320 3322
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 1.669944e-11 2.220446e-16
## 3323 3324 3326 3327 3329 3330
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3331 3332 3334 3336 3337 3338
## 2.220446e-16 2.220446e-16 2.220446e-16 2.129646e-10 2.220446e-16 2.220446e-16
## 3340 3341 3344 3345 3347 3350
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 5.810002e-10 2.220446e-16
## 3352 3354 3355 3356 3357 3358
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3360 3361 3362 3365 3366 3368
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3369 3370 3372 3373 3375 3377
## 5.850446e-10 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3379 3380 3382 3383 3384 3385
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3386 3388 3389 3390 3391 3392
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 1.702088e-12
## 3393 3394 3395 3397 3398 3399
## 1.290541e-09 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3400 3401 3402 3403 3404 3405
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3406 3408 3410 3411 3412 3413
## 8.657994e-11 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3416 3418 3420 3421 3422 3424
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3425 3426 3428 3429 3431 3432
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3433 3434 3435 3436 3439 3440
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3441 3443 3444 3445 3446 3447
## 2.220446e-16 2.220446e-16 2.220446e-16 3.135547e-11 2.220446e-16 2.220446e-16
## 3448 3449 3450 3451 3452 3453
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3454 3455 3456 3457 3458 3459
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3460 3462 3463 3464 3465 3468
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3469 3470 3471 3472 3475 3476
## 2.220446e-16 2.220446e-16 2.220446e-16 1.263909e-09 2.220446e-16 2.220446e-16
## 3477 3478 3479 3481 3482 3483
## 1.179084e-10 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3484 3485 3486 3491 3492 3493
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3495 3498 3499 3500 3501 3502
## 2.220446e-16 2.220446e-16 2.473381e-09 2.220446e-16 2.220446e-16 2.220446e-16
## 3504 3505 3506 3507 3508 3509
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3512 3513 3514 3515 3516 3517
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 1.396320e-09 2.220446e-16
## 3518 3520 3521 3522 3523 3524
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3525 3526 3527 3531 3533 3534
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3536 3538 3539 3540 3541 3543
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3544 3547 3549 3552 3555 3557
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3558 3559 3560 3561 3562 3563
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3564 3565 3567 3569 3572 3573
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3577 3578 3579 3580 3582 3583
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3586 3587 3589 3590 3591 3592
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3593 3594 3595 3597 3599 3600
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 9.034473e-11
## 3601 3602 3603 3604 3605 3608
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3610 3611 3612 3613 3614 3615
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3616 3617 3618 3619 3621 3622
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 1.756595e-09 2.220446e-16
## 3623 3624 3625 3627 3628 3629
## 2.220446e-16 2.220446e-16 4.588538e-09 2.220446e-16 2.220446e-16 2.220446e-16
## 3630 3631 3632 3633 3634 3636
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3637 3638 3639 3640 3641 3642
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3644 3645 3647 3648 3649 3652
## 2.220446e-16 2.220446e-16 1.376630e-09 2.454298e-10 2.220446e-16 7.657641e-10
## 3653 3656 3657 3658 3660 3661
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3663 3665 3666 3667 3668 3669
## 2.220446e-16 2.220446e-16 1.194555e-09 2.220446e-16 2.220446e-16 2.220446e-16
## 3672 3673 3676 3678 3679 3680
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3681 3683 3685 3686 3690 3691
## 2.220446e-16 3.461367e-09 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3692 3693 3694 3695 3696 3697
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3699 3700 3701 3702 3704 3707
## 2.220446e-16 2.220446e-16 4.896641e-10 2.220446e-16 2.220446e-16 2.220446e-16
## 3708 3710 3711 3712 3714 3716
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3717 3719 3720 3722 3723 3725
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3726 3727 3728 3729 3730 3732
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3733 3734 3735 3738 3740 3742
## 2.220446e-16 8.229532e-12 7.615291e-10 2.220446e-16 2.220446e-16 2.220446e-16
## 3744 3745 3747 3748 3750 3752
## 2.220446e-16 2.220446e-16 2.220446e-16 3.621583e-09 2.220446e-16 2.220446e-16
## 3754 3755 3756 3757 3758 3760
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3761 3763 3767 3769 3770 3774
## 2.220446e-16 2.220446e-16 2.220446e-16 4.869528e-10 2.220446e-16 2.220446e-16
## 3775 3778 3779 3781 3782 3784
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 7.231477e-08
## 3786 3787 3788 3790 3791 3792
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3793 3795 3797 3800 3802 3803
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3804 3805 3808 3809 3810 3811
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3813 3814 3815 3816 3817 3818
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 1.423208e-09 2.220446e-16
## 3820 3823 3824 3827 3828 3829
## 2.220446e-16 2.220446e-16 3.950263e-09 2.220446e-16 2.220446e-16 2.220446e-16
## 3830 3832 3833 3834 3835 3837
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3838 3840 3841 3842 3844 3845
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.568391e-09
## 3847 3848 3849 3852 3853 3854
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3855 3856 3858 3859 3861 3862
## 1.082488e-09 2.220446e-16 1.268708e-12 1.532873e-09 2.220446e-16 2.220446e-16
## 3866 3867 3871 3873 3874 3876
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3877 3879 3882 3883 3886 3887
## 2.220446e-16 2.220446e-16 1.166762e-09 2.220446e-16 2.220446e-16 2.220446e-16
## 3888 3889 3890 3892 3893 3894
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3895 3896 3897 3898 3900 3901
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 9.558971e-10
## 3902 3903 3904 3905 3906 3907
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 5.639299e-10
## 3911 3912 3913 3914 3915 3916
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3917 3918 3921 3922 3924 3925
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3926 3928 3929 3934 3935 3937
## 2.220446e-16 7.223629e-09 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3938 3939 3942 3943 3944 3945
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 8.302675e-13
## 3946 3949 3950 3953 3954 3955
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3956 3957 3958 3960 3961 3962
## 2.220446e-16 2.220446e-16 2.220446e-16 6.364320e-10 2.220446e-16 2.220446e-16
## 3964 3965 3966 3967 3968 3970
## 3.845547e-09 2.220446e-16 2.220446e-16 3.962899e-10 2.220446e-16 2.220446e-16
## 3971 3973 3976 3977 3980 3981
## 2.220446e-16 7.732871e-10 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 3982 3984 3985 3987 3988 3989
## 2.220446e-16 2.220446e-16 2.220446e-16 1.982296e-09 2.220446e-16 2.220446e-16
## 3990 3991 3992 3993 3995 3996
## 2.220446e-16 2.220446e-16 2.220446e-16 2.329618e-11 2.220446e-16 2.220446e-16
## 3998 3999 4000 4001 4003 4005
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4006 4008 4009 4011 4013 4014
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4015 4019 4020 4021 4024 4025
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4028 4029 4030 4032 4033 4034
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4035 4037 4040 4041 4042 4044
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 3.174428e-09 2.020631e-09
## 4046 4047 4048 4049 4051 4052
## 2.220446e-16 2.220446e-16 2.220446e-16 6.429543e-10 2.220446e-16 2.220446e-16
## 4053 4054 4055 4058 4059 4060
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4061 4062 4063 4064 4066 4068
## 2.078819e-07 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4069 4070 4071 4072 4073 4074
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4079 4080 4081 4082 4085 4087
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4088 4090 4091 4092 4093 4094
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4095 4096 4097 4099 4100 4101
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 5.109469e-09
## 4102 4103 4106 4109 4111 4112
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4113 4114 4116 4117 4118 4119
## 2.220446e-16 1.086376e-09 2.220446e-16 2.220446e-16 2.761138e-10 2.220446e-16
## 4123 4124 4127 4129 4130 4131
## 1.410873e-11 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4132 4133 4135 4136 4137 4138
## 4.557290e-09 7.252646e-11 2.220446e-16 2.220446e-16 5.091595e-09 2.220446e-16
## 4139 4142 4143 4144 4145 4147
## 2.220446e-16 2.220446e-16 2.220446e-16 8.418287e-10 2.220446e-16 2.220446e-16
## 4148 4149 4150 4151 4152 4155
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 5.068746e-10 2.220446e-16
## 4156 4157 4158 4159 4161 4162
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4163 4164 4165 4166 4167 4168
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4169 4171 4173 4174 4175 4177
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4178 4179 4180 4183 4185 4186
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4187 4188 4189 4191 4192 4193
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4195 4196 4199 4200 4201 4202
## 1.301587e-09 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4203 4204 4206 4207 4209 4210
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4211 4213 4214 4215 4216 4217
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4218 4219 4220 4221 4222 4223
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4224 4225 4226 4227 4228 4230
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4231 4232 4233 4235 4236 4237
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4238 4239 4240 4241 4243 4244
## 2.220446e-16 1.929950e-11 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4246 4248 4252 4253 4255 4257
## 2.220446e-16 2.220446e-16 2.220446e-16 5.109014e-10 2.220446e-16 2.220446e-16
## 4258 4260 4261 4262 4263 4265
## 2.220446e-16 2.220446e-16 2.220446e-16 4.000000e-01 2.220446e-16 2.220446e-16
## 4268 4269 4271 4273 4274 4275
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4276 4277 4278 4279 4280 4283
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.501102e-10 2.220446e-16
## 4285 4286 4287 4288 4289 4290
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4291 4292 4293 4294 4295 4296
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4297 4298 4299 4300 4301 4305
## 1.126710e-09 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4308 4309 4310 4311 4313 4314
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.039371e-10 2.220446e-16
## 4315 4317 4318 4320 4321 4322
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 4.000000e-01 2.220446e-16
## 4324 4325 4326 4327 4328 4329
## 1.661377e-11 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4330 4331 4333 4334 4335 4336
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4337 4338 4339 4340 4341 4343
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4344 4345 4346 4347 4348 4349
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4350 4351 4352 4353 4355 4356
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4358 4359 4362 4363 4364 4365
## 2.220446e-16 3.245492e-10 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4368 4369 4371 4372 4373 4377
## 1.137843e-09 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4378 4379 4381 4382 4383 4384
## 2.220446e-16 4.132797e-10 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4385 4386 4387 4388 4389 4390
## 2.220446e-16 2.220446e-16 2.220446e-16 4.030100e-10 2.220446e-16 2.220446e-16
## 4393 4394 4395 4396 4397 4400
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4403 4404 4405 4406 4411 4412
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4414 4415 4417 4418 4420 4421
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4423 4425 4428 4430 4431 4432
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 1.671982e-11
## 4434 4435 4437 4438 4441 4442
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4445 4446 4447 4448 4449 4450
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4451 4452 4455 4457 4458 4459
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4460 4461 4462 4463 4464 4468
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4473 4474 4476 4477 4478 4479
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4480 4481 4482 4483 4485 4486
## 2.220446e-16 2.220446e-16 2.220446e-16 4.926913e-10 2.220446e-16 2.220446e-16
## 4487 4488 4489 4490 4491 4492
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4493 4494 4495 4496 4498 4499
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4500 4501 4502 4503 4504 4505
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4506 4507 4508 4512 4513 4514
## 6.042147e-10 4.656042e-10 2.220446e-16 2.220446e-16 2.220446e-16 1.070700e-09
## 4515 4516 4517 4518 4519 4520
## 3.738758e-10 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4521 4523 4525 4526 4527 4529
## 2.220446e-16 2.220446e-16 2.220446e-16 8.648163e-09 2.220446e-16 2.220446e-16
## 4530 4533 4535 4536 4537 4538
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4541 4542 4543 4544 4546 4547
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4548 4550 4551 4553 4554 4555
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4556 4557 4558 4559 4560 4561
## 2.220446e-16 2.220446e-16 2.220446e-16 5.388503e-11 2.220446e-16 2.220446e-16
## 4562 4563 4564 4565 4567 4569
## 2.220446e-16 2.220446e-16 2.220446e-16 4.622374e-09 2.220446e-16 4.808549e-09
## 4571 4574 4575 4578 4580 4581
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4582 4583 4586 4587 4588 4589
## 1.082652e-09 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4591 4592 4595 4596 4597 4598
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4599 4600 4601 4603 4604 4605
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 3.610065e-09 2.882849e-10
## 4606 4607 4609 4610 4612 4617
## 2.220446e-16 2.220446e-16 2.187493e-09 2.220446e-16 2.220446e-16 2.220446e-16
## 4618 4619 4621 4622 4626 4627
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4629 4631 4632 4634 4638 4639
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4641 4642 4643 4644 4645 4646
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4649 4651 4652 4655 4656 4658
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.402759e-09
## 4660 4663 4664 4665 4666 4667
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 1.975903e-09 2.220446e-16
## 4669 4670 4671 4672 4673 4674
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4675 4676 4677 4678 4679 4680
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4681 4682 4683 4685 4689 4690
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4691 4692 4693 4694 4695 4696
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4697 4698 4699 4700 4701 4704
## 3.541102e-10 9.819470e-10 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4705 4706 4707 4708 4712 4714
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4715 4716 4717 4718 4719 4721
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4722 4724 4727 4728 4729 4731
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4734 4735 4736 4739 4741 4742
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4743 4744 4745 4746 4748 4749
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4751 4756 4758 4759 4760 4761
## 2.220446e-16 1.132379e-10 2.220446e-16 2.220446e-16 2.220446e-16 3.186463e-09
## 4762 4763 4765 4766 4769 4770
## 1.100148e-08 2.220446e-16 2.220446e-16 2.220446e-16 6.516174e-09 2.220446e-16
## 4771 4772 4775 4776 4777 4778
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4779 4781 4782 4783 4784 4786
## 1.395957e-10 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4789 4790 4791 4792 4794 4796
## 2.033324e-08 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4798 4800 4801 4802 4803 4804
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4805 4806 4807 4808 4810 4811
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.338992e-13
## 4812 4813 4814 4815 4817 4819
## 2.220446e-16 2.220446e-16 2.220446e-16 3.080176e-10 7.673034e-11 2.220446e-16
## 4820 4821 4822 4823 4825 4826
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4828 4829 4830 4831 4832 4833
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4834 4835 4836 4837 4839 4841
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4842 4843 4844 4845 4846 4847
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4848 4850 4851 4853 4854 4855
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4856 4857 4858 4860 4861 4864
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4865 4867 4868 4869 4870 4874
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4875 4876 4877 4878 4879 4880
## 2.220446e-16 6.755876e-11 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4881 4882 4884 4885 4886 4887
## 3.533903e-10 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4888 4892 4893 4894 4895 4896
## 2.220446e-16 2.220446e-16 5.661856e-09 2.220446e-16 2.220446e-16 2.220446e-16
## 4897 4898 4899 4900 4901 4905
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4906 4907 4909 4910 4911 4914
## 2.220446e-16 2.220446e-16 6.947409e-09 2.220446e-16 2.220446e-16 2.220446e-16
## 4915 4916 4917 4918 4919 4920
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4921 4922 4923 4924 4925 4927
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 1.794728e-09 7.990805e-12
## 4928 4929 4931 4932 4936 4938
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4939 4940 4941 4942 4943 4944
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 4.809274e-10 2.220446e-16
## 4946 4947 4948 4949 4951 4952
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4953 4954 4955 4956 4957 4958
## 2.220446e-16 1.671785e-11 2.220446e-16 2.220446e-16 2.220446e-16 2.934386e-10
## 4960 4963 4964 4965 4966 4967
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4968 4969 4970 4972 4975 4977
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4979 4980 4982 4983 4984 4985
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 4986 4988 4989 4990 4992 4994
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 4.112510e-10
## 4995 4996 4998 5000 5001 5004
## 9.860445e-10 2.899949e-10 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5005 5006 5007 5008 5010 5011
## 2.220446e-16 2.220446e-16 3.182140e-11 2.220446e-16 2.220446e-16 2.220446e-16
## 5013 5017 5018 5020 5024 5025
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5026 5027 5029 5031 5032 5033
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5034 5035 5038 5042 5045 5048
## 2.220446e-16 2.220446e-16 8.596667e-12 2.220446e-16 2.220446e-16 2.220446e-16
## 5049 5051 5052 5055 5056 5057
## 5.717026e-09 2.220446e-16 1.463114e-09 2.220446e-16 2.220446e-16 2.220446e-16
## 5059 5060 5061 5063 5064 5065
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5067 5068 5069 5070 5071 5072
## 2.220446e-16 6.393388e-11 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5073 5075 5076 5080 5081 5082
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5084 5085 5086 5087 5088 5089
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5090 5091 5092 5094 5096 5097
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 1.740677e-10
## 5099 5100 5101 5104 5106 5107
## 2.220446e-16 5.424216e-10 2.209700e-09 2.220446e-16 2.220446e-16 2.220446e-16
## 5108 5111 5112 5114 5115 5116
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5119 5120 5121 5124 5125 5126
## 2.220446e-16 2.220446e-16 4.854980e-10 2.220446e-16 2.220446e-16 2.220446e-16
## 5129 5132 5133 5134 5137 5140
## 6.755876e-11 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5141 5142 5144 5145 5146 5147
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5148 5149 5150 5152 5153 5154
## 6.010030e-09 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 7.669959e-11
## 5156 5158 5159 5160 5162 5163
## 3.630090e-10 4.077635e-10 6.163762e-10 7.650529e-10 2.220446e-16 4.932331e-10
## 5164 5166 5168 5169 5170 5171
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5172 5173 5174 5175 5176 5177
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5178 5180 5181 5183 5184 5188
## 2.220446e-16 2.343355e-09 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5192 5193 5194 5195 5197 5202
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5203 5204 5205 5206 5209 5212
## 4.291702e-10 3.783003e-09 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5214 5215 5216 5217 5219 5221
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5222 5223 5225 5226 5227 5229
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5230 5232 5234 5235 5236 5238
## 2.220446e-16 2.220446e-16 6.320801e-10 2.220446e-16 2.220446e-16 2.220446e-16
## 5239 5240 5242 5243 5244 5246
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5247 5248 5249 5250 5251 5252
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5254 5255 5258 5259 5260 5261
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5262 5263 5264 5265 5266 5267
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5268 5270 5272 5274 5275 5276
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 3.174185e-09
## 5277 5278 5279 5280 5281 5282
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5283 5284 5285 5286 5287 5288
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 1.194555e-09 2.220446e-16
## 5290 5291 5293 5294 5295 5297
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5298 5299 5301 5303 5304 5306
## 2.220446e-16 7.567538e-10 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5308 5309 5310 5311 5312 5313
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5314 5315 5316 5317 5318 5319
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5320 5323 5324 5326 5327 5328
## 1.270846e-09 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5329 5330 5331 5332 5333 5334
## 2.220446e-16 2.220446e-16 2.220446e-16 2.947588e-09 2.220446e-16 1.298169e-09
## 5336 5337 5338 5339 5340 5341
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 8.498931e-11 2.220446e-16
## 5342 5343 5344 5345 5346 5347
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5348 5349 5350 5352 5353 5354
## 2.220446e-16 1.090141e-08 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5355 5357 5358 5361 5363 5365
## 2.220446e-16 8.011545e-09 2.220446e-16 1.684599e-09 2.220446e-16 2.220446e-16
## 5367 5371 5372 5373 5374 5375
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5377 5379 5382 5384 5385 5387
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5389 5390 5392 5393 5394 5395
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5396 5397 5398 5399 5400 5401
## 2.220446e-16 2.220446e-16 8.206323e-10 2.220446e-16 2.220446e-16 2.220446e-16
## 5402 5403 5405 5406 5407 5408
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5409 5410 5411 5413 5414 5415
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5416 5417 5418 5419 5421 5423
## 2.220446e-16 1.858564e-11 2.220446e-16 1.671785e-11 2.220446e-16 2.220446e-16
## 5424 5425 5427 5428 5429 5430
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5431 5434 5435 5436 5439 5440
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5442 5445 5447 5448 5449 5450
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5452 5453 5455 5456 5457 5458
## 2.220446e-16 2.097213e-09 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5459 5460 5462 5464 5466 5467
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5468 5472 5474 5476 5477 5479
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5480 5481 5482 5483 5485 5486
## 2.220446e-16 2.220446e-16 2.220446e-16 1.512090e-09 2.220446e-16 2.220446e-16
## 5488 5489 5490 5491 5493 5494
## 9.609931e-10 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5495 5496 5498 5499 5500 5501
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5502 5503 5504 5506 5508 5509
## 2.220446e-16 2.220446e-16 1.591387e-09 2.220446e-16 2.220446e-16 2.220446e-16
## 5510 5511 5512 5513 5516 5519
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5520 5521 5522 5523 5525 5527
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5528 5529 5531 5532 5533 5537
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5538 5540 5541 5542 5543 5544
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5545 5546 5548 5549 5550 5552
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5554 5556 5557 5559 5560 5561
## 2.220446e-16 9.191672e-10 2.220446e-16 2.220446e-16 6.264894e-11 2.942334e-09
## 5563 5564 5566 5567 5568 5569
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5570 5574 5575 5579 5582 5583
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5585 5586 5587 5588 5589 5591
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5592 5593 5594 5595 5596 5597
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5598 5599 5600 5601 5602 5603
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5604 5605 5606 5609 5610 5611
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 4.438708e-09 2.220446e-16
## 5612 5613 5614 5617 5618 5619
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5621 5622 5623 5624 5627 5628
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5630 5631 5633 5634 5635 5636
## 2.220446e-16 1.050513e-09 5.864350e-12 2.220446e-16 2.220446e-16 2.220446e-16
## 5637 5640 5641 5642 5643 5645
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5646 5647 5648 5650 5653 5655
## 7.494408e-09 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.781030e-09
## 5656 5657 5658 5660 5661 5662
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5663 5664 5665 5666 5667 5668
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5669 5670 5671 5672 5674 5675
## 2.220446e-16 1.542770e-13 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5678 5680 5681 5682 5683 5684
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5685 5686 5687 5688 5689 5692
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5693 5695 5696 5697 5698 5699
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5700 5701 5702 5704 5705 5708
## 2.220446e-16 2.220446e-16 1.547123e-10 2.220446e-16 2.220446e-16 2.220446e-16
## 5710 5712 5713 5716 5717 5718
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5720 5721 5722 5723 5724 5725
## 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16 2.220446e-16
## 5726 5728
## 2.220446e-16 2.220446e-16length(which(predLog<0.00001))## [1] 3046length(which(predLog>0.99999))## [1] 954length(which(predLog>0.00001 & predLog<0.99999))## [1] 10table(train$spam, predLog > 0.5)##
## FALSE TRUE
## 0 3052 0
## 1 4 954(3052+954)/nrow(train)## [1] 0.9990025summary(spamLog)##
## Call:
## glm(formula = spam ~ ., family = binomial, data = train)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.011 0.000 0.000 0.000 1.354
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -3.082e+01 1.055e+04 -0.003 0.998
## busi -4.803e+00 1.000e+04 0.000 1.000
## chang -2.717e+01 2.215e+04 -0.001 0.999
## compani 4.781e+00 9.186e+03 0.001 1.000
## corpor -8.286e-01 2.818e+04 0.000 1.000
## day -6.100e+00 5.866e+03 -0.001 0.999
## done 6.828e+00 1.882e+04 0.000 1.000
## effect 1.948e+01 2.100e+04 0.001 0.999
## effort 1.606e+01 5.670e+04 0.000 1.000
## even -1.654e+01 2.289e+04 -0.001 0.999
## full 2.125e+01 2.190e+04 0.001 0.999
## good 5.399e+00 1.619e+04 0.000 1.000
## inform 2.078e+01 8.549e+03 0.002 0.998
## interest 2.698e+01 1.159e+04 0.002 0.998
## list -8.692e+00 2.149e+03 -0.004 0.997
## look -7.031e+00 1.563e+04 0.000 1.000
## made 2.820e+00 2.743e+04 0.000 1.000
## make 2.901e+01 1.528e+04 0.002 0.998
## manag 6.014e+00 1.445e+04 0.000 1.000
## market 7.895e+00 8.012e+03 0.001 0.999
## much 3.775e-01 1.392e+04 0.000 1.000
## order 6.533e+00 1.242e+04 0.001 1.000
## origin 3.226e+01 3.818e+04 0.001 0.999
## product 1.016e+01 1.345e+04 0.001 0.999
## provid 2.422e-01 1.859e+04 0.000 1.000
## realli -2.667e+01 4.640e+04 -0.001 1.000
## result -5.002e-01 3.140e+04 0.000 1.000
## see -1.120e+01 1.293e+04 -0.001 0.999
## special 1.777e+01 2.755e+04 0.001 0.999
## subject 3.041e+01 1.055e+04 0.003 0.998
## system 3.778e+00 9.149e+03 0.000 1.000
## use -1.385e+01 9.382e+03 -0.001 0.999
## websit -2.563e+01 1.848e+04 -0.001 0.999
## will -1.119e+01 5.980e+03 -0.002 0.999
## within 2.900e+01 2.163e+04 0.001 0.999
## without 1.942e+01 1.763e+04 0.001 0.999
## continu 1.487e+01 1.535e+04 0.001 0.999
## group 5.264e-01 1.037e+04 0.000 1.000
## like 5.649e+00 7.660e+03 0.001 0.999
## trade -1.755e+01 1.483e+04 -0.001 0.999
## tri 9.278e-01 1.282e+04 0.000 1.000
## approv -1.302e+00 1.589e+04 0.000 1.000
## ask -7.746e+00 1.976e+04 0.000 1.000
## complet -1.363e+01 2.024e+04 -0.001 0.999
## credit 2.617e+01 1.314e+04 0.002 0.998
## form 8.483e+00 1.674e+04 0.001 1.000
## hear 2.887e+01 2.281e+04 0.001 0.999
## home 5.973e+00 8.965e+03 0.001 0.999
## new 1.003e+00 1.009e+04 0.000 1.000
## offer 1.174e+01 1.084e+04 0.001 0.999
## opportun -4.131e+00 1.918e+04 0.000 1.000
## rate -3.112e+00 1.319e+04 0.000 1.000
## take 5.731e+00 1.716e+04 0.000 1.000
## time -5.921e+00 8.335e+03 -0.001 0.999
## visit 2.585e+01 1.170e+04 0.002 0.998
## want -2.555e+00 1.106e+04 0.000 1.000
## way 1.339e+01 1.138e+04 0.001 0.999
## addit 1.463e+00 2.703e+04 0.000 1.000
## click 1.376e+01 7.077e+03 0.002 0.998
## com 1.936e+00 4.039e+03 0.000 1.000
## fax 3.537e+00 3.386e+04 0.000 1.000
## mail 7.584e+00 1.021e+04 0.001 0.999
## messag 1.716e+01 2.562e+03 0.007 0.995
## now 3.790e+01 1.219e+04 0.003 0.998
## phone -6.957e+00 1.172e+04 -0.001 1.000
## request -1.232e+01 1.167e+04 -0.001 0.999
## version -3.606e+01 2.939e+04 -0.001 0.999
## best -8.201e+00 1.333e+03 -0.006 0.995
## end -1.311e+01 2.938e+04 0.000 1.000
## get 5.154e+00 9.737e+03 0.001 1.000
## great 1.222e+01 1.090e+04 0.001 0.999
## money 3.264e+01 1.321e+04 0.002 0.998
## softwar 2.575e+01 1.059e+04 0.002 0.998
## custom 1.829e+01 1.008e+04 0.002 0.999
## hello 2.166e+01 1.361e+04 0.002 0.999
## one 1.241e+01 6.652e+03 0.002 0.999
## onlin 3.589e+01 1.665e+04 0.002 0.998
## pleas -7.961e+00 9.484e+03 -0.001 0.999
## access -1.480e+01 1.335e+04 -0.001 0.999
## account 2.488e+01 8.165e+03 0.003 0.998
## allow 1.899e+01 6.436e+03 0.003 0.998
## alreadi -2.407e+01 3.319e+04 -0.001 0.999
## also 2.990e+01 1.378e+04 0.002 0.998
## applic -2.649e+00 1.674e+04 0.000 1.000
## area 2.041e+01 2.266e+04 0.001 0.999
## assist -1.128e+01 2.490e+04 0.000 1.000
## base -1.354e+01 2.122e+04 -0.001 0.999
## believ 3.233e+01 2.136e+04 0.002 0.999
## buy 4.170e+01 3.892e+04 0.001 0.999
## can 3.762e+00 7.674e+03 0.000 1.000
## cost -1.938e+00 1.833e+04 0.000 1.000
## creat 1.338e+01 3.946e+04 0.000 1.000
## current 3.629e+00 1.707e+04 0.000 1.000
## design -7.923e+00 2.939e+04 0.000 1.000
## develop 5.976e+00 9.455e+03 0.001 0.999
## differ -2.293e+00 1.075e+04 0.000 1.000
## director -1.770e+01 1.793e+04 -0.001 0.999
## discuss -1.051e+01 1.915e+04 -0.001 1.000
## due -4.163e+00 3.532e+04 0.000 1.000
## email 3.833e+00 1.186e+04 0.000 1.000
## event 1.694e+01 1.851e+04 0.001 0.999
## expect -1.179e+01 1.914e+04 -0.001 1.000
## file -2.943e+01 2.165e+04 -0.001 0.999
## forward -3.484e+00 1.864e+04 0.000 1.000
## futur 4.146e+01 1.439e+04 0.003 0.998
## gas -3.901e+00 4.160e+03 -0.001 0.999
## give -2.518e+01 2.130e+04 -0.001 0.999
## given -2.186e+01 5.426e+04 0.000 1.000
## high -1.982e+00 2.554e+04 0.000 1.000
## import -1.859e+00 2.236e+04 0.000 1.000
## includ -3.454e+00 1.799e+04 0.000 1.000
## increas 6.476e+00 2.329e+04 0.000 1.000
## industri -3.160e+01 2.373e+04 -0.001 0.999
## invest 3.201e+01 2.393e+04 0.001 0.999
## involv 3.815e+01 3.315e+04 0.001 0.999
## just -1.021e+01 1.114e+04 -0.001 0.999
## know 1.277e+01 1.526e+04 0.001 0.999
## locat 2.073e+01 1.597e+04 0.001 0.999
## mani 1.885e+01 1.442e+04 0.001 0.999
## may -9.434e+00 1.397e+04 -0.001 0.999
## mean 6.078e-01 2.952e+04 0.000 1.000
## mention -2.279e+01 2.714e+04 -0.001 0.999
## might 1.244e+01 1.753e+04 0.001 0.999
## month -3.727e+00 1.112e+04 0.000 1.000
## need 8.437e-01 1.221e+04 0.000 1.000
## note 1.446e+01 2.294e+04 0.001 0.999
## number -9.622e+00 1.591e+04 -0.001 1.000
## offic -1.344e+01 2.311e+04 -0.001 1.000
## oper -1.696e+01 2.757e+04 -0.001 1.000
## person 1.870e+01 9.575e+03 0.002 0.998
## posit -1.543e+01 2.316e+04 -0.001 0.999
## possibl -1.366e+01 2.492e+04 -0.001 1.000
## present -6.163e+00 1.278e+04 0.000 1.000
## price 3.428e+00 7.850e+03 0.000 1.000
## problem 1.262e+01 9.763e+03 0.001 0.999
## process -2.957e-01 1.191e+04 0.000 1.000
## project 2.173e+00 1.497e+04 0.000 1.000
## read -1.527e+01 2.145e+04 -0.001 0.999
## relat -5.114e+01 1.793e+04 -0.003 0.998
## report -1.482e+01 1.477e+04 -0.001 0.999
## requir 5.004e-01 2.937e+04 0.000 1.000
## research -2.826e+01 1.553e+04 -0.002 0.999
## resourc -2.735e+01 3.522e+04 -0.001 0.999
## return 1.745e+01 1.844e+04 0.001 0.999
## review -4.825e+00 1.013e+04 0.000 1.000
## risk -4.001e+00 1.718e+04 0.000 1.000
## secur -1.604e+01 2.201e+03 -0.007 0.994
## servic -7.164e+00 1.235e+04 -0.001 1.000
## set -9.353e+00 2.627e+04 0.000 1.000
## short -8.974e+00 1.721e+04 -0.001 1.000
## specif -2.337e+01 3.083e+04 -0.001 0.999
## state 1.221e+01 1.677e+04 0.001 0.999
## term 2.013e+01 2.303e+04 0.001 0.999
## thing 2.579e+01 1.341e+04 0.002 0.998
## today -1.762e+01 1.965e+04 -0.001 0.999
## two -2.573e+01 1.844e+04 -0.001 0.999
## understand 9.307e+00 2.342e+04 0.000 1.000
## unit -4.020e+00 3.008e+04 0.000 1.000
## well -2.222e+01 9.713e+03 -0.002 0.998
## work -1.099e+01 1.160e+04 -0.001 0.999
## hour 2.478e+00 1.333e+04 0.000 1.000
## lot -1.964e+01 1.321e+04 -0.001 0.999
## real 2.046e+01 2.358e+04 0.001 0.999
## right 2.312e+01 1.590e+04 0.001 0.999
## start 1.437e+01 1.897e+04 0.001 0.999
## X000 1.474e+01 1.058e+04 0.001 0.999
## X2001 -3.215e+01 1.318e+04 -0.002 0.998
## follow 1.766e+01 3.080e+03 0.006 0.995
## name 1.672e+01 1.322e+04 0.001 0.999
## sent -1.488e+01 2.195e+04 -0.001 0.999
## last 1.046e+00 1.372e+04 0.000 1.000
## avail 8.651e+00 1.709e+04 0.001 1.000
## first -4.666e-01 2.043e+04 0.000 1.000
## http 2.528e+01 2.107e+04 0.001 0.999
## join -3.824e+01 2.334e+04 -0.002 0.999
## line 8.743e+00 1.236e+04 0.001 0.999
## next. 1.492e+01 1.724e+04 0.001 0.999
## remov 2.325e+01 2.484e+04 0.001 0.999
## repli 1.538e+01 2.916e+04 0.001 1.000
## wish 1.173e+01 3.175e+04 0.000 1.000
## www -7.867e+00 2.224e+04 0.000 1.000
## year -1.010e+01 1.039e+04 -0.001 0.999
## back -1.323e+01 2.272e+04 -0.001 1.000
## internet 8.749e+00 1.100e+04 0.001 0.999
## member 1.381e+01 2.343e+04 0.001 1.000
## receiv 5.765e-01 1.585e+04 0.000 1.000
## site 8.689e+00 1.496e+04 0.001 1.000
## anoth -8.744e+00 2.032e+04 0.000 1.000
## associ 9.049e+00 1.909e+04 0.000 1.000
## comment -3.251e+00 3.387e+04 0.000 1.000
## corp 1.606e+01 2.708e+04 0.001 1.000
## date -2.786e+00 1.699e+04 0.000 1.000
## find -2.623e+00 9.727e+03 0.000 1.000
## free 6.113e+00 8.121e+03 0.001 0.999
## issu -3.708e+01 3.396e+04 -0.001 0.999
## long -1.489e+01 1.934e+04 -0.001 0.999
## move -3.834e+01 3.011e+04 -0.001 0.999
## particip -1.154e+01 1.738e+04 -0.001 0.999
## recent -2.067e+00 1.780e+04 0.000 1.000
## respons -1.960e+01 3.667e+04 -0.001 1.000
## say 7.366e+00 2.217e+04 0.000 1.000
## week -6.795e+00 1.046e+04 -0.001 0.999
## dear -2.313e+00 2.306e+04 0.000 1.000
## regard -3.668e+00 1.511e+04 0.000 1.000
## thank -3.890e+01 1.059e+04 -0.004 0.997
## address -4.613e+00 1.113e+04 0.000 1.000
## contact 1.530e+00 1.262e+04 0.000 1.000
## engin 2.664e+01 2.394e+04 0.001 0.999
## etc 9.470e-01 1.569e+04 0.000 1.000
## immedi 6.285e+01 3.346e+04 0.002 0.999
## net 1.256e+01 2.197e+04 0.001 1.000
## per 1.367e+01 1.273e+04 0.001 0.999
## place 9.005e+00 3.661e+04 0.000 1.000
## respond 2.974e+01 3.888e+04 0.001 0.999
## sincer -2.073e+01 3.515e+04 -0.001 1.000
## type -1.447e+01 2.755e+04 -0.001 1.000
## come -1.166e+00 1.511e+04 0.000 1.000
## confirm -1.300e+01 1.514e+04 -0.001 0.999
## analysi -2.405e+01 3.860e+04 -0.001 1.000
## bring 1.607e+01 6.767e+04 0.000 1.000
## call -1.145e+00 1.111e+04 0.000 1.000
## data -2.609e+01 2.271e+04 -0.001 0.999
## detail 1.197e+01 2.301e+04 0.001 1.000
## happi 1.939e-02 1.202e+04 0.000 1.000
## idea -1.845e+01 3.892e+04 0.000 1.000
## info -1.255e+00 4.857e+03 0.000 1.000
## send -2.427e+01 1.222e+04 -0.002 0.998
## success 4.344e+00 2.783e+04 0.000 1.000
## sure -5.503e+00 2.078e+04 0.000 1.000
## team 7.940e+00 2.570e+04 0.000 1.000
## web 2.791e+00 1.686e+04 0.000 1.000
## don 2.129e+01 1.456e+04 0.001 0.999
## copi -4.274e+01 3.070e+04 -0.001 0.999
## help 1.731e+01 2.791e+03 0.006 0.995
## part 4.594e+00 3.483e+04 0.000 1.000
## life 5.812e+01 3.864e+04 0.002 0.999
## meet -1.063e+00 1.263e+04 0.000 1.000
## sever 2.041e+01 3.093e+04 0.001 0.999
## question -3.467e+01 1.859e+04 -0.002 0.999
## write 4.406e+01 2.825e+04 0.002 0.999
## think -1.218e+01 2.077e+04 -0.001 1.000
## point 5.498e+00 3.403e+04 0.000 1.000
## let -2.763e+01 1.462e+04 -0.002 0.998
## link -6.929e+00 1.345e+04 -0.001 1.000
## communic 1.580e+01 8.958e+03 0.002 0.999
## contract -1.295e+01 1.498e+04 -0.001 0.999
## either -2.744e+01 4.000e+04 -0.001 0.999
## final 8.075e+00 5.008e+04 0.000 1.000
## howev -3.449e+01 3.562e+04 -0.001 0.999
## peopl -1.864e+01 1.439e+04 -0.001 0.999
## power -5.643e+00 1.173e+04 0.000 1.000
## put -1.052e+01 2.681e+04 0.000 1.000
## run -5.162e+01 4.434e+04 -0.001 0.999
## shall 1.930e+01 3.075e+04 0.001 0.999
## soon 2.350e+01 3.731e+04 0.001 0.999
## support -1.539e+01 1.976e+04 -0.001 0.999
## attach -1.037e+01 1.534e+04 -0.001 0.999
## abl -2.049e+00 2.088e+04 0.000 1.000
## program 1.444e+00 1.183e+04 0.000 1.000
## sorri 6.036e+00 2.299e+04 0.000 1.000
## valu 9.024e-01 1.360e+04 0.000 1.000
## check 1.425e+00 1.963e+04 0.000 1.000
## feel 2.596e+00 2.348e+04 0.000 1.000
## better 4.263e+01 2.360e+04 0.002 0.999
## plan -1.830e+01 6.320e+03 -0.003 0.998
## experi 2.460e+00 2.240e+04 0.000 1.000
## hope -1.435e+01 2.179e+04 -0.001 0.999
## begin 2.228e+01 2.973e+04 0.001 0.999
## X2000 -3.631e+01 1.556e+04 -0.002 0.998
## case -3.372e+01 2.880e+04 -0.001 0.999
## depart -4.068e+01 2.509e+04 -0.002 0.999
## financi -9.747e+00 1.727e+04 -0.001 1.000
## houston -1.855e+01 7.305e+03 -0.003 0.998
## intern -7.991e+00 3.351e+04 0.000 1.000
## john -5.326e-01 2.856e+04 0.000 1.000
## juli -1.358e+01 3.009e+04 0.000 1.000
## mark -3.350e+01 3.208e+04 -0.001 0.999
## open 2.114e+01 2.961e+04 0.001 0.999
## public -5.250e+01 2.341e+04 -0.002 0.998
## sinc -3.438e+00 3.546e+04 0.000 1.000
## still 3.878e+00 2.622e+04 0.000 1.000
## thought 1.243e+01 3.023e+04 0.000 1.000
## univers 1.228e+01 2.197e+04 0.001 1.000
## appreci -2.145e+01 2.762e+04 -0.001 0.999
## keep 1.867e+01 2.782e+04 0.001 0.999
## cours 1.665e+01 1.834e+04 0.001 0.999
## direct -2.051e+01 3.194e+04 -0.001 0.999
## togeth -2.355e+01 1.869e+04 -0.001 0.999
## energi -1.620e+01 1.646e+04 -0.001 0.999
## london 6.745e+00 1.642e+04 0.000 1.000
## updat -1.510e+01 1.448e+04 -0.001 0.999
## suggest -3.842e+01 4.475e+04 -0.001 0.999
## option -1.085e+00 9.325e+03 0.000 1.000
## monday -1.034e+00 3.233e+04 0.000 1.000
## kevin -3.779e+01 4.738e+04 -0.001 0.999
## book 4.301e+00 2.024e+04 0.000 1.000
## deal -1.129e+01 1.448e+04 -0.001 0.999
## invit 4.304e+00 2.215e+04 0.000 1.000
## tuesday -2.808e+01 3.959e+04 -0.001 0.999
## interview -1.640e+01 1.873e+04 -0.001 0.999
## schedul 1.919e+00 3.580e+04 0.000 1.000
## school -3.870e+00 2.882e+04 0.000 1.000
## model -2.292e+01 1.049e+04 -0.002 0.998
## financ -9.122e+00 7.524e+03 -0.001 0.999
## morn -2.645e+01 3.403e+04 -0.001 0.999
## attend -3.451e+01 3.257e+04 -0.001 0.999
## robert -2.096e+01 2.907e+04 -0.001 0.999
## student -1.815e+01 2.186e+04 -0.001 0.999
## april -2.620e+01 2.208e+04 -0.001 0.999
## talk -1.011e+01 2.021e+04 -0.001 1.000
## arrang 1.069e+01 2.135e+04 0.001 1.000
## deriv -4.971e+01 3.587e+04 -0.001 0.999
## thursday -1.491e+01 3.262e+04 0.000 1.000
## resum -9.219e+00 2.100e+04 0.000 1.000
## doc -2.597e+01 2.603e+04 -0.001 0.999
## confer -7.503e-01 8.557e+03 0.000 1.000
## wednesday -1.526e+01 2.642e+04 -0.001 1.000
## edu -2.122e-01 6.917e+02 0.000 1.000
## friday -1.146e+01 1.996e+04 -0.001 1.000
## ect 8.685e-01 5.342e+03 0.000 1.000
## hou 6.852e+00 6.437e+03 0.001 0.999
## vinc -3.735e+01 8.647e+03 -0.004 0.997
## X853 -1.212e+00 5.942e+04 0.000 1.000
## shirley -7.133e+01 6.329e+04 -0.001 0.999
## enron -8.789e+00 5.719e+03 -0.002 0.999
## kaminski -1.812e+01 6.029e+03 -0.003 0.998
## X713 -2.427e+01 2.914e+04 -0.001 0.999
## crenshaw 9.994e+01 6.769e+04 0.001 0.999
## vkamin -6.649e+01 5.703e+04 -0.001 0.999
## gibner 2.901e+01 2.460e+04 0.001 0.999
## stinson -4.345e+01 2.697e+04 -0.002 0.999
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 4409.49 on 4009 degrees of freedom
## Residual deviance: 13.46 on 3679 degrees of freedom
## AIC: 675.46
##
## Number of Fisher Scoring iterations: 25prp(spamCART)
predROCR <- prediction(predLog, train$spam)
perfROCR <- performance(predROCR, "tpr", "fpr")
plot(perfROCR, colorize = TRUE)
performance(predROCR, "auc")@y.values## [[1]]
## [1] 0.9999959as.numeric(performance(predROCR, "auc")@y.values) ## [1] 0.9999959Moving to CART model
What is the training set accuracy of spamCART, using a threshold of 0.5 for predictions? (Remember that if you used the type=“class” argument when making predictions, you automatically used a threshold of 0.5. If you did not add in the type argument to the predict function, the probabilities are in the second column of the predict output.)
predCARTmail <- predict(spamCART, newdata = train, type = "class")
table(train$spam, predCARTmail)## predCARTmail
## 0 1
## 0 2885 167
## 1 64 894(2885+894)/nrow(train)## [1] 0.942394predCARTmail2 <- predict(spamCART, newdata = train)
pred.prob2 <- predCARTmail2[,2]
predCartAUC <- prediction(pred.prob2, train$spam)
as.numeric(performance(predCartAUC, "auc")@y.values)## [1] 0.9696044Random forest models
What is the training set accuracy of spamRF, using a threshold of 0.5 for predictions? (Remember that your answer might not match ours exactly, due to random behavior in the random forest algorithm on different operating systems.)
predRFmail <- predict(spamRF, newdata = train)
table(train$spam, predRFmail)## predRFmail
## 0 1
## 0 3046 6
## 1 0 958(3046+968)/nrow(train)## [1] 1.000998predRFmail.prob <- predict(spamRF, newdata = train, type = "prob")
probRF <- predRFmail.prob[,2]
predRFAUC <- prediction(probRF, train$spam)
as.numeric(performance(predRFAUC, "auc")@y.values)## [1] 0.9999959Evaluating on test set
Obtain predicted probabilities for the testing set for each of the models, again ensuring that probabilities instead of classes are obtained.
What is the testing set accuracy of spamLog, using a threshold of 0.5 for predictions?
predLogTest <- predict(spamLog, newdata = test, type = "response")
table(test$spam, predLogTest>0.5)##
## FALSE TRUE
## 0 1257 51
## 1 34 376(1257+376)/nrow(test)## [1] 0.9505239predROCRlogTest <- prediction(predLogTest, test$spam)
as.numeric(performance(predROCRlogTest, "auc")@y.values) ## [1] 0.9627517# now spamCART TEST
predCARTmailtest <- predict(spamCART, newdata = test, type = "class")
table(test$spam, predCARTmailtest)## predCARTmailtest
## 0 1
## 0 1228 80
## 1 24 386(1228+386)/nrow(test)## [1] 0.9394645predCARTmail2test <- predict(spamCART, newdata = test)
pred.prob2test <- predCARTmail2test[,2]
predCartAUC2test <- prediction(pred.prob2test, test$spam)
as.numeric(performance(predCartAUC2test, "auc")@y.values)## [1] 0.963176# now spam RF TEST
predRFmailtest <- predict(spamRF, newdata = test)
table(test$spam, predRFmailtest)## predRFmailtest
## 0 1
## 0 1291 17
## 1 25 385(1291+385)/nrow(test)## [1] 0.975553predRFmail.probtest <- predict(spamRF, newdata = test, type = "prob")
probRFtest <- predRFmail.probtest[,2]
predRFAUC_test <- prediction(probRFtest, test$spam)
as.numeric(performance(predRFAUC_test, "auc")@y.values)## [1] 0.997768