ML-Titanic
Wei-Ting,Lin (s3698773)
7/23/2018
library(readr)
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(missForest)## Loading required package: randomForest## Warning: package 'randomForest' was built under R version 3.4.4## randomForest 4.6-14## Type rfNews() to see new features/changes/bug fixes.##
## Attaching package: 'randomForest'## The following object is masked from 'package:dplyr':
##
## combine## Loading required package: foreach## Loading required package: itertools## Loading required package: iteratorslibrary(mice)## Loading required package: lattice##
## Attaching package: 'mice'## The following objects are masked from 'package:base':
##
## cbind, rbindlibrary(MASS)## Warning: package 'MASS' was built under R version 3.4.4##
## Attaching package: 'MASS'## The following object is masked from 'package:dplyr':
##
## selectimport data
train <- read_csv("train.csv")## Parsed with column specification:
## cols(
## PassengerId = col_integer(),
## Survived = col_integer(),
## Pclass = col_integer(),
## Name = col_character(),
## Sex = col_character(),
## Age = col_double(),
## SibSp = col_integer(),
## Parch = col_integer(),
## Ticket = col_character(),
## Fare = col_double(),
## Cabin = col_character(),
## Embarked = col_character()
## )test <- read_csv("test.csv")## Parsed with column specification:
## cols(
## PassengerId = col_integer(),
## Pclass = col_integer(),
## Name = col_character(),
## Sex = col_character(),
## Age = col_double(),
## SibSp = col_integer(),
## Parch = col_integer(),
## Ticket = col_character(),
## Fare = col_double(),
## Cabin = col_character(),
## Embarked = col_character()
## )data wrangling
train[c(3,5,12)] <- lapply(train[c(3,5,12)],as.factor)
test[c(2,4,11)] <- lapply(test[c(2,4,11)],as.factor)#missing value
missing_train <- colSums(is.na(train))
missing_train## PassengerId Survived Pclass Name Sex Age
## 0 0 0 0 0 177
## SibSp Parch Ticket Fare Cabin Embarked
## 0 0 0 0 687 2missing_test <- colSums(is.na(test))
missing_test## PassengerId Pclass Name Sex Age SibSp
## 0 0 0 0 86 0
## Parch Ticket Fare Cabin Embarked
## 0 0 1 327 0- check the relationship between missing age value with other variables
# mean age group by sex
train %>% group_by(Sex) %>% summarise( mean_Age = mean(Age, na.rm = T))## # A tibble: 2 x 2
## Sex mean_Age
## <fct> <dbl>
## 1 female 27.9
## 2 male 30.7# avg. for those who has Parent & child
train %>% group_by(SibSp) %>% summarise( mean_Age = mean(Age, na.rm = T))## # A tibble: 7 x 2
## SibSp mean_Age
## <int> <dbl>
## 1 0 31.4
## 2 1 30.1
## 3 2 22.6
## 4 3 13.9
## 5 4 7.06
## 6 5 10.2
## 7 8 NaN- impute missing age, using
micepackage
#overview of the pattern of missing value
md.pattern(train)
## PassengerId Survived Pclass Name Sex SibSp Parch Ticket Fare Embarked
## 183 1 1 1 1 1 1 1 1 1 1
## 529 1 1 1 1 1 1 1 1 1 1
## 19 1 1 1 1 1 1 1 1 1 1
## 158 1 1 1 1 1 1 1 1 1 1
## 2 1 1 1 1 1 1 1 1 1 0
## 0 0 0 0 0 0 0 0 0 2
## Age Cabin
## 183 1 1 0
## 529 1 0 1
## 19 0 1 1
## 158 0 0 2
## 2 1 1 1
## 177 687 866md.pattern(test)
## PassengerId Pclass Name Sex SibSp Parch Ticket Embarked Fare Age Cabin
## 87 1 1 1 1 1 1 1 1 1 1 1
## 244 1 1 1 1 1 1 1 1 1 1 0
## 4 1 1 1 1 1 1 1 1 1 0 1
## 82 1 1 1 1 1 1 1 1 1 0 0
## 1 1 1 1 1 1 1 1 1 0 1 0
## 0 0 0 0 0 0 0 0 1 86 327
##
## 87 0
## 244 1
## 4 1
## 82 2
## 1 2
## 414impute missing values
train.imp <- mice(train,meth='pmm',seed=500)##
## iter imp variable
## 1 1 Age Embarked
## 1 2 Age Embarked
## 1 3 Age Embarked
## 1 4 Age Embarked
## 1 5 Age Embarked
## 2 1 Age Embarked
## 2 2 Age Embarked
## 2 3 Age Embarked
## 2 4 Age Embarked
## 2 5 Age Embarked
## 3 1 Age Embarked
## 3 2 Age Embarked
## 3 3 Age Embarked
## 3 4 Age Embarked
## 3 5 Age Embarked
## 4 1 Age Embarked
## 4 2 Age Embarked
## 4 3 Age Embarked
## 4 4 Age Embarked
## 4 5 Age Embarked
## 5 1 Age Embarked
## 5 2 Age Embarked
## 5 3 Age Embarked
## 5 4 Age Embarked
## 5 5 Age Embarked## Warning: Number of logged events: 3summary(train.imp)## Class: mids
## Number of multiple imputations: 5
## Imputation methods:
## PassengerId Survived Pclass Name Sex Age
## "" "" "" "" "" "pmm"
## SibSp Parch Ticket Fare Cabin Embarked
## "" "" "" "" "" "pmm"
## PredictorMatrix:
## PassengerId Survived Pclass Name Sex Age SibSp Parch Ticket
## PassengerId 0 1 1 0 1 1 1 1 0
## Survived 1 0 1 0 1 1 1 1 0
## Pclass 1 1 0 0 1 1 1 1 0
## Name 1 1 1 0 1 1 1 1 0
## Sex 1 1 1 0 0 1 1 1 0
## Age 1 1 1 0 1 0 1 1 0
## Fare Cabin Embarked
## PassengerId 1 0 1
## Survived 1 0 1
## Pclass 1 0 1
## Name 1 0 1
## Sex 1 0 1
## Age 1 0 1
## Number of logged events: 3
## it im dep meth out
## 1 0 0 constant Name
## 2 0 0 constant Ticket
## 3 0 0 constant Cabintrain.complete <- complete(train.imp)md.pattern(train.complete)
## PassengerId Survived Pclass Name Sex Age SibSp Parch Ticket Fare
## 204 1 1 1 1 1 1 1 1 1 1
## 687 1 1 1 1 1 1 1 1 1 1
## 0 0 0 0 0 0 0 0 0 0
## Embarked Cabin
## 204 1 1 0
## 687 1 0 1
## 0 687 687- impute missing value for train data
test.imp <- mice(test,meth='pmm',seed=500)##
## iter imp variable
## 1 1 Age Fare
## 1 2 Age Fare
## 1 3 Age Fare
## 1 4 Age Fare
## 1 5 Age Fare
## 2 1 Age Fare
## 2 2 Age Fare
## 2 3 Age Fare
## 2 4 Age Fare
## 2 5 Age Fare
## 3 1 Age Fare
## 3 2 Age Fare
## 3 3 Age Fare
## 3 4 Age Fare
## 3 5 Age Fare
## 4 1 Age Fare
## 4 2 Age Fare
## 4 3 Age Fare
## 4 4 Age Fare
## 4 5 Age Fare
## 5 1 Age Fare
## 5 2 Age Fare
## 5 3 Age Fare
## 5 4 Age Fare
## 5 5 Age Fare## Warning: Number of logged events: 3summary(test.imp)## Class: mids
## Number of multiple imputations: 5
## Imputation methods:
## PassengerId Pclass Name Sex Age SibSp
## "" "" "" "" "pmm" ""
## Parch Ticket Fare Cabin Embarked
## "" "" "pmm" "" ""
## PredictorMatrix:
## PassengerId Pclass Name Sex Age SibSp Parch Ticket Fare Cabin
## PassengerId 0 1 0 1 1 1 1 0 1 0
## Pclass 1 0 0 1 1 1 1 0 1 0
## Name 1 1 0 1 1 1 1 0 1 0
## Sex 1 1 0 0 1 1 1 0 1 0
## Age 1 1 0 1 0 1 1 0 1 0
## SibSp 1 1 0 1 1 0 1 0 1 0
## Embarked
## PassengerId 1
## Pclass 1
## Name 1
## Sex 1
## Age 1
## SibSp 1
## Number of logged events: 3
## it im dep meth out
## 1 0 0 constant Name
## 2 0 0 constant Ticket
## 3 0 0 constant Cabintest.complete <- complete(test.imp)md.pattern(test.complete)
## PassengerId Pclass Name Sex Age SibSp Parch Ticket Fare Embarked Cabin
## 91 1 1 1 1 1 1 1 1 1 1 1
## 327 1 1 1 1 1 1 1 1 1 1 0
## 0 0 0 0 0 0 0 0 0 0 327
##
## 91 0
## 327 1
## 327there’s still 687 missing value in Cabin (train), i’ll exclude this attribute for now.
- build 1st Model : logistic regression
logit.model <- glm(Survived ~ Pclass + Sex + Age + SibSp + Parch + Ticket + Fare + Embarked
,maxit = 100, family = binomial , train.complete )## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurredsummary(logit.model)##
## Call:
## glm(formula = Survived ~ Pclass + Sex + Age + SibSp + Parch +
## Ticket + Fare + Embarked, family = binomial, data = train.complete,
## maxit = 100)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -8.49 0.00 0.00 0.00 8.49
##
## Coefficients: (3 not defined because of singularities)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.754e+16 1.305e+10 -1343957 <2e-16 ***
## Pclass2 1.302e+16 1.147e+10 1135432 <2e-16 ***
## Pclass3 1.765e+16 1.191e+10 1481585 <2e-16 ***
## Sexmale -1.752e+15 9.349e+06 -187445946 <2e-16 ***
## Age -3.849e+13 3.803e+05 -101211609 <2e-16 ***
## SibSp -4.732e+14 1.070e+07 -44218855 <2e-16 ***
## Parch -3.623e+14 1.133e+07 -31987995 <2e-16 ***
## Ticket110413 1.946e+15 1.035e+09 1879611 <2e-16 ***
## Ticket110465 3.789e+15 5.206e+09 727789 <2e-16 ***
## Ticket110564 1.802e+16 9.046e+09 1991632 <2e-16 ***
## Ticket110813 6.378e+15 1.701e+09 3750224 <2e-16 ***
## Ticket111240 1.308e+16 7.997e+09 1635336 <2e-16 ***
## Ticket111320 6.810e+15 7.243e+09 940227 <2e-16 ***
## Ticket111361 7.094e+15 4.304e+09 1648308 <2e-16 ***
## Ticket111369 1.294e+16 8.525e+09 1517650 <2e-16 ***
## Ticket111426 1.413e+16 9.046e+09 1562113 <2e-16 ***
## Ticket111427 1.436e+16 9.046e+09 1587343 <2e-16 ***
## Ticket111428 1.417e+16 9.046e+09 1566073 <2e-16 ***
## Ticket112050 2.044e+16 1.305e+10 1566453 <2e-16 ***
## Ticket112052 1.571e+16 1.305e+10 1203695 <2e-16 ***
## Ticket112053 1.057e+16 8.525e+09 1239552 <2e-16 ***
## Ticket112058 2.048e+16 1.305e+10 1569402 <2e-16 ***
## Ticket112059 2.048e+16 1.305e+10 1569402 <2e-16 ***
## Ticket112277 1.323e+16 8.375e+09 1580044 <2e-16 ***
## Ticket112379 6.889e+15 7.077e+09 973493 <2e-16 ***
## Ticket113028 9.432e+15 9.046e+09 1042674 <2e-16 ***
## Ticket113043 1.371e+16 8.751e+09 1566291 <2e-16 ***
## Ticket113050 9.663e+15 9.046e+09 1068200 <2e-16 ***
## Ticket113051 1.364e+16 8.865e+09 1539124 <2e-16 ***
## Ticket113055 1.890e+16 9.046e+09 2089467 <2e-16 ***
## Ticket113056 1.492e+16 9.129e+09 1634052 <2e-16 ***
## Ticket113059 3.970e+15 5.945e+09 667790 <2e-16 ***
## Ticket113501 1.270e+16 8.525e+09 1490254 <2e-16 ***
## Ticket113503 -3.080e+16 1.886e+10 -1632850 <2e-16 ***
## Ticket113505 9.458e+15 4.753e+09 1989859 <2e-16 ***
## Ticket113509 2.458e+15 3.701e+09 664099 <2e-16 ***
## Ticket113510 1.217e+16 7.771e+09 1566312 <2e-16 ***
## Ticket113514 1.482e+16 9.046e+09 1638389 <2e-16 ***
## Ticket113572 2.103e+15 9.848e+08 2135716 <2e-16 ***
## Ticket113760 -6.970e+15 5.055e+09 -1378815 <2e-16 ***
## Ticket113767 3.375e+15 5.508e+09 612707 <2e-16 ***
## Ticket113773 2.626e+15 5.040e+09 521021 <2e-16 ***
## Ticket113776 3.194e+15 3.003e+09 1063468 <2e-16 ***
## Ticket113781 -1.815e+16 9.815e+09 -1848916 <2e-16 ***
## Ticket113783 1.742e+16 9.046e+09 1925511 <2e-16 ***
## Ticket113784 1.197e+16 7.695e+09 1555736 <2e-16 ***
## Ticket113786 1.347e+16 8.450e+09 1593796 <2e-16 ***
## Ticket113787 1.358e+16 8.450e+09 1607458 <2e-16 ***
## Ticket113788 1.132e+16 7.695e+09 1470727 <2e-16 ***
## Ticket113789 7.274e+15 5.206e+09 1397200 <2e-16 ***
## Ticket113792 1.459e+16 9.046e+09 1612866 <2e-16 ***
## Ticket113794 1.374e+16 9.046e+09 1519278 <2e-16 ***
## Ticket113796 1.036e+16 6.654e+09 1556465 <2e-16 ***
## Ticket113798 1.176e+16 8.374e+09 1404066 <2e-16 ***
## Ticket113800 1.474e+16 9.046e+09 1629882 <2e-16 ***
## Ticket113803 6.908e+15 5.040e+09 1370609 <2e-16 ***
## Ticket113804 1.250e+16 8.450e+09 1479944 <2e-16 ***
## Ticket113806 1.118e+16 5.040e+09 2218404 <2e-16 ***
## Ticket113807 1.032e+16 9.046e+09 1140522 <2e-16 ***
## Ticket11668 -3.054e+15 1.586e+09 -1925237 <2e-16 ***
## Ticket11751 1.214e+16 5.122e+09 2369741 <2e-16 ***
## Ticket11752 1.220e+16 9.086e+09 1343098 <2e-16 ***
## Ticket11753 8.149e+15 5.122e+09 1590769 <2e-16 ***
## Ticket11755 1.466e+16 7.077e+09 2070895 <2e-16 ***
## Ticket11765 1.164e+16 4.687e+09 2483238 <2e-16 ***
## Ticket11767 1.125e+15 5.118e+08 2198420 <2e-16 ***
## Ticket11769 1.206e+16 5.285e+09 2282035 <2e-16 ***
## Ticket11771 9.740e+15 8.571e+09 1136427 <2e-16 ***
## Ticket11774 1.736e+16 8.571e+09 2025761 <2e-16 ***
## Ticket11813 6.778e+13 1.543e+09 43911 <2e-16 ***
## Ticket11967 1.911e+15 6.965e+08 2742980 <2e-16 ***
## Ticket12233 4.045e+15 3.889e+08 10399284 <2e-16 ***
## Ticket12460 1.899e+15 1.179e+08 16107934 <2e-16 ***
## Ticket12749 -1.484e+15 1.058e+09 -1403202 <2e-16 ***
## Ticket13049 6.337e+15 6.998e+09 905624 <2e-16 ***
## Ticket13213 1.725e+16 7.696e+09 2241288 <2e-16 ***
## Ticket13214 1.755e+16 8.450e+09 2076992 <2e-16 ***
## Ticket13502 1.627e+15 1.290e+09 1261068 <2e-16 ***
## Ticket13507 6.548e+15 4.617e+09 1418170 <2e-16 ***
## Ticket13509 1.494e+16 9.046e+09 1651151 <2e-16 ***
## Ticket13567 3.020e+15 1.106e+09 2730065 <2e-16 ***
## Ticket13568 1.148e+16 5.583e+09 2056006 <2e-16 ***
## Ticket14311 4.034e+15 1.176e+08 34300751 <2e-16 ***
## Ticket14312 4.073e+15 1.176e+08 34634737 <2e-16 ***
## Ticket14313 3.187e+15 1.184e+08 26915354 <2e-16 ***
## Ticket14973 -4.336e+15 1.227e+08 -35336787 <2e-16 ***
## Ticket1601 -1.012e+16 7.385e+09 -1369627 <2e-16 ***
## Ticket16966 -1.121e+16 7.243e+09 -1547242 <2e-16 ***
## Ticket16988 1.328e+16 8.525e+09 1557963 <2e-16 ***
## Ticket17421 -5.745e+15 3.680e+09 -1561074 <2e-16 ***
## Ticket17453 3.646e+15 4.027e+08 9053934 <2e-16 ***
## Ticket17463 3.804e+15 5.227e+09 727750 <2e-16 ***
## Ticket17464 5.642e+15 5.227e+09 1079469 <2e-16 ***
## Ticket17465 1.722e+16 9.139e+09 1884540 <2e-16 ***
## Ticket17466 1.719e+16 9.139e+09 1880330 <2e-16 ***
## Ticket17474 9.993e+15 4.451e+09 2244971 <2e-16 ***
## Ticket17764 9.419e+15 8.421e+09 1118569 <2e-16 ***
## Ticket19877 1.656e+14 1.156e+09 143231 <2e-16 ***
## Ticket19928 -1.457e+15 5.354e+08 -2720724 <2e-16 ***
## Ticket19943 1.321e+14 5.317e+08 248410 <2e-16 ***
## Ticket19947 1.598e+16 7.695e+09 2075949 <2e-16 ***
## Ticket19950 -4.307e+16 2.663e+10 -1617390 <2e-16 ***
## Ticket19952 1.879e+16 9.046e+09 2076707 <2e-16 ***
## Ticket19972 2.041e+16 1.305e+10 1563505 <2e-16 ***
## Ticket19988 1.786e+16 8.450e+09 2113120 <2e-16 ***
## Ticket19996 1.189e+16 5.206e+09 2284484 <2e-16 ***
## Ticket2003 -6.526e+14 2.341e+09 -278839 <2e-16 ***
## Ticket211536 -7.284e+14 3.890e+08 -1872574 <2e-16 ***
## Ticket21440 1.283e+15 1.217e+08 10544562 <2e-16 ***
## Ticket218629 -8.125e+14 4.625e+08 -1756729 <2e-16 ***
## Ticket219533 5.439e+15 3.013e+08 18048149 <2e-16 ***
## Ticket220367 -7.279e+14 3.890e+08 -1871429 <2e-16 ***
## Ticket220845 -4.678e+15 8.223e+09 -568861 <2e-16 ***
## Ticket2223 -4.804e+13 1.492e+08 -322075 <2e-16 ***
## Ticket223596 7.097e+15 4.625e+08 15343444 <2e-16 ***
## Ticket226593 3.378e+15 3.014e+08 11208494 <2e-16 ***
## Ticket226875 -3.447e+14 2.341e+09 -147285 <2e-16 ***
## Ticket228414 -6.142e+14 2.341e+09 -262395 <2e-16 ***
## Ticket229236 -3.820e+14 3.889e+08 -982119 <2e-16 ***
## Ticket230080 8.798e+14 2.340e+09 375962 <2e-16 ***
## Ticket230136 1.394e+15 4.301e+09 324104 <2e-16 ***
## Ticket230433 1.854e+15 2.340e+09 792223 <2e-16 ***
## Ticket230434 2.061e+15 3.891e+08 5298054 <2e-16 ***
## Ticket231919 4.399e+15 1.888e+09 2329869 <2e-16 ***
## Ticket231945 3.797e+15 1.784e+08 21285050 <2e-16 ***
## Ticket233639 3.621e+15 3.890e+08 9308985 <2e-16 ***
## Ticket233866 3.660e+15 3.890e+08 9408133 <2e-16 ***
## Ticket234360 4.584e+15 3.889e+08 11785540 <2e-16 ***
## Ticket234604 6.719e+15 3.890e+08 17270129 <2e-16 ***
## Ticket234686 3.698e+15 3.890e+08 9507274 <2e-16 ***
## Ticket234818 2.647e+15 3.014e+08 8782775 <2e-16 ***
## Ticket236171 3.429e+15 3.891e+08 8813192 <2e-16 ***
## Ticket236852 2.600e+15 3.890e+08 6683830 <2e-16 ***
## Ticket236853 9.843e+14 2.341e+09 420533 <2e-16 ***
## Ticket237442 4.884e+15 4.624e+08 10562051 <2e-16 ***
## Ticket237565 4.055e+15 6.855e+08 5915040 <2e-16 ***
## Ticket237668 6.565e+15 3.891e+08 16873523 <2e-16 ***
## Ticket237671 2.446e+15 3.890e+08 6287895 <2e-16 ***
## Ticket237736 -6.079e+14 2.955e+09 -205759 <2e-16 ***
## Ticket237789 3.117e+15 2.944e+09 1058867 <2e-16 ***
## Ticket237798 8.856e+15 3.889e+08 22771673 <2e-16 ***
## Ticket239853 4.319e+15 1.586e+09 2723041 <2e-16 ***
## Ticket239854 2.497e+15 1.587e+09 1573507 <2e-16 ***
## Ticket239855 6.539e+15 1.587e+09 4120334 <2e-16 ***
## Ticket239856 7.116e+15 1.587e+09 4483903 <2e-16 ***
## Ticket239865 -3.973e+15 2.340e+09 -1697886 <2e-16 ***
## Ticket240929 2.147e+15 3.381e+08 6350182 <2e-16 ***
## Ticket24160 -2.876e+16 1.884e+10 -1526927 <2e-16 ***
## Ticket243847 5.886e+14 2.491e+09 236299 <2e-16 ***
## Ticket243880 2.292e+15 3.890e+08 5892055 <2e-16 ***
## Ticket244252 -1.220e+15 2.340e+09 -521345 <2e-16 ***
## Ticket244270 3.929e+15 3.890e+08 10102006 <2e-16 ***
## Ticket244278 4.234e+15 9.494e+07 44596669 <2e-16 ***
## Ticket244310 4.353e+15 3.889e+08 11191665 <2e-16 ***
## Ticket244358 5.881e+14 2.341e+09 251246 <2e-16 ***
## Ticket244361 3.698e+15 3.890e+08 9507274 <2e-16 ***
## Ticket244367 2.621e+14 2.340e+09 111983 <2e-16 ***
## Ticket244373 8.048e+15 3.890e+08 20687304 <2e-16 ***
## Ticket248698 8.548e+15 3.889e+08 21978593 <2e-16 ***
## Ticket248706 2.365e+15 8.352e+08 2831692 <2e-16 ***
## Ticket248723 4.237e+15 3.889e+08 10894589 <2e-16 ***
## Ticket248727 -2.119e+15 3.396e+09 -624017 <2e-16 ***
## Ticket248731 4.615e+15 4.624e+08 9979725 <2e-16 ***
## Ticket248733 1.907e+15 3.891e+08 4902007 <2e-16 ***
## Ticket248738 3.660e+15 2.793e+09 1310587 <2e-16 ***
## Ticket248740 -6.899e+14 3.890e+08 -1773652 <2e-16 ***
## Ticket248747 1.907e+15 3.891e+08 4902007 <2e-16 ***
## Ticket250643 4.660e+15 3.889e+08 11983408 <2e-16 ***
## Ticket250644 3.043e+15 1.361e+09 2236870 <2e-16 ***
## Ticket250646 3.891e+15 3.890e+08 10002899 <2e-16 ***
## Ticket250647 2.139e+15 3.860e+08 5542057 <2e-16 ***
## Ticket250648 6.642e+15 3.891e+08 17071854 <2e-16 ***
## Ticket250649 4.999e+15 6.097e+08 8198527 <2e-16 ***
## Ticket250651 -3.673e+14 2.341e+09 -156931 <2e-16 ***
## Ticket250652 2.401e+15 3.899e+08 6157914 <2e-16 ***
## Ticket250653 3.891e+15 3.890e+08 10002899 <2e-16 ***
## Ticket250655 -2.112e+14 2.340e+09 -90240 <2e-16 ***
## Ticket2620 5.222e+15 1.248e+08 41847803 <2e-16 ***
## Ticket2623 1.412e+15 1.242e+08 11363416 <2e-16 ***
## Ticket2624 -3.669e+15 1.247e+08 -29431104 <2e-16 ***
## Ticket2625 -6.619e+13 1.875e+08 -353038 <2e-16 ***
## Ticket2626 3.469e+15 1.240e+08 27975460 <2e-16 ***
## Ticket2627 -6.762e+15 1.048e+09 -6452823 <2e-16 ***
## Ticket2628 1.623e+15 1.241e+08 13077952 <2e-16 ***
## Ticket2629 6.406e+14 1.246e+08 5139662 <2e-16 ***
## Ticket2631 9.882e+14 1.245e+08 7935819 <2e-16 ***
## Ticket26360 1.502e+15 2.340e+09 641724 <2e-16 ***
## Ticket2641 1.449e+15 1.240e+08 11690256 <2e-16 ***
## Ticket2647 1.065e+15 1.245e+08 8558492 <2e-16 ***
## Ticket2648 1.429e+15 5.457e+08 2618953 <2e-16 ***
## Ticket2649 4.009e+15 1.238e+08 32378659 <2e-16 ***
## Ticket2650 2.498e+15 1.167e+09 2139732 <2e-16 ***
## Ticket2651 1.237e+15 5.671e+08 2180608 <2e-16 ***
## Ticket2653 2.596e+15 1.241e+09 2091554 <2e-16 ***
## Ticket2659 -1.495e+15 1.047e+09 -1427674 <2e-16 ***
## Ticket2661 3.437e+15 1.167e+09 2946501 <2e-16 ***
## Ticket2662 -2.648e+15 2.135e+09 -1240155 <2e-16 ***
## Ticket2663 5.144e+15 1.246e+08 41275622 <2e-16 ***
## Ticket2664 1.219e+15 1.243e+08 9804713 <2e-16 ***
## Ticket2665 -4.575e+15 1.047e+09 -4369014 <2e-16 ***
## Ticket2666 1.220e+15 1.770e+09 689170 <2e-16 ***
## Ticket2667 -1.303e+15 1.246e+08 -10461919 <2e-16 ***
## Ticket2668 -2.058e+15 2.237e+09 -920058 <2e-16 ***
## Ticket2669 7.178e+14 1.245e+08 5763071 <2e-16 ***
## Ticket26707 1.716e+15 2.340e+09 733014 <2e-16 ***
## Ticket2671 9.487e+14 1.243e+08 7631495 <2e-16 ***
## Ticket2672 -3.669e+15 1.247e+08 -29431103 <2e-16 ***
## Ticket2674 -3.554e+15 1.246e+08 -28530185 <2e-16 ***
## Ticket2677 5.298e+15 1.245e+08 42568386 <2e-16 ***
## Ticket2678 -6.839e+15 1.166e+09 -5863727 <2e-16 ***
## Ticket2680 -4.264e+14 1.048e+09 -406734 <2e-16 ***
## Ticket2683 -3.111e+15 2.030e+08 -15325030 <2e-16 ***
## Ticket2685 -3.478e+15 1.242e+08 -27991272 <2e-16 ***
## Ticket2686 -3.555e+15 1.243e+08 -28595179 <2e-16 ***
## Ticket2687 3.123e+15 1.244e+08 25100686 <2e-16 ***
## Ticket2689 -3.104e+15 1.049e+09 -2958400 <2e-16 ***
## Ticket2690 1.361e+15 1.267e+08 10737931 <2e-16 ***
## Ticket2691 -4.330e+15 1.047e+09 -4134965 <2e-16 ***
## Ticket2693 7.755e+14 1.245e+08 6229720 <2e-16 ***
## Ticket2694 1.027e+15 1.245e+08 8247112 <2e-16 ***
## Ticket2695 1.284e+15 1.268e+08 10121865 <2e-16 ***
## Ticket2697 9.680e+14 1.243e+08 7787299 <2e-16 ***
## Ticket2699 -2.251e+15 1.699e+09 -1324678 <2e-16 ***
## Ticket2700 -3.055e+15 1.240e+08 -24641454 <2e-16 ***
## Ticket27042 1.467e+16 8.525e+09 1720451 <2e-16 ***
## Ticket27267 6.738e+15 3.890e+08 17319689 <2e-16 ***
## Ticket27849 2.369e+15 3.890e+08 6090028 <2e-16 ***
## Ticket28134 4.385e+15 1.786e+08 24549677 <2e-16 ***
## Ticket28206 4.696e+15 9.493e+07 49471007 <2e-16 ***
## Ticket28213 4.237e+15 3.889e+08 10894589 <2e-16 ***
## Ticket28220 2.851e+15 3.321e+09 858417 <2e-16 ***
## Ticket28228 3.891e+15 3.890e+08 10002899 <2e-16 ***
## Ticket28403 -7.785e+14 2.340e+09 -332681 <2e-16 ***
## Ticket28424 3.467e+15 3.890e+08 8912358 <2e-16 ***
## Ticket28425 3.621e+15 3.890e+08 9308986 <2e-16 ***
## Ticket28551 6.873e+15 3.890e+08 17666506 <2e-16 ***
## Ticket28664 2.557e+15 1.587e+09 1610846 <2e-16 ***
## Ticket28665 4.080e+15 9.500e+07 42950264 <2e-16 ***
## Ticket29011 4.569e+15 5.365e+08 8517264 <2e-16 ***
## Ticket2908 4.631e+15 2.340e+09 1978931 <2e-16 ***
## Ticket29103 4.025e+15 1.889e+09 2131058 <2e-16 ***
## Ticket29104 5.298e+15 1.810e+08 29268861 <2e-16 ***
## Ticket29105 2.171e+15 1.889e+09 1149131 <2e-16 ***
## Ticket29106 6.838e+15 1.248e+09 5479800 <2e-16 ***
## Ticket29108 3.797e+15 1.784e+08 21285050 <2e-16 ***
## Ticket2926 -6.142e+14 2.341e+09 -262395 <2e-16 ***
## Ticket29750 -1.755e+15 4.301e+09 -407948 <2e-16 ***
## Ticket29751 3.621e+15 3.890e+08 9308986 <2e-16 ***
## Ticket3101264 1.010e+15 1.856e+08 5441914 <2e-16 ***
## Ticket3101265 -1.600e+15 9.657e+07 -16566829 <2e-16 ***
## Ticket3101267 8.675e+14 1.862e+08 4658183 <2e-16 ***
## Ticket3101276 -2.782e+15 1.132e+08 -24565223 <2e-16 ***
## Ticket3101277 -3.128e+15 1.136e+08 -27542555 <2e-16 ***
## Ticket3101278 -1.271e+15 1.255e+09 -1012203 <2e-16 ***
## Ticket3101281 5.374e+15 1.282e+08 41931791 <2e-16 ***
## Ticket3101295 -1.053e+16 4.850e+09 -2171281 <2e-16 ***
## Ticket3101296 8.522e+14 1.113e+08 7655704 <2e-16 ***
## Ticket3101298 1.472e+15 7.220e+08 2038883 <2e-16 ***
## Ticket31027 2.077e+15 1.586e+09 1308916 <2e-16 ***
## Ticket31028 4.350e+15 9.492e+07 45825005 <2e-16 ***
## Ticket312991 4.007e+15 1.038e+08 38587738 <2e-16 ***
## Ticket312992 -4.307e+15 1.025e+08 -42011822 <2e-16 ***
## Ticket312993 -3.807e+15 1.019e+08 -37375872 <2e-16 ***
## Ticket31418 7.027e+15 3.890e+08 18062635 <2e-16 ***
## Ticket315037 4.212e+14 1.935e+08 2176216 <2e-16 ***
## Ticket315082 4.795e+14 1.081e+08 4437151 <2e-16 ***
## Ticket315084 -5.931e+15 1.933e+08 -30679061 <2e-16 ***
## Ticket315086 -1.754e+14 1.941e+08 -903830 <2e-16 ***
## Ticket315088 -3.717e+15 1.933e+08 -19226233 <2e-16 ***
## Ticket315089 -3.871e+15 1.934e+08 -20013496 <2e-16 ***
## Ticket315090 -4.679e+15 1.941e+08 -24110587 <2e-16 ***
## Ticket315093 -4.679e+15 1.941e+08 -24110587 <2e-16 ***
## Ticket315094 -5.993e+13 1.939e+08 -308999 <2e-16 ***
## Ticket315096 -1.812e+15 1.936e+08 -9359534 <2e-16 ***
## Ticket315097 -2.144e+13 1.939e+08 -110566 <2e-16 ***
## Ticket315098 2.095e+14 1.937e+08 1081524 <2e-16 ***
## Ticket315151 1.117e+15 1.948e+08 5736502 <2e-16 ***
## Ticket315153 -4.760e+14 2.187e+09 -217688 <2e-16 ***
## Ticket323592 5.943e+14 1.063e+08 5591701 <2e-16 ***
## Ticket323951 -4.452e+15 1.229e+08 -36230628 <2e-16 ***
## Ticket324669 1.672e+14 1.227e+08 1362612 <2e-16 ***
## Ticket330877 -3.527e+15 1.786e+08 -19752624 <2e-16 ***
## Ticket330909 -1.133e+15 1.149e+08 -9858028 <2e-16 ***
## Ticket330919 3.726e+15 1.214e+08 30680315 <2e-16 ***
## Ticket330923 3.003e+15 1.356e+08 22141857 <2e-16 ***
## Ticket330931 3.791e+15 1.242e+08 30518101 <2e-16 ***
## Ticket330932 3.602e+15 1.195e+08 30132517 <2e-16 ***
## Ticket330935 -9.879e+14 1.445e+08 -6837058 <2e-16 ***
## Ticket330958 3.194e+15 1.248e+08 25592135 <2e-16 ***
## Ticket330959 4.002e+15 1.241e+08 32260062 <2e-16 ***
## Ticket330979 -4.164e+15 1.227e+08 -33928619 <2e-16 ***
## Ticket330980 -1.348e+15 1.249e+08 -10796004 <2e-16 ***
## Ticket334912 -3.409e+15 1.177e+08 -28971165 <2e-16 ***
## Ticket335097 9.365e+14 1.184e+08 7907737 <2e-16 ***
## Ticket335677 -1.124e+15 1.182e+08 -9509116 <2e-16 ***
## Ticket33638 -2.470e+14 7.050e+08 -350392 <2e-16 ***
## Ticket336439 2.245e+15 1.179e+08 19048530 <2e-16 ***
## Ticket3411 -3.688e+15 2.095e+08 -17599735 <2e-16 ***
## Ticket341826 3.212e+14 1.225e+08 2621422 <2e-16 ***
## Ticket34218 2.636e+15 9.536e+07 27639214 <2e-16 ***
## Ticket342826 -4.240e+15 1.226e+08 -34587900 <2e-16 ***
## Ticket343095 -5.935e+15 1.221e+08 -48625085 <2e-16 ***
## Ticket343120 -1.526e+15 9.727e+07 -15684059 <2e-16 ***
## Ticket343275 -4.259e+15 1.226e+08 -34737963 <2e-16 ***
## Ticket343276 -4.067e+15 1.224e+08 -33231072 <2e-16 ***
## Ticket345364 2.113e+15 2.198e+08 9612484 <2e-16 ***
## Ticket345572 1.638e+15 1.489e+09 1099897 <2e-16 ***
## Ticket345763 -3.205e+15 1.580e+09 -2028740 <2e-16 ***
## Ticket345764 -6.898e+15 1.579e+09 -4367648 <2e-16 ***
## Ticket345765 -3.607e+15 2.388e+08 -15103836 <2e-16 ***
## Ticket345767 -6.571e+13 2.394e+08 -274495 <2e-16 ***
## Ticket345769 -4.769e+15 3.100e+08 -15385814 <2e-16 ***
## Ticket345770 4.253e+13 3.098e+08 137286 <2e-16 ***
## Ticket345773 -8.525e+15 2.506e+09 -3401544 <2e-16 ***
## Ticket345774 4.623e+15 3.097e+08 14927077 <2e-16 ***
## Ticket345777 -3.999e+15 3.095e+08 -12919657 <2e-16 ***
## Ticket345778 -4.923e+15 3.101e+08 -15876833 <2e-16 ***
## Ticket345779 4.585e+15 3.097e+08 14801955 <2e-16 ***
## Ticket345780 2.351e+14 3.097e+08 759226 <2e-16 ***
## Ticket345781 -1.113e+14 3.099e+08 -359263 <2e-16 ***
## Ticket345783 -4.461e+15 3.098e+08 -14401191 <2e-16 ***
## Ticket3460 1.155e+15 1.229e+08 9396775 <2e-16 ***
## Ticket347054 -6.332e+15 4.480e+08 -14131478 <2e-16 ***
## Ticket347060 2.236e+15 1.013e+08 22075502 <2e-16 ***
## Ticket347061 1.316e+15 1.290e+08 10200342 <2e-16 ***
## Ticket347062 -3.846e+15 1.019e+08 -37737751 <2e-16 ***
## Ticket347063 5.809e+14 1.020e+08 5695529 <2e-16 ***
## Ticket347064 -3.147e+15 1.001e+08 -31422847 <2e-16 ***
## Ticket347067 -4.000e+15 1.021e+08 -39176851 <2e-16 ***
## Ticket347068 3.886e+14 1.022e+08 3800404 <2e-16 ***
## Ticket347069 1.192e+14 1.027e+08 1160834 <2e-16 ***
## Ticket347071 -1.402e+15 1.017e+08 -13783209 <2e-16 ***
## Ticket347073 -5.130e+15 9.978e+07 -51412913 <2e-16 ***
## Ticket347074 -4.500e+15 1.028e+08 -43752298 <2e-16 ***
## Ticket347076 8.233e+14 1.027e+08 8014058 <2e-16 ***
## Ticket347077 -3.088e+15 3.598e+09 -858142 <2e-16 ***
## Ticket347078 8.680e+13 1.015e+08 855008 <2e-16 ***
## Ticket347080 -3.336e+15 1.037e+09 -3215696 <2e-16 ***
## Ticket347081 -1.512e+15 1.007e+08 -15011421 <2e-16 ***
## Ticket347082 -7.715e+15 3.581e+09 -2154222 <2e-16 ***
## Ticket347083 5.327e+15 1.027e+08 51850917 <2e-16 ***
## Ticket347085 2.986e+15 1.019e+08 29300528 <2e-16 ***
## Ticket347087 -6.175e+15 1.021e+08 -60460861 <2e-16 ***
## Ticket347088 -5.898e+15 3.072e+09 -1919895 <2e-16 ***
## Ticket347089 5.127e+15 1.295e+08 39595651 <2e-16 ***
## Ticket3474 -4.143e+15 1.091e+08 -37971914 <2e-16 ***
## Ticket347464 4.462e+14 1.067e+08 4180200 <2e-16 ***
## Ticket347466 -4.366e+15 1.072e+08 -40734988 <2e-16 ***
## Ticket347468 2.537e+14 1.070e+08 2371215 <2e-16 ***
## Ticket347470 -1.383e+15 1.063e+08 -13012464 <2e-16 ***
## Ticket347742 1.608e+15 5.474e+08 2937156 <2e-16 ***
## Ticket347743 -2.976e+15 1.212e+08 -24547330 <2e-16 ***
## Ticket348121 1.035e+15 9.688e+07 10684145 <2e-16 ***
## Ticket348123 3.807e+14 9.763e+07 3899837 <2e-16 ***
## Ticket348124 1.498e+14 9.799e+07 1528761 <2e-16 ***
## Ticket349201 1.052e+15 1.090e+08 9651183 <2e-16 ***
## Ticket349203 3.205e+14 1.097e+08 2920433 <2e-16 ***
## Ticket349204 -4.260e+15 1.098e+08 -38781855 <2e-16 ***
## Ticket349205 8.955e+13 1.101e+08 813500 <2e-16 ***
## Ticket349206 2.050e+14 1.099e+08 1865334 <2e-16 ***
## Ticket349207 -4.068e+15 1.096e+08 -37116758 <2e-16 ***
## Ticket349208 5.129e+14 1.095e+08 4683871 <2e-16 ***
## Ticket349209 -4.124e+15 9.680e+07 -42596732 <2e-16 ***
## Ticket349210 8.419e+14 9.623e+07 8749712 <2e-16 ***
## Ticket349212 -4.414e+15 1.101e+08 -40099544 <2e-16 ***
## Ticket349213 -3.449e+15 1.257e+08 -27428181 <2e-16 ***
## Ticket349214 5.106e+13 1.101e+08 463579 <2e-16 ***
## Ticket349215 -4.414e+15 1.101e+08 -40099547 <2e-16 ***
## Ticket349216 4.360e+14 1.096e+08 3978111 <2e-16 ***
## Ticket349217 -4.183e+15 1.097e+08 -38118213 <2e-16 ***
## Ticket349218 1.437e+15 1.088e+08 13208238 <2e-16 ***
## Ticket349219 -4.106e+15 1.096e+08 -37451593 <2e-16 ***
## Ticket349221 -4.453e+15 1.101e+08 -40426925 <2e-16 ***
## Ticket349222 9.363e+14 1.091e+08 8584687 <2e-16 ***
## Ticket349223 5.514e+14 1.094e+08 5038204 <2e-16 ***
## Ticket349224 3.590e+14 1.097e+08 3272713 <2e-16 ***
## Ticket349225 -4.529e+15 1.103e+08 -41077598 <2e-16 ***
## Ticket349227 -4.530e+15 1.103e+08 -41079193 <2e-16 ***
## Ticket349228 -4.682e+14 4.074e+08 -1149375 <2e-16 ***
## Ticket349231 8.954e+13 1.101e+08 813450 <2e-16 ***
## Ticket349233 -4.222e+15 1.098e+08 -38450163 <2e-16 ***
## Ticket349234 -3.221e+15 1.088e+08 -29592054 <2e-16 ***
## Ticket349236 -6.208e+15 2.185e+08 -28408503 <2e-16 ***
## Ticket349237 -7.149e+15 1.549e+09 -4615097 <2e-16 ***
## Ticket349239 7.898e+14 2.033e+08 3885295 <2e-16 ***
## Ticket349240 8.238e+14 1.260e+08 6540504 <2e-16 ***
## Ticket349241 9.777e+14 1.258e+08 7771769 <2e-16 ***
## Ticket349242 -3.914e+15 1.094e+08 -35772065 <2e-16 ***
## Ticket349243 4.360e+14 1.096e+08 3978128 <2e-16 ***
## Ticket349244 3.110e+15 1.960e+08 15862617 <2e-16 ***
## Ticket349245 -5.821e+15 1.091e+08 -53361735 <2e-16 ***
## Ticket349246 -3.991e+15 1.095e+08 -36446297 <2e-16 ***
## Ticket349247 7.439e+14 1.092e+08 6809364 <2e-16 ***
## Ticket349248 -4.145e+15 1.097e+08 -37785303 <2e-16 ***
## Ticket349249 -3.683e+15 1.092e+08 -33733878 <2e-16 ***
## Ticket349251 -3.606e+15 1.091e+08 -33049345 <2e-16 ***
## Ticket349252 2.050e+14 1.099e+08 1865450 <2e-16 ***
## Ticket349253 3.619e+14 1.265e+08 2861040 <2e-16 ***
## Ticket349254 1.016e+15 1.258e+08 8079868 <2e-16 ***
## Ticket349256 1.621e+15 8.931e+08 1815479 <2e-16 ***
## Ticket349257 -3.875e+15 1.094e+08 -35434037 <2e-16 ***
## Ticket349909 -6.462e+15 2.043e+09 -3163095 <2e-16 ***
## Ticket349910 -6.594e+14 1.211e+09 -544530 <2e-16 ***
## Ticket349912 -4.423e+15 1.027e+08 -43059274 <2e-16 ***
## Ticket350025 8.424e+14 1.073e+08 7854361 <2e-16 ***
## Ticket350026 3.597e+14 9.945e+08 361691 <2e-16 ***
## Ticket350029 1.767e+14 1.071e+08 1649969 <2e-16 ***
## Ticket350034 4.695e+15 1.036e+08 45307036 <2e-16 ***
## Ticket350035 3.065e+14 1.034e+08 2963089 <2e-16 ***
## Ticket350036 -4.428e+15 1.038e+08 -42657223 <2e-16 ***
## Ticket350042 -4.043e+15 1.032e+08 -39165667 <2e-16 ***
## Ticket350043 4.220e+14 1.033e+08 4085749 <2e-16 ***
## Ticket350046 -1.179e+15 1.071e+08 -11010076 <2e-16 ***
## Ticket350047 1.216e+15 1.060e+08 11469940 <2e-16 ***
## Ticket350048 6.921e+14 1.226e+08 5644465 <2e-16 ***
## Ticket350050 1.382e+14 1.072e+08 1289672 <2e-16 ***
## Ticket350052 2.295e+14 1.036e+08 2216467 <2e-16 ***
## Ticket350060 2.970e+14 9.669e+07 3071369 <2e-16 ***
## Ticket350404 -3.607e+15 1.096e+08 -32909538 <2e-16 ***
## Ticket350406 -1.845e+15 1.070e+08 -17246772 <2e-16 ***
## Ticket350407 -1.191e+15 1.061e+08 -11226117 <2e-16 ***
## Ticket350417 5.104e+15 1.065e+08 47902122 <2e-16 ***
## Ticket35273 -6.152e+15 4.041e+09 -1522442 <2e-16 ***
## Ticket35281 -4.511e+14 1.391e+09 -324190 <2e-16 ***
## Ticket35851 3.115e+15 1.179e+08 26416665 <2e-16 ***
## Ticket35852 -8.888e+14 1.173e+08 -7575917 <2e-16 ***
## Ticket358585 -5.360e+15 1.052e+09 -5094305 <2e-16 ***
## Ticket36209 4.808e+14 1.181e+08 4072300 <2e-16 ***
## Ticket362316 1.441e+15 1.056e+08 13642240 <2e-16 ***
## Ticket363291 -2.587e+15 1.960e+09 -1320125 <2e-16 ***
## Ticket363294 -3.875e+15 1.222e+08 -31710905 <2e-16 ***
## Ticket363592 -3.490e+15 1.219e+08 -28634740 <2e-16 ***
## Ticket364498 -1.068e+15 1.053e+09 -1013760 <2e-16 ***
## Ticket364499 4.944e+14 1.223e+08 4041690 <2e-16 ***
## Ticket364500 1.787e+15 1.056e+08 16933776 <2e-16 ***
## Ticket364506 6.291e+14 1.222e+08 5148850 <2e-16 ***
## Ticket364511 -3.490e+15 1.219e+08 -28634740 <2e-16 ***
## Ticket364512 -3.836e+15 1.221e+08 -31405365 <2e-16 ***
## Ticket364516 -5.915e+14 7.480e+08 -790690 <2e-16 ***
## Ticket364846 -5.704e+15 1.183e+08 -48230019 <2e-16 ***
## Ticket364848 -1.298e+14 1.205e+08 -1076764 <2e-16 ***
## Ticket364849 -3.064e+15 1.204e+09 -2543804 <2e-16 ***
## Ticket364850 -8.352e+14 1.179e+08 -7084316 <2e-16 ***
## Ticket364851 7.826e+14 1.186e+08 6598875 <2e-16 ***
## Ticket365222 7.198e+14 1.665e+08 4322079 <2e-16 ***
## Ticket365226 -5.575e+15 1.662e+08 -33550385 <2e-16 ***
## Ticket36568 -7.711e+14 1.205e+09 -639851 <2e-16 ***
## Ticket367226 9.212e+14 2.371e+09 388460 <2e-16 ***
## Ticket367228 5.825e+15 1.181e+08 49315330 <2e-16 ***
## Ticket367229 -4.210e+15 1.203e+08 -34983581 <2e-16 ***
## Ticket367230 2.203e+15 1.204e+09 1829603 <2e-16 ***
## Ticket367231 3.110e+15 1.185e+08 26242538 <2e-16 ***
## Ticket367232 1.302e+15 1.181e+08 11023164 <2e-16 ***
## Ticket367655 -3.716e+15 1.178e+08 -31538050 <2e-16 ***
## Ticket368323 8.247e+14 1.461e+08 5646223 <2e-16 ***
## Ticket36864 -3.796e+15 1.184e+08 -32071270 <2e-16 ***
## Ticket36865 5.932e+14 1.183e+08 5012144 <2e-16 ***
## Ticket36866 3.845e+15 1.173e+08 32784944 <2e-16 ***
## Ticket368703 -3.681e+15 1.185e+08 -31047872 <2e-16 ***
## Ticket36928 -1.648e+16 1.182e+10 -1393975 <2e-16 ***
## Ticket36947 5.369e+15 1.246e+09 4310179 <2e-16 ***
## Ticket36963 1.337e+16 8.175e+09 1635111 <2e-16 ***
## Ticket36967 1.241e+16 7.919e+09 1567407 <2e-16 ***
## Ticket36973 -3.853e+14 4.608e+08 -836236 <2e-16 ***
## Ticket370129 -4.874e+15 1.913e+09 -2548146 <2e-16 ***
## Ticket370365 -1.443e+15 1.204e+09 -1198707 <2e-16 ***
## Ticket370369 2.457e+15 1.179e+08 20837193 <2e-16 ***
## Ticket370370 3.341e+15 1.182e+08 28261045 <2e-16 ***
## Ticket370371 -4.903e+14 1.205e+09 -406835 <2e-16 ***
## Ticket370372 1.360e+15 1.181e+08 11515525 <2e-16 ***
## Ticket370373 3.342e+15 1.182e+08 28262948 <2e-16 ***
## Ticket370375 -8.544e+14 1.179e+08 -7246480 <2e-16 ***
## Ticket370376 9.750e+14 1.184e+08 8235295 <2e-16 ***
## Ticket370377 -2.528e+15 1.179e+08 -21446652 <2e-16 ***
## Ticket371060 1.706e+15 1.179e+08 14469189 <2e-16 ***
## Ticket371110 -4.277e+15 2.507e+09 -1706129 <2e-16 ***
## Ticket371362 -5.973e+14 1.294e+09 -461659 <2e-16 ***
## Ticket372622 1.090e+15 1.183e+08 9218616 <2e-16 ***
## Ticket373450 -3.836e+15 1.221e+08 -31404222 <2e-16 ***
## Ticket374746 -4.452e+15 1.229e+08 -36229365 <2e-16 ***
## Ticket374887 4.788e+14 1.064e+08 4499342 <2e-16 ***
## Ticket374910 1.707e+15 1.216e+08 14036893 <2e-16 ***
## Ticket376564 -2.383e+15 1.293e+09 -1842597 <2e-16 ***
## Ticket376566 -5.760e+15 1.294e+09 -4451534 <2e-16 ***
## Ticket382649 -4.665e+15 1.175e+08 -39716587 <2e-16 ***
## Ticket382651 8.595e+14 1.185e+08 7253017 <2e-16 ***
## Ticket382652 -4.120e+15 3.257e+09 -1264777 <2e-16 ***
## Ticket383121 -3.913e+15 1.188e+08 -32937839 <2e-16 ***
## Ticket384461 -4.106e+15 1.191e+08 -34483415 <2e-16 ***
## Ticket386525 1.110e+15 1.294e+09 857892 <2e-16 ***
## Ticket392091 -1.696e+15 2.888e+08 -5871611 <2e-16 ***
## Ticket392092 -3.644e+15 1.220e+08 -29870578 <2e-16 ***
## Ticket392096 2.860e+15 7.483e+08 3822550 <2e-16 ***
## Ticket394140 -3.194e+15 1.547e+08 -20649515 <2e-16 ***
## Ticket4133 -8.815e+15 2.705e+09 -3258582 <2e-16 ***
## Ticket4134 4.120e+15 3.217e+08 12804820 <2e-16 ***
## Ticket4135 -5.888e+15 3.220e+08 -18287703 <2e-16 ***
## Ticket4136 -6.128e+15 3.568e+08 -17173395 <2e-16 ***
## Ticket4137 -6.089e+15 3.568e+08 -17066539 <2e-16 ***
## Ticket4138 2.325e+15 3.592e+08 6473875 <2e-16 ***
## Ticket4579 -3.291e+15 1.612e+08 -20416122 <2e-16 ***
## Ticket54636 -6.204e+15 1.293e+09 -4798311 <2e-16 ***
## Ticket5727 1.448e+16 9.191e+09 1575377 <2e-16 ***
## Ticket65303 -6.361e+15 1.876e+09 -3390754 <2e-16 ***
## Ticket65304 -2.204e+15 1.876e+09 -1174819 <2e-16 ***
## Ticket65306 5.310e+15 1.281e+08 41461902 <2e-16 ***
## Ticket6563 -4.701e+15 2.708e+08 -17358652 <2e-16 ***
## Ticket693 1.503e+16 9.129e+09 1646698 <2e-16 ***
## Ticket695 1.899e+16 1.230e+10 1544090 <2e-16 ***
## Ticket7267 -4.586e+15 2.708e+08 -16937459 <2e-16 ***
## Ticket7534 -3.500e+14 3.109e+08 -1125931 <2e-16 ***
## Ticket7540 4.425e+14 1.924e+08 2299232 <2e-16 ***
## Ticket7545 -4.418e+15 3.073e+08 -14375828 <2e-16 ***
## Ticket7546 -7.686e+14 3.059e+08 -2512217 <2e-16 ***
## Ticket7552 -2.190e+15 4.580e+08 -4781357 <2e-16 ***
## Ticket7553 -6.527e+15 3.585e+08 -18208401 <2e-16 ***
## Ticket7598 5.556e+15 1.218e+08 45601202 <2e-16 ***
## Ticket8471 -4.028e+15 1.559e+08 -25839219 <2e-16 ***
## Ticket8475 3.475e+13 1.648e+08 210825 <2e-16 ***
## Ticket9234 -6.235e+14 1.177e+08 -5296397 <2e-16 ***
## TicketA./5. 2152 1.287e+14 1.228e+08 1048259 <2e-16 ***
## TicketA./5. 3235 1.325e+13 1.229e+08 107810 <2e-16 ***
## TicketA.5. 11206 -3.047e+15 1.216e+08 -25045120 <2e-16 ***
## TicketA.5. 18509 4.751e+14 1.223e+08 3883692 <2e-16 ***
## TicketA/4 45380 -4.375e+15 1.228e+08 -35635329 <2e-16 ***
## TicketA/4 48871 -7.445e+15 2.506e+09 -2970509 <2e-16 ***
## TicketA/4. 20589 -4.567e+15 1.230e+08 -37119029 <2e-16 ***
## TicketA/4. 34244 -4.256e+15 1.067e+08 -39872416 <2e-16 ***
## TicketA/4. 39886 1.898e+14 1.038e+08 1827674 <2e-16 ***
## TicketA/5 21171 8.331e+14 1.070e+08 7786415 <2e-16 ***
## TicketA/5 21172 -4.140e+15 1.066e+08 -38849827 <2e-16 ***
## TicketA/5 21173 3.056e+14 1.067e+08 2865530 <2e-16 ***
## TicketA/5 21174 3.633e+14 1.066e+08 3409449 <2e-16 ***
## TicketA/5 2466 -4.105e+15 1.224e+08 -33532921 <2e-16 ***
## TicketA/5 2817 -4.452e+15 1.229e+08 -36230211 <2e-16 ***
## TicketA/5 3536 -3.528e+15 1.219e+08 -28944333 <2e-16 ***
## TicketA/5 3540 4.517e+15 1.229e+08 36742972 <2e-16 ***
## TicketA/5 3594 -3.259e+15 1.217e+08 -26768908 <2e-16 ***
## TicketA/5 3902 -3.178e+15 1.057e+08 -30071331 <2e-16 ***
## TicketA/5. 10482 4.555e+15 1.229e+08 37072842 <2e-16 ***
## TicketA/5. 13032 5.557e+14 1.182e+08 4699671 <2e-16 ***
## TicketA/5. 2151 -4.413e+15 1.228e+08 -35933281 <2e-16 ***
## TicketA/5. 3336 -4.230e+15 1.293e+09 -3271788 <2e-16 ***
## TicketA/5. 3337 -1.731e+15 1.053e+09 -1643869 <2e-16 ***
## TicketA/5. 851 -4.481e+15 1.053e+09 -4253540 <2e-16 ***
## TicketA/S 2816 -4.105e+15 1.224e+08 -33533543 <2e-16 ***
## TicketA4. 54510 -4.028e+15 1.223e+08 -32928069 <2e-16 ***
## TicketC 17369 4.970e+15 1.143e+08 43470250 <2e-16 ***
## TicketC 4001 -7.654e+15 2.262e+09 -3384300 <2e-16 ***
## TicketC 7075 -3.136e+15 1.915e+08 -16379033 <2e-16 ***
## TicketC 7076 -3.832e+15 1.062e+08 -36087886 <2e-16 ***
## TicketC 7077 3.114e+15 1.060e+08 29371380 <2e-16 ***
## TicketC.A. 17248 2.309e+14 9.493e+07 2432667 <2e-16 ***
## TicketC.A. 18723 4.542e+15 9.491e+07 47858309 <2e-16 ***
## TicketC.A. 2315 -2.033e+15 1.968e+09 -1033033 <2e-16 ***
## TicketC.A. 24579 1.386e+15 9.589e+07 14450585 <2e-16 ***
## TicketC.A. 24580 6.043e+15 9.612e+07 62873059 <2e-16 ***
## TicketC.A. 2673 -2.730e+15 1.918e+09 -1422974 <2e-16 ***
## TicketC.A. 29178 -8.054e+14 3.890e+08 -2070409 <2e-16 ***
## TicketC.A. 29395 7.216e+15 9.536e+07 75672121 <2e-16 ***
## TicketC.A. 29566 4.273e+15 9.493e+07 45006764 <2e-16 ***
## TicketC.A. 31026 2.405e+15 9.539e+07 25209012 <2e-16 ***
## TicketC.A. 31921 1.517e+15 2.378e+09 638027 <2e-16 ***
## TicketC.A. 33111 4.581e+15 9.491e+07 48262704 <2e-16 ***
## TicketC.A. 33112 -1.732e+15 3.962e+09 -437084 <2e-16 ***
## TicketC.A. 33595 6.353e+15 7.978e+08 7962807 <2e-16 ***
## TicketC.A. 34260 2.905e+15 9.539e+07 30454531 <2e-16 ***
## TicketC.A. 34651 1.600e+15 2.604e+09 614390 <2e-16 ***
## TicketC.A. 37671 2.966e+15 1.263e+09 2347733 <2e-16 ***
## TicketC.A. 5547 1.060e+15 9.568e+07 11074583 <2e-16 ***
## TicketC.A. 6212 -5.949e+15 1.143e+09 -5202998 <2e-16 ***
## TicketC.A./SOTON 34068 4.427e+15 9.491e+07 46640514 <2e-16 ***
## TicketCA 2144 -9.420e+15 5.938e+09 -1586365 <2e-16 ***
## TicketCA. 2314 3.079e+15 9.594e+07 32096586 <2e-16 ***
## TicketCA. 2343 -1.356e+16 9.356e+09 -1449338 <2e-16 ***
## TicketF.C. 12750 7.861e+15 5.206e+09 1510009 <2e-16 ***
## TicketF.C.C. 13528 4.873e+15 1.587e+09 3070446 <2e-16 ***
## TicketF.C.C. 13529 1.838e+15 2.378e+09 772940 <2e-16 ***
## TicketF.C.C. 13531 8.025e+15 9.574e+07 83813243 <2e-16 ***
## TicketFa 265302 -3.463e+15 1.022e+08 -33888191 <2e-16 ***
## TicketLINE 2.540e+15 1.142e+09 2225023 <2e-16 ***
## TicketP/PP 3381 1.102e+15 2.039e+09 540195 <2e-16 ***
## TicketPC 17318 1.016e+16 9.140e+09 1111838 <2e-16 ***
## TicketPC 17473 1.389e+16 9.085e+09 1528317 <2e-16 ***
## TicketPC 17474 1.836e+16 9.070e+09 2024579 <2e-16 ***
## TicketPC 17475 1.385e+16 9.085e+09 1523975 <2e-16 ***
## TicketPC 17476 1.412e+16 9.085e+09 1553623 <2e-16 ***
## TicketPC 17477 1.474e+15 2.597e+09 567658 <2e-16 ***
## TicketPC 17482 6.327e+15 5.583e+09 1133343 <2e-16 ***
## TicketPC 17483 -3.335e+16 2.041e+10 -1633982 <2e-16 ***
## TicketPC 17485 8.468e+15 4.463e+09 1897574 <2e-16 ***
## TicketPC 17558 -4.048e+16 2.429e+10 -1666224 <2e-16 ***
## TicketPC 17569 -1.433e+16 9.056e+09 -1582821 <2e-16 ***
## TicketPC 17572 4.806e+15 1.477e+09 3254520 <2e-16 ***
## TicketPC 17582 -1.786e+16 1.010e+10 -1767959 <2e-16 ***
## TicketPC 17585 -7.607e+14 1.106e+09 -687851 <2e-16 ***
## TicketPC 17590 7.757e+15 5.433e+09 1427722 <2e-16 ***
## TicketPC 17592 8.509e+15 7.107e+09 1197376 <2e-16 ***
## TicketPC 17593 -1.029e+15 1.105e+09 -931372 <2e-16 ***
## TicketPC 17595 7.922e+15 8.720e+09 908494 <2e-16 ***
## TicketPC 17596 9.294e+15 8.571e+09 1084411 <2e-16 ***
## TicketPC 17597 6.570e+15 3.792e+09 1732706 <2e-16 ***
## TicketPC 17599 6.505e+15 2.298e+09 2830546 <2e-16 ***
## TicketPC 17600 9.073e+15 8.420e+09 1077437 <2e-16 ***
## TicketPC 17601 9.533e+15 8.869e+09 1074800 <2e-16 ***
## TicketPC 17603 5.529e+15 4.090e+09 1351756 <2e-16 ***
## TicketPC 17604 6.246e+13 6.592e+08 94752 <2e-16 ***
## TicketPC 17605 9.763e+15 8.869e+09 1100812 <2e-16 ***
## TicketPC 17608 -3.986e+16 2.654e+10 -1502095 <2e-16 ***
## TicketPC 17609 5.385e+15 5.583e+09 964539 <2e-16 ***
## TicketPC 17610 1.244e+16 8.869e+09 1402322 <2e-16 ***
## TicketPC 17611 -1.004e+16 7.114e+09 -1411851 <2e-16 ***
## TicketPC 17612 9.917e+15 8.869e+09 1118165 <2e-16 ***
## TicketPC 17754 1.353e+16 7.823e+09 1729348 <2e-16 ***
## TicketPC 17755 -1.039e+17 6.425e+10 -1617381 <2e-16 ***
## TicketPC 17756 3.993e+15 5.144e+08 7762650 <2e-16 ***
## TicketPC 17757 -3.526e+16 2.128e+10 -1657107 <2e-16 ***
## TicketPC 17758 -7.135e+15 3.381e+09 -2110274 <2e-16 ***
## TicketPC 17759 5.007e+15 3.493e+09 1433501 <2e-16 ***
## TicketPC 17760 -1.405e+16 7.414e+09 -1895397 <2e-16 ***
## TicketPC 17761 -5.899e+15 3.007e+09 -1961495 <2e-16 ***
## TicketPP 4348 -1.515e+14 2.885e+08 -525275 <2e-16 ***
## TicketPP 9549 -9.819e+14 1.384e+09 -709668 <2e-16 ***
## TicketS.C./A.4. 23567 -3.490e+15 1.219e+08 -28634788 <2e-16 ***
## TicketS.C./PARIS 2079 -1.404e+15 4.000e+09 -350906 <2e-16 ***
## TicketS.O./P.P. 3 1.626e+15 8.238e+07 19736185 <2e-16 ***
## TicketS.O./P.P. 751 -4.060e+15 9.637e+07 -42129748 <2e-16 ***
## TicketS.O.C. 14879 -1.514e+16 9.506e+09 -1592645 <2e-16 ***
## TicketS.O.P. 1166 3.114e+14 3.199e+08 973376 <2e-16 ***
## TicketS.P. 3464 -4.478e+15 1.336e+08 -33529935 <2e-16 ***
## TicketS.W./PP 752 5.735e+15 9.568e+07 59940314 <2e-16 ***
## TicketSC 1748 2.232e+15 2.533e+08 8811629 <2e-16 ***
## TicketSC/AH 29037 -3.057e+15 2.341e+09 -1306288 <2e-16 ***
## TicketSC/AH 3085 -1.138e+14 2.341e+09 -48616 <2e-16 ***
## TicketSC/AH Basle 541 6.528e+15 5.095e+08 12811486 <2e-16 ***
## TicketSC/PARIS 2131 4.430e+15 6.957e+08 6367735 <2e-16 ***
## TicketSC/PARIS 2133 3.469e+15 6.952e+08 4989843 <2e-16 ***
## TicketSC/PARIS 2146 4.067e+15 5.198e+08 7823615 <2e-16 ***
## TicketSC/PARIS 2149 7.139e+15 5.194e+08 13743777 <2e-16 ***
## TicketSC/PARIS 2167 -3.438e+15 2.601e+09 -1321869 <2e-16 ***
## TicketSC/Paris 2123 -1.749e+15 4.691e+09 -372897 <2e-16 ***
## TicketSC/Paris 2163 4.502e+15 3.758e+08 11977700 <2e-16 ***
## TicketSCO/W 1585 -3.197e+14 2.841e+08 -1125240 <2e-16 ***
## TicketSO/C 14885 6.754e+15 9.544e+07 70767689 <2e-16 ***
## TicketSOTON/O.Q. 3101305 -3.937e+15 1.222e+08 -32207896 <2e-16 ***
## TicketSOTON/O.Q. 3101306 1.028e+15 1.219e+08 8437964 <2e-16 ***
## TicketSOTON/O.Q. 3101307 3.354e+14 1.225e+08 2737894 <2e-16 ***
## TicketSOTON/O.Q. 3101310 -3.591e+15 1.219e+08 -29448125 <2e-16 ***
## TicketSOTON/O.Q. 3101311 4.894e+14 1.223e+08 4000449 <2e-16 ***
## TicketSOTON/O.Q. 3101312 -3.976e+15 1.223e+08 -32512121 <2e-16 ***
## TicketSOTON/O.Q. 392078 5.056e+15 1.223e+08 41352469 <2e-16 ***
## TicketSOTON/O.Q. 392087 -5.973e+15 1.221e+08 -48922803 <2e-16 ***
## TicketSOTON/O2 3101272 -3.378e+15 1.151e+08 -29342575 <2e-16 ***
## TicketSOTON/O2 3101287 1.209e+14 1.122e+08 1077504 <2e-16 ***
## TicketSOTON/OQ 3101316 -3.759e+15 1.221e+08 -30792844 <2e-16 ***
## TicketSOTON/OQ 3101317 3.249e+14 1.066e+08 3046760 <2e-16 ***
## TicketSOTON/OQ 392076 -3.976e+15 1.223e+08 -32512121 <2e-16 ***
## TicketSOTON/OQ 392082 2.057e+14 1.227e+08 1676959 <2e-16 ***
## TicketSOTON/OQ 392086 -3.990e+15 1.223e+08 -32624295 <2e-16 ***
## TicketSOTON/OQ 392089 4.440e+15 1.230e+08 36083068 <2e-16 ***
## TicketSOTON/OQ 392090 -4.028e+15 1.223e+08 -32928055 <2e-16 ***
## TicketSTON/O 2. 3101269 1.045e+15 1.112e+08 9397453 <2e-16 ***
## TicketSTON/O 2. 3101273 -3.609e+15 1.153e+08 -31303831 <2e-16 ***
## TicketSTON/O 2. 3101274 -4.302e+15 1.161e+08 -37065575 <2e-16 ***
## TicketSTON/O 2. 3101275 -4.110e+15 1.158e+08 -35487057 <2e-16 ***
## TicketSTON/O 2. 3101280 -4.344e+15 1.121e+08 -38741882 <2e-16 ***
## TicketSTON/O 2. 3101285 5.941e+14 1.126e+08 5277556 <2e-16 ***
## TicketSTON/O 2. 3101286 5.086e+15 1.116e+08 45584245 <2e-16 ***
## TicketSTON/O 2. 3101288 5.443e+14 1.116e+08 4875904 <2e-16 ***
## TicketSTON/O 2. 3101289 5.356e+15 1.113e+08 48113954 <2e-16 ***
## TicketSTON/O 2. 3101292 5.828e+14 1.116e+08 5222746 <2e-16 ***
## TicketSTON/O 2. 3101293 5.828e+14 1.116e+08 5222730 <2e-16 ***
## TicketSTON/O 2. 3101294 -4.344e+15 1.121e+08 -38743722 <2e-16 ***
## TicketSTON/O2. 3101271 -9.659e+14 1.118e+08 -8636450 <2e-16 ***
## TicketSTON/O2. 3101279 -1.994e+15 1.255e+09 -1588526 <2e-16 ***
## TicketSTON/O2. 3101282 3.107e+15 1.114e+08 27906049 <2e-16 ***
## TicketSTON/O2. 3101283 3.141e+15 1.113e+08 28224216 <2e-16 ***
## TicketSTON/O2. 3101290 -1.516e+15 1.115e+08 -13597200 <2e-16 ***
## TicketSW/PP 751 8.584e+15 9.500e+07 90357368 <2e-16 ***
## TicketW./C. 14258 3.521e+15 9.574e+07 36775105 <2e-16 ***
## TicketW./C. 14263 4.465e+15 9.491e+07 47047195 <2e-16 ***
## TicketW./C. 6607 -5.250e+15 2.401e+09 -2186592 <2e-16 ***
## TicketW./C. 6608 -9.305e+15 4.049e+09 -2298430 <2e-16 ***
## TicketW./C. 6609 NA NA NA NA
## TicketW.E.P. 5734 1.685e+15 3.822e+09 440989 <2e-16 ***
## TicketW/C 14208 NA NA NA NA
## TicketWE/P 5735 3.480e+15 2.340e+09 1487553 <2e-16 ***
## Fare 2.452e+14 1.509e+08 1624908 <2e-16 ***
## EmbarkedQ NA NA NA NA
## EmbarkedS 3.493e+14 6.215e+07 5620837 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1186.66 on 890 degrees of freedom
## Residual deviance: 792.96 on 204 degrees of freedom
## AIC: 2167
##
## Number of Fisher Scoring iterations: 33*model selection
logit.model.new <- stepAIC(logit.model, trace = 0)## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred## Warning in stepAIC(logit.model, trace = 0): 0 df terms are changing AICsummary(logit.model.new)##
## Call:
## glm(formula = Survived ~ Pclass + Sex + Age + SibSp + Embarked,
## family = binomial, data = train.complete, maxit = 100)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.6965 -0.6276 -0.3793 0.6241 2.5002
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 4.530336 0.431778 10.492 < 2e-16 ***
## Pclass2 -1.185583 0.277728 -4.269 1.96e-05 ***
## Pclass3 -2.505056 0.269014 -9.312 < 2e-16 ***
## Sexmale -2.693632 0.197818 -13.617 < 2e-16 ***
## Age -0.044081 0.007601 -5.799 6.66e-09 ***
## SibSp -0.404876 0.107162 -3.778 0.000158 ***
## EmbarkedQ 0.057572 0.383166 0.150 0.880564
## EmbarkedS -0.428482 0.238021 -1.800 0.071832 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1186.66 on 890 degrees of freedom
## Residual deviance: 775.66 on 883 degrees of freedom
## AIC: 791.66
##
## Number of Fisher Scoring iterations: 5- predict
test.complete$Survived.prob <- predict(logit.model.new, type = "response", newdata = test.complete)
test.complete$Survived <- ifelse(test.complete$Survived.prob > 0.5 , 1,0)- export the predicted data
write.csv(test.complete[c(1,12)],file = "submision_1_logisticRegression.csv", row.names = F)