699 Assignment 3
Hsin-Hsin Wu
4/29/2018
Read and follow the data mining steps in the textbook for the Charles Book Club case (pp.499-505 in the text).
A. Partition your data into a training set (60%) and a validation set (40%). For your data partition, do not use the seed value mentioned in the book. Instead, use your individual seed value (listed on the PDF that is posted in the folder for this assignment). Show the code you used to make the partition.
Import data
c1<-read.csv("charlesbookclub.csv")
head(c1,5)## Seq. ID. Gender M R F FirstPurch ChildBks YouthBks CookBks DoItYBks
## 1 1 25 1 297 14 2 22 0 1 1 0
## 2 2 29 0 128 8 2 10 0 0 0 0
## 3 3 46 1 138 22 7 56 2 1 2 0
## 4 4 47 1 228 2 1 2 0 0 0 0
## 5 5 51 1 257 10 1 10 0 0 0 0
## RefBks ArtBks GeogBks ItalCook ItalAtlas ItalArt Florence
## 1 0 0 0 0 0 0 0
## 2 0 0 0 0 0 0 0
## 3 1 0 1 1 0 0 0
## 4 0 0 0 0 0 0 0
## 5 0 0 0 0 0 0 0
## Related.Purchase Mcode Rcode Fcode Yes_Florence No_Florence
## 1 0 5 4 2 0 1
## 2 0 4 3 2 0 1
## 3 2 4 4 3 0 1
## 4 0 5 1 1 0 1
## 5 0 5 3 1 0 1names(c1)## [1] "Seq." "ID." "Gender"
## [4] "M" "R" "F"
## [7] "FirstPurch" "ChildBks" "YouthBks"
## [10] "CookBks" "DoItYBks" "RefBks"
## [13] "ArtBks" "GeogBks" "ItalCook"
## [16] "ItalAtlas" "ItalArt" "Florence"
## [19] "Related.Purchase" "Mcode" "Rcode"
## [22] "Fcode" "Yes_Florence" "No_Florence"Create training and validation sets
set.seed(60)
train.index<-sample(rownames(c1), dim(c1)[1]*0.6)
train.df<-c1[train.index, ]
valid.index <- setdiff(rownames(c1), train.index)
valid.df<-c1[valid.index, ]1.Show the RFM combinations for the training data and the validation data. the code you used, along with the results, to determine:
a)The response rate for each category from your training data;
mean(train.df$Florence) #The average response rate of column "Florence"## [1] 0.08125Melting things
library(reshape)
m<-melt(train.df, id = c("Mcode", "Fcode", "Rcode"),measure = "Florence", na.rm = F)
cst<-cast(m, variable ~ Mcode + Fcode + Rcode, mean)Reshaping the validation data
m2<-melt(valid.df, id = c("Mcode", "Fcode", "Rcode"), measure = "Florence", na.rm = F)
cst2<-cast(m2, variable ~ Mcode + Fcode + Rcode, mean)b) The response rate in the validation data for combinations that exceeded the mean response rate for the training data;
above.average.index <- which(t(cst2) > mean(train.df$Florence))
above.average <- rownames(t(cst2))[above.average.index]
above.average #this shows the identities of the rows in the validation set that exceeded the mean from the training set## [1] "1_1_3" "2_1_2" "2_1_4" "2_2_1" "2_2_2" "2_2_3" "2_2_4" "3_1_2"
## [9] "3_1_4" "3_2_2" "3_2_3" "3_3_2" "3_3_4" "4_1_1" "4_1_2" "4_2_3"
## [17] "4_3_2" "4_3_3" "4_3_4" "5_1_1" "5_1_2" "5_1_4" "5_3_1" "5_3_2"
## [25] "5_3_3"cst.length <- cast(m2, variable ~ Mcode + Fcode + Rcode, length)
ind <- colnames(cst2) %in% above.average #the %in% uses the special binary operator
rate<-sum(cst2[ind]*cst.length[ind])/sum(cst.length[ind])
rate #this gives the response rate among groups in the validation set that exceeded the training set mean## [1] 0.1328125c) The combinations that have response rates that exceed twice the overall response rate (for training data only)
Groups those exceed 2 times the mean in Training Data
above.average.index <- which(t(cst) > 2*mean(train.df$Florence))
above.average <- rownames(t(cst))[above.average.index]
ind<-colnames(cst) %in% above.average
rate.s1<-sum(cst[ind]*cst.length[ind])/sum(cst.length[ind])
n.s1<-sum(cst.length[ind])
above.average## [1] "1_1_2" "1_1_3" "2_1_1" "2_2_1" "2_3_1" "3_3_1" "3_3_2" "4_2_2" "5_3_2"rate.s1## [1] 0.1867754d) The combinations that exceed the overall response rate but do not exceed twice the overall response rate (for training data only)
Groups those greater than mean, but less than 2 times mean
above.average.index <- intersect(which(t(cst) < 2*mean(train.df$Florence)), which(t(cst) > mean(train.df$Florence)))
above.average <- rownames(t(cst))[above.average.index]
ind<-colnames(cst) %in% above.average
rate.s2<-sum(cst[ind]*cst.length[ind])/sum(cst.length[ind])
n.s2<-sum(cst.length[ind])
above.average## [1] "3_1_4" "4_1_1" "4_1_4" "4_3_2" "5_1_1" "5_1_2" "5_2_1" "5_2_2"
## [9] "5_3_1" "5_3_3"rate.s2## [1] 0.1234764e) The remaining RFM combinations (less than the mean) for the training data only
The below average segment
below.average.index<-which(t(cst) < mean(train.df$Florence))
below.average<-rownames(t(cst))[below.average.index]
ind<-colnames(cst) %in% below.average
rate.s3<-sum(cst[ind]*cst.length[ind])/sum(cst.length[ind])
n.s3<-sum(cst.length[ind])
below.average## [1] "1_1_1" "1_1_4" "2_1_2" "2_1_3" "2_1_4" "2_2_2" "2_2_3" "2_2_4"
## [9] "2_3_4" "3_1_1" "3_1_2" "3_1_3" "3_2_1" "3_2_2" "3_2_3" "3_2_4"
## [17] "3_3_3" "3_3_4" "4_1_2" "4_1_3" "4_2_1" "4_2_3" "4_2_4" "4_3_1"
## [25] "4_3_3" "4_3_4" "5_1_3" "5_1_4" "5_2_3" "5_2_4" "5_3_4"rate.s3## [1] 0.05689315f) We will also do the lift curve together in class for the three points for the various segments. Show the code used to create it, along with the result.
Plotting the Rates Aganist the Lengths (group sizes)
plot(c(rate.s1, rate.s2, rate.s3) ~ c(n.s1, n.s2, n.s3), type = "b")
C. For the k-nn portion of this assignment:
1. Convert Florence into a factor. Show how you did this.
c1$Florence<-as.factor(c1$Florence)
str(c1)## 'data.frame': 4000 obs. of 24 variables:
## $ Seq. : int 1 2 3 4 5 6 7 8 9 10 ...
## $ ID. : int 25 29 46 47 51 60 61 79 81 90 ...
## $ Gender : int 1 0 1 1 1 1 1 1 1 1 ...
## $ M : int 297 128 138 228 257 145 190 187 252 240 ...
## $ R : int 14 8 22 2 10 6 16 14 10 6 ...
## $ F : int 2 2 7 1 1 2 1 1 1 3 ...
## $ FirstPurch : int 22 10 56 2 10 12 16 14 10 20 ...
## $ ChildBks : int 0 0 2 0 0 0 0 1 0 0 ...
## $ YouthBks : int 1 0 1 0 0 0 0 0 0 0 ...
## $ CookBks : int 1 0 2 0 0 0 0 0 0 1 ...
## $ DoItYBks : int 0 0 0 0 0 0 0 0 0 0 ...
## $ RefBks : int 0 0 1 0 0 0 0 0 0 0 ...
## $ ArtBks : int 0 0 0 0 0 0 0 0 0 0 ...
## $ GeogBks : int 0 0 1 0 0 0 1 0 0 0 ...
## $ ItalCook : int 0 0 1 0 0 0 0 0 0 0 ...
## $ ItalAtlas : int 0 0 0 0 0 0 0 0 0 0 ...
## $ ItalArt : int 0 0 0 0 0 0 0 0 0 0 ...
## $ Florence : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
## $ Related.Purchase: int 0 0 2 0 0 0 1 0 0 0 ...
## $ Mcode : int 5 4 4 5 5 4 4 4 5 5 ...
## $ Rcode : int 4 3 4 1 3 2 4 4 3 2 ...
## $ Fcode : int 2 2 3 1 1 2 1 1 1 3 ...
## $ Yes_Florence : int 0 0 0 0 0 0 0 0 0 0 ...
## $ No_Florence : int 1 1 1 1 1 1 1 1 1 1 ...2. Run the knn() function from the fnn package to predict the outcome for Florence for a consumer with an Fcode of 3, an MCode of 3, and an Rcode of 3. Use preProcess() for normalization. Use k =7, and show the result. What did it predict for this consumer? (Use Table 7.2 from the book and/or your own process from the k-nn candy challenge, as a guide here). Show your steps and show the result.
train.norm.df<-train.df #normalizing training and validation data
valid.norm.df<-valid.df
c1.norm.df<-c1
library(caret)## Warning: package 'caret' was built under R version 3.4.4## Loading required package: lattice## Loading required package: ggplot2names(c1)## [1] "Seq." "ID." "Gender"
## [4] "M" "R" "F"
## [7] "FirstPurch" "ChildBks" "YouthBks"
## [10] "CookBks" "DoItYBks" "RefBks"
## [13] "ArtBks" "GeogBks" "ItalCook"
## [16] "ItalAtlas" "ItalArt" "Florence"
## [19] "Related.Purchase" "Mcode" "Rcode"
## [22] "Fcode" "Yes_Florence" "No_Florence"new.df<-data.frame("Mcode"=3,"Rcode"=3,"Fcode"=3)
new.df## Mcode Rcode Fcode
## 1 3 3 3norm.values<-preProcess(train.df[,20:22], method=c("center","scale"))
train.norm.df[, 20:22] <- predict(norm.values, train.df[, 20:22])
valid.norm.df[, 20:22] <- predict(norm.values, valid.df[, 20:22])
new.norm.df<-predict(norm.values,new.df)
library(FNN)
names(train.norm.df)## [1] "Seq." "ID." "Gender"
## [4] "M" "R" "F"
## [7] "FirstPurch" "ChildBks" "YouthBks"
## [10] "CookBks" "DoItYBks" "RefBks"
## [13] "ArtBks" "GeogBks" "ItalCook"
## [16] "ItalAtlas" "ItalArt" "Florence"
## [19] "Related.Purchase" "Mcode" "Rcode"
## [22] "Fcode" "Yes_Florence" "No_Florence"nn<-knn(train=train.norm.df[ ,20:22],test=new.norm.df,cl=train.norm.df[ ,18], k=7)
row.names(train.df)[attr(nn, "nn.index")]## [1] "3584" "3205" "3919" "3423" "2743" "3632" "2660"nn## [1] 0
## attr(,"nn.index")
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 1490 1433 278 1304 1209 209 1999
## attr(,"nn.dist")
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0 0 0 0 0 0 0
## Levels: 0If we use k=7,the 7 nearest neighbors are “3584” “3205” “3919” “3423” “2743” “3632” and “2660”.The outcome for a consumer with an Fcode of 3, an MCode of 3, and an Rcode of 3 would be classified as Florence of 0.
E.For the logistic regression portion:
1.Run the glm() function on your training data with the predictors in columns 3 through 19, and with Florence as the outcome variable (see p.245 for a coded example of such a function). Show the code you used, and show the result by using summary().
names(train.df)## [1] "Seq." "ID." "Gender"
## [4] "M" "R" "F"
## [7] "FirstPurch" "ChildBks" "YouthBks"
## [10] "CookBks" "DoItYBks" "RefBks"
## [13] "ArtBks" "GeogBks" "ItalCook"
## [16] "ItalAtlas" "ItalArt" "Florence"
## [19] "Related.Purchase" "Mcode" "Rcode"
## [22] "Fcode" "Yes_Florence" "No_Florence"logit.reg<-glm(Florence ~ Gender+M+R+F+FirstPurch+ChildBks+YouthBks+CookBks+DoItYBks+RefBks+
ArtBks+GeogBks+ItalCook+ItalAtlas+ItalArt+Related.Purchase,data = train.df,family = "binomial")
options(scipen=999)
summary(logit.reg)##
## Call:
## glm(formula = Florence ~ Gender + M + R + F + FirstPurch + ChildBks +
## YouthBks + CookBks + DoItYBks + RefBks + ArtBks + GeogBks +
## ItalCook + ItalAtlas + ItalArt + Related.Purchase, family = "binomial",
## data = train.df)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.0500 -0.4295 -0.3553 -0.3011 2.6959
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.3449911 0.2592120 -9.047 < 0.0000000000000002 ***
## Gender -0.4526930 0.1591063 -2.845 0.004438 **
## M -0.0007348 0.0009100 -0.807 0.419396
## R -0.0143865 0.0152358 -0.944 0.345038
## F 0.2273245 0.0669460 3.396 0.000685 ***
## FirstPurch 0.0002617 0.0111320 0.024 0.981244
## ChildBks -0.2646801 0.1108514 -2.388 0.016954 *
## YouthBks -0.2183066 0.1489582 -1.466 0.142769
## CookBks -0.3347406 0.1059120 -3.161 0.001575 **
## DoItYBks -0.1219760 0.1289821 -0.946 0.344311
## RefBks -0.2284536 0.1543036 -1.481 0.138728
## ArtBks 0.4572690 0.1031103 4.435 0.00000922 ***
## GeogBks 0.0852234 0.1021087 0.835 0.403924
## ItalCook -0.2493745 0.2147328 -1.161 0.245510
## ItalAtlas 0.0638245 0.3273920 0.195 0.845433
## ItalArt 0.3572926 0.2972874 1.202 0.229425
## Related.Purchase NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1352.7 on 2399 degrees of freedom
## Residual deviance: 1282.2 on 2384 degrees of freedom
## AIC: 1314.2
##
## Number of Fisher Scoring iterations: 52. Call the predict() function on your validation data. The code sample below might be helpful but bear in mind that if you are using different variable names, it will not work:
newdata<-data.frame(valid.df[3:19])
pred<-predict(logit.reg,newdata,type="response")3. Now sort out the records. You can do this with something like: sort(pred, decreasing=FALSE). Show your results.
sort(pred,decreasing = FALSE)## 1218 2702 2045 2707 1752 2907
## 0.01380184 0.01544257 0.01756401 0.01878696 0.02098483 0.02137832
## 869 1976 41 3267 31 219
## 0.02146570 0.02159823 0.02244677 0.02342351 0.02344536 0.02448722
## 145 1271 3294 576 3355 510
## 0.02505725 0.02538548 0.02582959 0.02584081 0.02661626 0.02663731
## 2728 2481 3100 3680 749 2035
## 0.02702463 0.02726816 0.02786113 0.02787781 0.02790412 0.02805509
## 404 167 3074 325 581 3768
## 0.02821764 0.02822079 0.02830222 0.02841644 0.02887376 0.02907828
## 1097 1702 3109 3268 2249 2914
## 0.02911116 0.02931054 0.02936869 0.02945189 0.02966915 0.02980887
## 2240 1302 660 3476 2821 972
## 0.02986212 0.03000343 0.03007047 0.03017024 0.03028913 0.03034136
## 2401 3826 345 2837 2522 3009
## 0.03034932 0.03059120 0.03060100 0.03065238 0.03085475 0.03090204
## 1814 291 1458 303 3208 1634
## 0.03093113 0.03098108 0.03114955 0.03124390 0.03139330 0.03152035
## 746 2835 462 3370 3892 3722
## 0.03163483 0.03165508 0.03169146 0.03177186 0.03192944 0.03203769
## 2987 2658 3215 3926 1062 1785
## 0.03252599 0.03258831 0.03311994 0.03315777 0.03323398 0.03350933
## 3908 2241 2562 3993 704 3406
## 0.03359559 0.03366820 0.03371264 0.03374308 0.03382057 0.03392438
## 3352 1483 1433 3569 1819 1732
## 0.03399485 0.03409676 0.03413058 0.03424548 0.03433667 0.03445462
## 1094 3860 3792 678 153 3455
## 0.03453172 0.03469639 0.03479321 0.03487941 0.03497054 0.03503677
## 2944 490 3282 3228 3347 3929
## 0.03504194 0.03519908 0.03525598 0.03534694 0.03549311 0.03549560
## 2553 2643 91 1012 364 3460
## 0.03560870 0.03576590 0.03578124 0.03579377 0.03587435 0.03589040
## 3741 1392 2398 2549 693 2834
## 0.03590536 0.03590699 0.03605212 0.03608964 0.03616319 0.03617714
## 3332 217 3953 65 3020 573
## 0.03628120 0.03636551 0.03636752 0.03642019 0.03650015 0.03652377
## 476 2095 2184 2335 674 82
## 0.03656041 0.03673207 0.03695008 0.03712924 0.03731517 0.03742793
## 1298 3750 2378 992 1331 1281
## 0.03744847 0.03756754 0.03760926 0.03774961 0.03778247 0.03780919
## 2928 3944 1769 3273 1669 2637
## 0.03782982 0.03783864 0.03786264 0.03788766 0.03790172 0.03790508
## 1818 383 2173 2916 1941 1157
## 0.03793415 0.03798756 0.03819156 0.03822424 0.03830472 0.03847624
## 3840 1231 2366 3575 940 240
## 0.03851317 0.03851475 0.03854579 0.03854779 0.03857450 0.03859213
## 3793 2512 2808 2423 2074 2150
## 0.03867448 0.03867695 0.03868390 0.03876999 0.03877434 0.03879163
## 2101 3459 2607 251 845 2698
## 0.03882476 0.03884370 0.03887631 0.03889270 0.03896203 0.03896455
## 2132 3905 3738 758 1550 209
## 0.03896621 0.03899122 0.03903351 0.03909814 0.03911845 0.03912874
## 2544 805 3719 2435 2319 498
## 0.03917121 0.03918604 0.03924232 0.03926566 0.03932531 0.03934920
## 867 1697 3817 155 2044 239
## 0.03935833 0.03940847 0.03941426 0.03947534 0.03948949 0.03950480
## 249 254 520 780 1397 1961
## 0.03957613 0.03962207 0.03966026 0.03968287 0.03975738 0.03993688
## 2851 3663 3712 2697 1867 1946
## 0.04000975 0.04003550 0.04004649 0.04005369 0.04006338 0.04013151
## 3600 1832 2469 8 733 2980
## 0.04013390 0.04013746 0.04018156 0.04030269 0.04043589 0.04046880
## 1737 3226 295 3616 899 1488
## 0.04047232 0.04051589 0.04054180 0.04068023 0.04068862 0.04070558
## 1984 1535 1610 628 2768 523
## 0.04075025 0.04077613 0.04092275 0.04100936 0.04104807 0.04105327
## 2887 3450 2329 2172 2273 2341
## 0.04109614 0.04110118 0.04112489 0.04119673 0.04122674 0.04128985
## 3893 2209 903 3218 1150 1825
## 0.04129185 0.04132050 0.04134462 0.04137258 0.04141877 0.04142573
## 2295 3909 3392 3960 2268 652
## 0.04143166 0.04158829 0.04162984 0.04163752 0.04164966 0.04166310
## 2976 2786 151 624 1660 305
## 0.04189423 0.04196410 0.04199310 0.04201919 0.04202875 0.04210285
## 3859 626 3756 3176 1351 188
## 0.04219443 0.04219978 0.04226020 0.04226197 0.04235953 0.04240280
## 2406 1817 2407 2071 2811 555
## 0.04241422 0.04244603 0.04245196 0.04248681 0.04249733 0.04266891
## 2008 2538 3734 3605 2793 536
## 0.04287534 0.04301244 0.04304477 0.04305001 0.04306956 0.04310254
## 1613 2881 2394 3797 1547 3740
## 0.04311875 0.04316001 0.04317233 0.04323150 0.04327541 0.04335112
## 962 417 1496 2736 3742 387
## 0.04339457 0.04339715 0.04343043 0.04343051 0.04349458 0.04358378
## 3957 3516 2039 297 2181 3184
## 0.04359888 0.04364141 0.04364592 0.04364817 0.04365209 0.04367317
## 3820 1853 1740 1649 735 1798
## 0.04367805 0.04370609 0.04374031 0.04378243 0.04381176 0.04387215
## 2647 787 164 1429 3593 2503
## 0.04387337 0.04389924 0.04390430 0.04391668 0.04397355 0.04417083
## 1599 1806 1030 927 1544 410
## 0.04420893 0.04420902 0.04423402 0.04433563 0.04434427 0.04435999
## 341 2475 3798 3154 3842 2236
## 0.04437907 0.04438757 0.04447133 0.04449429 0.04452203 0.04453991
## 347 3745 2229 3112 285 2453
## 0.04456646 0.04459487 0.04472901 0.04474513 0.04475730 0.04480456
## 3607 667 1654 3503 792 1189
## 0.04492498 0.04492540 0.04508067 0.04510346 0.04514064 0.04520960
## 2551 395 1683 3583 380 3804
## 0.04523009 0.04527366 0.04528213 0.04540098 0.04548088 0.04549504
## 2966 984 2783 1162 1723 3471
## 0.04564032 0.04565343 0.04565826 0.04567893 0.04575249 0.04595138
## 2791 2087 1575 302 3150 2681
## 0.04606450 0.04606671 0.04615925 0.04618168 0.04629175 0.04631673
## 2854 3556 569 3707 589 447
## 0.04633854 0.04633971 0.04639237 0.04639606 0.04641592 0.04641942
## 1372 3223 3897 3026 2518 2320
## 0.04646199 0.04654841 0.04668415 0.04672166 0.04675786 0.04698107
## 2011 1958 3276 3149 1904 2006
## 0.04703341 0.04703883 0.04718956 0.04722713 0.04722934 0.04724872
## 1804 1022 2939 255 2083 3595
## 0.04727830 0.04735659 0.04737236 0.04743902 0.04750294 0.04758890
## 1241 731 532 834 3672 828
## 0.04760278 0.04763073 0.04764723 0.04766762 0.04768359 0.04776375
## 1171 2246 450 485 529 2345
## 0.04779249 0.04782963 0.04785368 0.04790167 0.04792392 0.04794904
## 815 585 140 2776 553 1694
## 0.04797000 0.04809657 0.04814666 0.04823154 0.04823978 0.04832229
## 3658 1869 1934 2300 1718 1491
## 0.04833359 0.04838806 0.04849282 0.04860709 0.04871306 0.04873352
## 3384 3959 1211 563 1549 1568
## 0.04876927 0.04879495 0.04884042 0.04890299 0.04890668 0.04901256
## 2631 820 1198 1050 67 42
## 0.04916879 0.04918703 0.04928145 0.04935442 0.04940604 0.04945627
## 3230 990 2761 739 1304 3615
## 0.04945856 0.04951117 0.04952301 0.04953811 0.04963600 0.04963693
## 2415 3105 2719 2846 2646 2576
## 0.04965864 0.04972543 0.04976254 0.04976278 0.04979449 0.04989413
## 789 938 2642 2127 1915 3278
## 0.04992935 0.04997933 0.04997933 0.04998100 0.05000886 0.05004916
## 466 3528 3530 580 3251 2515
## 0.05006233 0.05015501 0.05015800 0.05020342 0.05022987 0.05030986
## 1781 3706 844 2820 3068 134
## 0.05042108 0.05045311 0.05045470 0.05046120 0.05048163 0.05052094
## 3978 2619 1460 2979 1353 114
## 0.05054476 0.05055621 0.05056300 0.05061508 0.05067395 0.05071714
## 2904 1319 1947 1321 3512 1338
## 0.05075136 0.05076825 0.05080084 0.05085544 0.05090243 0.05097763
## 2930 250 1227 710 2543 568
## 0.05099974 0.05100256 0.05100791 0.05107210 0.05111273 0.05120317
## 1023 1630 3931 2633 2862 97
## 0.05123059 0.05123059 0.05126631 0.05129454 0.05134188 0.05135775
## 2529 483 1369 352 1988 712
## 0.05141938 0.05142025 0.05142694 0.05143498 0.05153234 0.05155299
## 2452 3910 1899 778 1161 801
## 0.05161976 0.05162572 0.05163011 0.05165991 0.05166089 0.05166844
## 2243 3253 1597 2623 526 1753
## 0.05178706 0.05180410 0.05181162 0.05191143 0.05192802 0.05199306
## 2460 3010 2533 5 1931 2040
## 0.05204060 0.05205054 0.05211785 0.05213091 0.05216612 0.05216967
## 2277 2193 2850 3340 1138 371
## 0.05222121 0.05229250 0.05231276 0.05238455 0.05239095 0.05247101
## 1643 2037 1957 64 809 2227
## 0.05250269 0.05255839 0.05258839 0.05262690 0.05266070 0.05266380
## 1921 1122 3696 2465 3858 2534
## 0.05269198 0.05271494 0.05288297 0.05292614 0.05295917 0.05296826
## 233 83 366 428 1983 1515
## 0.05297239 0.05298877 0.05300927 0.05306670 0.05308268 0.05310364
## 923 527 1322 1891 1039 2286
## 0.05311489 0.05313537 0.05313645 0.05314068 0.05317759 0.05319401
## 1419 2117 3242 2059 1696 434
## 0.05321580 0.05322574 0.05335826 0.05339542 0.05353275 0.05356755
## 2797 2120 2934 3292 3639 711
## 0.05357223 0.05358599 0.05359103 0.05360760 0.05362248 0.05362628
## 2081 1013 1089 1624 3990 2605
## 0.05366336 0.05373111 0.05373111 0.05373112 0.05375608 0.05381008
## 3526 863 2287 3824 1131 1847
## 0.05384751 0.05388114 0.05389568 0.05394205 0.05394855 0.05406909
## 640 3260 3563 2690 1149 1220
## 0.05407258 0.05410499 0.05410692 0.05410863 0.05410959 0.05411017
## 1176 1011 3272 1948 1791 1243
## 0.05418122 0.05423985 0.05425708 0.05434960 0.05441898 0.05442863
## 1374 3390 3221 7 50 720
## 0.05444966 0.05458101 0.05462563 0.05464254 0.05467472 0.05475021
## 3297 2262 1386 2806 1102 2486
## 0.05477427 0.05477600 0.05486305 0.05486488 0.05490116 0.05496053
## 1850 1344 2632 3123 2316 3890
## 0.05501262 0.05504147 0.05504244 0.05506073 0.05508223 0.05509641
## 86 2790 270 1606 2974 278
## 0.05512491 0.05513038 0.05513478 0.05519922 0.05524657 0.05527611
## 3174 2993 2323 3785 178 206
## 0.05533415 0.05534966 0.05541128 0.05541165 0.05541601 0.05544173
## 1292 3524 1035 839 3029 3723
## 0.05548073 0.05553584 0.05556011 0.05561349 0.05561483 0.05563011
## 1029 469 873 3345 3939 3239
## 0.05564590 0.05565933 0.05575214 0.05580246 0.05582835 0.05584065
## 748 3942 1553 826 3887 272
## 0.05587534 0.05590532 0.05591383 0.05601698 0.05601742 0.05603903
## 1268 2573 1708 3580 774 2703
## 0.05610304 0.05610842 0.05612099 0.05620617 0.05620765 0.05629494
## 981 236 2933 649 1481 982
## 0.05629729 0.05631176 0.05644694 0.05646091 0.05647255 0.05648390
## 1673 2052 686 1143 348 3444
## 0.05650293 0.05653351 0.05658573 0.05658573 0.05660314 0.05665250
## 3064 2852 1108 1142 3646 1326
## 0.05668608 0.05671210 0.05678046 0.05688576 0.05690072 0.05699104
## 1587 979 2290 1015 2194 3285
## 0.05699681 0.05700015 0.05700133 0.05700992 0.05701297 0.05702630
## 399 3408 1128 613 2497 463
## 0.05703189 0.05705338 0.05705720 0.05714477 0.05719154 0.05729153
## 1581 256 33 3315 2892 790
## 0.05733334 0.05739752 0.05740250 0.05741517 0.05744067 0.05744086
## 1880 2046 2528 234 2049 172
## 0.05746608 0.05748930 0.05751378 0.05756997 0.05759663 0.05771192
## 888 1626 2853 2568 408 3287
## 0.05772517 0.05772944 0.05784969 0.05788439 0.05791654 0.05799628
## 129 1046 3196 377 1800 1707
## 0.05800559 0.05800808 0.05800970 0.05802206 0.05802222 0.05802368
## 1019 3865 757 2270 1743 287
## 0.05807262 0.05812826 0.05813520 0.05814854 0.05816840 0.05820668
## 2296 1370 2922 496 1340 1358
## 0.05831102 0.05832010 0.05837617 0.05839955 0.05839955 0.05843121
## 3874 1091 2430 3028 1163 3234
## 0.05845701 0.05846027 0.05848930 0.05851525 0.05853291 0.05860757
## 894 2873 2456 3808 1026 3470
## 0.05860869 0.05878562 0.05882299 0.05884470 0.05894672 0.05901329
## 3831 622 1249 549 1829 1987
## 0.05911667 0.05917571 0.05926290 0.05932668 0.05939129 0.05943620
## 1766 1066 718 3519 415 2293
## 0.05950345 0.05950918 0.05955032 0.05957702 0.05958615 0.05959297
## 2493 21 374 2014 3975 3202
## 0.05962364 0.05979772 0.05979935 0.05984740 0.05987133 0.05988966
## 3431 2577 3183 3438 2872 2244
## 0.05995410 0.06000124 0.06004792 0.06007381 0.06009280 0.06013841
## 2869 2684 3359 2464 1813 3416
## 0.06020612 0.06022153 0.06027910 0.06028067 0.06028459 0.06030009
## 3809 866 3592 3763 2744 1435
## 0.06033897 0.06036023 0.06039180 0.06049753 0.06059691 0.06069727
## 1838 2758 2926 1282 2186 1923
## 0.06071782 0.06078306 0.06079795 0.06086702 0.06087821 0.06092769
## 1592 892 876 2405 3771 238
## 0.06095881 0.06105867 0.06105988 0.06109892 0.06113156 0.06123711
## 1495 3270 1735 817 3732 378
## 0.06131193 0.06137992 0.06140206 0.06148564 0.06154060 0.06162750
## 1757 535 3061 2248 160 307
## 0.06165712 0.06172161 0.06181527 0.06185597 0.06189711 0.06192085
## 3783 3976 2705 724 3698 717
## 0.06203422 0.06213941 0.06215843 0.06217548 0.06222703 0.06232999
## 237 3578 2825 2403 1346 3463
## 0.06237689 0.06239836 0.06240947 0.06241089 0.06243503 0.06246321
## 156 3222 3335 3232 1521 3726
## 0.06261760 0.06263864 0.06275629 0.06278962 0.06279219 0.06283718
## 72 192 910 1214 438 1051
## 0.06288578 0.06289431 0.06295320 0.06299656 0.06311607 0.06311882
## 2757 680 1844 1120 1820 264
## 0.06313034 0.06323311 0.06325126 0.06325835 0.06327665 0.06328394
## 1570 3110 66 3856 257 2299
## 0.06328583 0.06329232 0.06329360 0.06343171 0.06361453 0.06363391
## 945 509 2421 392 497 2094
## 0.06363813 0.06365095 0.06385387 0.06387848 0.06388917 0.06389299
## 2709 2067 1400 3280 1618 525
## 0.06391337 0.06393829 0.06395759 0.06404464 0.06405429 0.06412776
## 3033 1167 117 3104 671 2983
## 0.06415337 0.06422205 0.06429081 0.06431798 0.06435466 0.06447553
## 3610 3807 3256 1528 1018 901
## 0.06450721 0.06453231 0.06453660 0.06458584 0.06459389 0.06482331
## 2337 1355 2139 3483 1828 3213
## 0.06485408 0.06502646 0.06504416 0.06508608 0.06514279 0.06520047
## 3198 277 1525 1232 3955 911
## 0.06526350 0.06529238 0.06546570 0.06553846 0.06565206 0.06569563
## 534 3403 1893 2649 1427 2485
## 0.06569642 0.06570861 0.06572376 0.06574674 0.06576587 0.06580416
## 1221 301 2945 2365 168 2152
## 0.06591586 0.06593277 0.06600263 0.06601202 0.06603141 0.06604827
## 191 3814 2773 2946 3971 2199
## 0.06606777 0.06612210 0.06614734 0.06615039 0.06620812 0.06627784
## 2750 829 2137 1065 1110 225
## 0.06627982 0.06640088 0.06643508 0.06643563 0.06649246 0.06653166
## 1003 788 484 1410 2685 2076
## 0.06659996 0.06661135 0.06662363 0.06669733 0.06676020 0.06678887
## 1413 2996 3291 2546 781 1670
## 0.06685791 0.06691835 0.06693221 0.06697455 0.06700502 0.06704206
## 2123 595 1666 1054 1883 2506
## 0.06704826 0.06719840 0.06749437 0.06752525 0.06754168 0.06759367
## 362 176 1330 3162 822 1917
## 0.06763534 0.06765623 0.06770509 0.06771661 0.06774694 0.06784840
## 3899 1364 322 843 1329 2732
## 0.06796044 0.06809528 0.06827604 0.06834672 0.06837035 0.06854504
## 1805 871 1563 2905 1540 1731
## 0.06858767 0.06867618 0.06870337 0.06874462 0.06890057 0.06894760
## 848 2166 3322 1004 440 157
## 0.06904122 0.06904279 0.06909366 0.06909525 0.06910737 0.06923257
## 2324 2161 2910 3090 2511 1308
## 0.06939697 0.06943276 0.06947594 0.06954772 0.06957446 0.06958192
## 2531 3755 424 934 2602 3011
## 0.06958494 0.06969884 0.06979330 0.06986221 0.06987906 0.06990252
## 3454 3366 2586 976 1662 3608
## 0.06997690 0.07016305 0.07018668 0.07019510 0.07023293 0.07025877
## 538 3233 1661 679 261 2043
## 0.07026935 0.07039531 0.07039567 0.07043577 0.07045104 0.07049098
## 1057 3402 1385 694 1848 2741
## 0.07053125 0.07058704 0.07068588 0.07069130 0.07085760 0.07093367
## 2157 3822 276 2314 495 1190
## 0.07099702 0.07099832 0.07102922 0.07104482 0.07106237 0.07108952
## 43 1677 2195 464 2937 2805
## 0.07110000 0.07112264 0.07121344 0.07127673 0.07129772 0.07137597
## 409 3195 1159 1090 3309 3912
## 0.07138894 0.07140036 0.07149324 0.07152395 0.07159321 0.07162577
## 2351 1693 948 3023 2297 2571
## 0.07163573 0.07175197 0.07190484 0.07194436 0.07204956 0.07216192
## 3674 2436 1517 1596 2664 130
## 0.07223345 0.07226119 0.07227009 0.07242927 0.07243248 0.07244997
## 292 3769 2863 3762 1199 2202
## 0.07256647 0.07263854 0.07264951 0.07269054 0.07276786 0.07280318
## 119 2455 1851 3991 2360 3339
## 0.07282517 0.07287389 0.07302270 0.07304191 0.07307238 0.07308228
## 1396 3156 2165 1646 3534 3523
## 0.07308418 0.07312217 0.07314435 0.07315943 0.07323749 0.07327958
## 1033 2557 152 6 385 3561
## 0.07335263 0.07350288 0.07354811 0.07359300 0.07369423 0.07370257
## 1052 642 1391 3495 182 715
## 0.07379611 0.07396585 0.07400414 0.07400928 0.07409057 0.07415208
## 1253 3718 791 1780 2984 1895
## 0.07419645 0.07419646 0.07431209 0.07440412 0.07440526 0.07443735
## 3629 1310 1031 1025 558 75
## 0.07444422 0.07447268 0.07448376 0.07450654 0.07461791 0.07465991
## 605 1457 1045 3551 2012 1821
## 0.07470904 0.07474364 0.07476000 0.07476477 0.07480444 0.07485598
## 2832 2084 232 1705 3854 1177
## 0.07490842 0.07492194 0.07501277 0.07508608 0.07516297 0.07517283
## 406 2598 480 2198 1456 3169
## 0.07518390 0.07521854 0.07540272 0.07546882 0.07550579 0.07553424
## 363 2912 1650 3582 2957 1285
## 0.07557889 0.07558804 0.07591984 0.07599068 0.07600400 0.07603419
## 1306 3418 339 3853 1486 980
## 0.07629952 0.07630222 0.07639735 0.07640172 0.07640813 0.07641323
## 2051 3542 3538 3557 1182 937
## 0.07646000 0.07651616 0.07655297 0.07655297 0.07669845 0.07670802
## 2603 1808 676 932 319 36
## 0.07674422 0.07679865 0.07684054 0.07685845 0.07692831 0.07698367
## 1127 2142 2670 426 2604 2566
## 0.07700685 0.07705593 0.07708282 0.07723511 0.07726840 0.07734350
## 1485 198 1431 570 3070 1315
## 0.07748106 0.07750344 0.07754343 0.07754525 0.07756922 0.07768539
## 3121 1716 2611 1709 3078 141
## 0.07799683 0.07819565 0.07820140 0.07825551 0.07836211 0.07839110
## 1056 1247 2578 482 3341 1383
## 0.07839939 0.07870321 0.07872132 0.07873290 0.07882620 0.07889290
## 2225 3515 2704 2113 1448 1181
## 0.07899745 0.07913695 0.07914593 0.07915952 0.07927969 0.07942958
## 11 759 818 2929 2124 193
## 0.07953051 0.07959650 0.07984775 0.07995196 0.08007628 0.08013831
## 2445 2563 1239 2444 773 3452
## 0.08019378 0.08026110 0.08034526 0.08040637 0.08042521 0.08050429
## 797 2666 1840 3054 1226 308
## 0.08082498 0.08084921 0.08086325 0.08091485 0.08098891 0.08104361
## 769 2352 53 3065 2350 887
## 0.08107122 0.08111878 0.08116321 0.08131089 0.08137184 0.08139770
## 1341 1360 2154 3151 1857 3079
## 0.08144050 0.08145822 0.08159133 0.08160509 0.08178872 0.08179187
## 2964 1175 1155 2078 2513 263
## 0.08182668 0.08186546 0.08188135 0.08199245 0.08199785 0.08203375
## 1399 608 1614 1759 601 3648
## 0.08216557 0.08216719 0.08217716 0.08217970 0.08224730 0.08239666
## 2737 2874 2608 842 1989 1967
## 0.08250611 0.08251465 0.08263113 0.08266966 0.08268232 0.08271306
## 2764 738 196 3125 422 893
## 0.08272874 0.08280012 0.08282813 0.08294746 0.08299300 0.08307358
## 394 3128 974 3702 1328 1629
## 0.08308542 0.08314186 0.08318942 0.08334643 0.08342524 0.08352806
## 1940 2967 1555 2224 3387 620
## 0.08358037 0.08358933 0.08362195 0.08364063 0.08364965 0.08365327
## 2443 633 2483 472 1104 269
## 0.08373463 0.08379097 0.08396607 0.08404502 0.08405169 0.08408314
## 936 279 2615 3627 1951 2156
## 0.08409821 0.08422920 0.08441442 0.08453334 0.08458961 0.08462078
## 1297 2462 2408 2222 226 2023
## 0.08471371 0.08479332 0.08494747 0.08498991 0.08503419 0.08514520
## 3317 1444 1973 2190 819 3851
## 0.08521218 0.08528849 0.08542577 0.08547070 0.08547856 0.08551853
## 2738 2069 3873 2118 3013 2217
## 0.08560109 0.08570951 0.08585085 0.08596004 0.08600502 0.08601083
## 432 554 2206 779 1493 283
## 0.08601754 0.08606884 0.08610630 0.08612489 0.08616347 0.08616721
## 3683 1639 3096 956 3587 3353
## 0.08617847 0.08618840 0.08622190 0.08626857 0.08640372 0.08642357
## 419 2644 1787 832 1088 2213
## 0.08647509 0.08674384 0.08676238 0.08684371 0.08689145 0.08701129
## 2900 2574 2205 3947 3832 1414
## 0.08714827 0.08717345 0.08728389 0.08752954 0.08755917 0.08784101
## 1725 772 3485 2021 1641 1520
## 0.08788430 0.08810695 0.08811174 0.08826567 0.08843599 0.08850500
## 1809 94 2618 333 68 2311
## 0.08851707 0.08852110 0.08854514 0.08856270 0.08860315 0.08863078
## 1121 2200 92 3349 1835 3998
## 0.08867943 0.08871112 0.08891058 0.08924856 0.08927385 0.08928179
## 3171 2220 880 964 2307 358
## 0.08934880 0.08941130 0.08951435 0.08954287 0.08966565 0.08989428
## 3240 2671 3494 293 2108 3934
## 0.08995441 0.08997883 0.08999462 0.09011238 0.09011769 0.09012291
## 1263 370 3691 1764 2777 2802
## 0.09014857 0.09020209 0.09050778 0.09063144 0.09064294 0.09069266
## 1815 1841 3994 3204 262 3649
## 0.09072619 0.09081376 0.09086764 0.09088551 0.09104884 0.09117957
## 328 3479 186 282 1068 2232
## 0.09160559 0.09208411 0.09215741 0.09218470 0.09249264 0.09262318
## 1775 1507 1170 2417 2234 1016
## 0.09263318 0.09280150 0.09301477 0.09333173 0.09338601 0.09366226
## 2624 3030 1223 2903 102 616
## 0.09378374 0.09379755 0.09407748 0.09407981 0.09412334 0.09413666
## 1380 2041 2542 2818 3736 2570
## 0.09420436 0.09464093 0.09465956 0.09467746 0.09503196 0.09526706
## 3714 3540 3766 3721 1564 1497
## 0.09533101 0.09541182 0.09543267 0.09546379 0.09548653 0.09631073
## 1272 957 968 3488 2795 3550
## 0.09668036 0.09695877 0.09714878 0.09733528 0.09750259 0.09762614
## 2510 2616 765 3375 1286 3396
## 0.09765649 0.09825175 0.09825321 0.09849782 0.09893527 0.09894577
## 425 1756 3382 1467 2911 268
## 0.09904788 0.09912216 0.09949392 0.09961125 0.09966006 0.09977767
## 2386 1999 2379 846 435 1210
## 0.10006596 0.10031020 0.10038581 0.10055476 0.10109772 0.10134895
## 1403 2143 2901 2836 1296 2867
## 0.10147002 0.10153782 0.10167199 0.10170801 0.10180797 0.10189864
## 369 220 3199 1309 1008 2554
## 0.10194293 0.10208386 0.10243290 0.10246246 0.10270711 0.10281293
## 1807 2804 1659 1526 3224 488
## 0.10282060 0.10297114 0.10305073 0.10306444 0.10322080 0.10374572
## 1499 2847 1548 966 2032 1970
## 0.10398153 0.10406945 0.10426313 0.10433987 0.10461885 0.10467604
## 3446 465 3422 606 2054 2943
## 0.10471410 0.10482553 0.10566671 0.10571824 0.10580262 0.10588969
## 2437 1684 324 3778 2369 3956
## 0.10594319 0.10650158 0.10667478 0.10700800 0.10724752 0.10727820
## 2467 3084 499 3558 883 3708
## 0.10750112 0.10755637 0.10776720 0.10823260 0.10830048 0.10830321
## 473 3727 154 2492 280 3049
## 0.10834081 0.10885529 0.10890220 0.10902711 0.10922921 0.10923269
## 559 2 1455 811 3932 2047
## 0.10924753 0.10940092 0.11010841 0.11016044 0.11035078 0.11079918
## 3624 1267 1777 831 1686 2677
## 0.11098481 0.11103448 0.11106497 0.11112371 0.11116630 0.11125545
## 2657 1475 3914 3728 2775 2325
## 0.11149455 0.11162246 0.11173708 0.11184944 0.11205720 0.11222029
## 51 3055 593 1727 3480 2494
## 0.11226384 0.11263049 0.11274503 0.11284441 0.11296583 0.11321196
## 2292 3861 896 468 1179 2958
## 0.11325066 0.11358959 0.11365535 0.11369746 0.11372940 0.11414784
## 3016 924 213 2514 2541 3539
## 0.11437557 0.11480098 0.11509449 0.11518460 0.11571371 0.11573225
## 2919 2278 1278 1462 2265 3764
## 0.11573365 0.11576873 0.11579720 0.11604676 0.11627303 0.11642084
## 2780 2866 3637 3440 2778 3203
## 0.11648847 0.11658316 0.11669166 0.11690265 0.11705546 0.11747539
## 3098 1830 965 750 2636 786
## 0.11789068 0.11797879 0.11802194 0.11830753 0.11836100 0.11851758
## 929 2105 1522 375 2328 1452
## 0.11868870 0.11875287 0.11912350 0.11912996 0.11937206 0.11947157
## 3381 3716 3279 2829 3057 3214
## 0.11950403 0.11956730 0.11959352 0.11966039 0.11986977 0.12012584
## 3849 872 1509 562 709 3094
## 0.12025111 0.12033249 0.12057997 0.12064463 0.12078620 0.12093452
## 3532 1919 551 248 3668 1095
## 0.12116375 0.12150716 0.12170724 0.12208828 0.12219126 0.12225567
## 950 3237 3715 2404 2397 2354
## 0.12238419 0.12241922 0.12281055 0.12319378 0.12346052 0.12364864
## 3576 1505 661 1156 3116 2970
## 0.12386405 0.12390321 0.12419006 0.12433837 0.12450860 0.12477699
## 3045 3379 3535 2706 1711 3085
## 0.12489670 0.12570328 0.12570948 0.12572027 0.12617628 0.12653115
## 1207 2672 2419 1571 1283 3012
## 0.12703382 0.12704112 0.12737913 0.12745846 0.12979866 0.12997571
## 2864 625 1738 2519 2109 1773
## 0.13040926 0.13043809 0.13054956 0.13092961 0.13106001 0.13138567
## 32 1086 1774 2313 1412 1352
## 0.13219839 0.13301920 0.13347781 0.13381900 0.13382239 0.13432829
## 3004 3573 935 2141 3651 889
## 0.13452739 0.13456921 0.13457382 0.13478423 0.13488186 0.13502517
## 721 603 2208 1114 2425 3301
## 0.13554004 0.13554470 0.13575843 0.13596212 0.13600988 0.13618390
## 3136 3498 2029 3391 588 3456
## 0.13623978 0.13646096 0.13654657 0.13664367 0.13682465 0.13742294
## 3602 1992 2499 3314 3657 825
## 0.13767812 0.13776505 0.13779975 0.13860028 0.13959844 0.14053069
## 975 2555 2629 673 2948 396
## 0.14091064 0.14132942 0.14135363 0.14145188 0.14189488 0.14211155
## 2085 3518 3570 48 3653 1879
## 0.14219280 0.14329351 0.14329950 0.14369720 0.14405954 0.14433675
## 2985 1884 149 1871 2650 3979
## 0.14454533 0.14459436 0.14491490 0.14575760 0.14609092 0.14792861
## 2155 1868 63 611 598 970
## 0.14825829 0.14854068 0.14860306 0.14866241 0.14924688 0.14931375
## 1733 807 1706 3369 502 2106
## 0.14950548 0.14962175 0.14968759 0.14982143 0.14985870 0.15057048
## 760 1178 2489 3791 3618 1289
## 0.15076287 0.15120470 0.15174592 0.15311013 0.15325912 0.15372468
## 52 1168 744 1450 1240 1676
## 0.15449864 0.15529287 0.15629791 0.15661160 0.15677915 0.15684181
## 312 1081 1703 1898 3623 3117
## 0.15695157 0.15720095 0.15774175 0.15833037 0.15860472 0.15915024
## 3458 1301 3868 1810 207 2723
## 0.15947481 0.15950263 0.15971518 0.16003466 0.16144618 0.16161390
## 2458 2476 3389 2125 3140 1103
## 0.16235118 0.16324059 0.16341348 0.16399041 0.16421294 0.16523523
## 971 591 2526 3266 113 2567
## 0.16648510 0.16720892 0.16784380 0.16918629 0.16929707 0.16949268
## 2950 3072 921 697 3604 2414
## 0.16979397 0.17060374 0.17151145 0.17237329 0.17241298 0.17282933
## 1682 3209 2413 3866 1252 2700
## 0.17340911 0.17368283 0.17500678 0.17552025 0.17763129 0.17873898
## 3628 2747 1469 2720 1558 1349
## 0.17926547 0.18006430 0.18016431 0.18025966 0.18127975 0.18241245
## 338 2713 747 1890 315 12
## 0.18359193 0.18386063 0.18393381 0.18594495 0.18755133 0.18771054
## 755 1536 3675 2380 2065 405
## 0.18777502 0.18924814 0.18974599 0.19089111 0.19115626 0.19148103
## 3052 3913 1126 137 2457 539
## 0.19151148 0.19165604 0.19261704 0.19314177 0.19371408 0.19379773
## 3311 439 3972 3191 1644 3690
## 0.19418748 0.19433820 0.19465789 0.19626971 0.19637657 0.19644978
## 2935 2072 1480 3507 2226 2447
## 0.19790618 0.19827737 0.19883595 0.19985840 0.20092098 0.20175097
## 1623 3457 57 1954 55 2701
## 0.20573806 0.21026841 0.21063265 0.21239679 0.21581575 0.21729799
## 614 3679 1569 1982 942 47
## 0.21924412 0.22228474 0.22404744 0.22416946 0.22728475 0.22856576
## 3673 3966 2347 2110 1165 1202
## 0.22925063 0.23101550 0.23235170 0.23266799 0.23574156 0.23790915
## 668 3192 1441 1608 40 1287
## 0.24138956 0.24151676 0.24474332 0.24617920 0.24673473 0.24676285
## 3553 602 958 691 60 2429
## 0.24769923 0.24999327 0.25187127 0.25188453 0.25374341 0.25629614
## 875 3435 20 3967 1609 1473
## 0.25699839 0.25741369 0.26138785 0.26363419 0.26749556 0.26860436
## 2675 1873 2359 870 2596 98
## 0.26940503 0.26981336 0.27087264 0.27225821 0.27658640 0.27838685
## 1631 2584 1422 1700 3915 943
## 0.27967878 0.28491738 0.28683462 0.29409895 0.30353269 0.30597594
## 390 56 1213 2590 87 70
## 0.30801942 0.30924196 0.31277121 0.31523203 0.32477208 0.32899194
## 864 726 955 853 3497 194
## 0.35200130 0.35861403 0.35975626 0.36337988 0.37904522 0.40610645
## 847 1365 1125 90
## 0.46008411 0.48322861 0.50381494 0.539262224. Which records does your model predict to have a greater than 40% probability of responding to the Florence mailing? What are the Rcode, Fcode, and Mcode values for these particular records? (you can simply look at your validation data and inspect it manually – there won’t be very many rows to check here).
The records that have a greater 40% probability of responding are 194, 847, 1365, 1125 and 90 with the corresponding probabilities of 0.40610645, 0.46008411, 0.48322861, 0.50381494 and 0.53926222.
library(dplyr)
d2<-valid.df %>% select(Seq.,Rcode,Fcode,Mcode) %>% filter(Seq. %in% c(194,847,1365,1125,90))
d2## Seq. Rcode Fcode Mcode
## 1 90 1 3 5
## 2 194 3 3 5
## 3 847 4 3 5
## 4 1125 3 3 5
## 5 1365 3 3 5II. Read the German Credit case (pp. 505-509 in the text)
A. Create a data partition. Again, for the data partition, use your unique seed value. Show the code that you used to do this.
g1<-read.csv("germancredit.csv") #importing the data
head(g1,10)## OBS. CHK_ACCT DURATION HISTORY NEW_CAR USED_CAR FURNITURE RADIO.TV
## 1 1 0 6 4 0 0 0 1
## 2 2 1 48 2 0 0 0 1
## 3 3 3 12 4 0 0 0 0
## 4 4 0 42 2 0 0 1 0
## 5 5 0 24 3 1 0 0 0
## 6 6 3 36 2 0 0 0 0
## 7 7 3 24 2 0 0 1 0
## 8 8 1 36 2 0 1 0 0
## 9 9 3 12 2 0 0 0 1
## 10 10 1 30 4 1 0 0 0
## EDUCATION RETRAINING AMOUNT SAV_ACCT EMPLOYMENT INSTALL_RATE MALE_DIV
## 1 0 0 1169 4 4 4 0
## 2 0 0 5951 0 2 2 0
## 3 1 0 2096 0 3 2 0
## 4 0 0 7882 0 3 2 0
## 5 0 0 4870 0 2 3 0
## 6 1 0 9055 4 2 2 0
## 7 0 0 2835 2 4 3 0
## 8 0 0 6948 0 2 2 0
## 9 0 0 3059 3 3 2 1
## 10 0 0 5234 0 0 4 0
## MALE_SINGLE MALE_MAR_or_WID CO.APPLICANT GUARANTOR PRESENT_RESIDENT
## 1 1 0 0 0 4
## 2 0 0 0 0 2
## 3 1 0 0 0 3
## 4 1 0 0 1 4
## 5 1 0 0 0 4
## 6 1 0 0 0 4
## 7 1 0 0 0 4
## 8 1 0 0 0 2
## 9 0 0 0 0 4
## 10 0 1 0 0 2
## REAL_ESTATE PROP_UNKN_NONE AGE OTHER_INSTALL RENT OWN_RES NUM_CREDITS
## 1 1 0 67 0 0 1 2
## 2 1 0 22 0 0 1 1
## 3 1 0 49 0 0 1 1
## 4 0 0 45 0 0 0 1
## 5 0 1 53 0 0 0 2
## 6 0 1 35 0 0 0 1
## 7 0 0 53 0 0 1 1
## 8 0 0 35 0 1 0 1
## 9 1 0 61 0 0 1 1
## 10 0 0 28 0 0 1 2
## JOB NUM_DEPENDENTS TELEPHONE FOREIGN RESPONSE
## 1 2 1 1 0 1
## 2 2 1 0 0 0
## 3 1 2 0 0 1
## 4 2 2 0 0 1
## 5 2 2 0 0 0
## 6 1 2 1 0 1
## 7 2 1 0 0 1
## 8 3 1 1 0 1
## 9 1 1 0 0 1
## 10 3 1 0 0 0names(g1)## [1] "OBS." "CHK_ACCT" "DURATION"
## [4] "HISTORY" "NEW_CAR" "USED_CAR"
## [7] "FURNITURE" "RADIO.TV" "EDUCATION"
## [10] "RETRAINING" "AMOUNT" "SAV_ACCT"
## [13] "EMPLOYMENT" "INSTALL_RATE" "MALE_DIV"
## [16] "MALE_SINGLE" "MALE_MAR_or_WID" "CO.APPLICANT"
## [19] "GUARANTOR" "PRESENT_RESIDENT" "REAL_ESTATE"
## [22] "PROP_UNKN_NONE" "AGE" "OTHER_INSTALL"
## [25] "RENT" "OWN_RES" "NUM_CREDITS"
## [28] "JOB" "NUM_DEPENDENTS" "TELEPHONE"
## [31] "FOREIGN" "RESPONSE"A.Create a data partition. Again, for the data partition, use your unique seed value. Show the code that you used to do this.
Create training and validation sets
set.seed(60)
train.index2 <- sample(rownames(g1), dim(g1)[1]*0.6)
train.df2<- g1[train.index,]
valid.index <- setdiff(rownames(g1), train.index)
valid.df2<- g1[valid.index, ]B. Using your training data, build a classification tree model with RESPONSE as the outcome variable, and with the following input variables: CHK_ACCT, DURATION, HISTORY, EMPLOYMENT, REAL_ESTATE, and JOB.
C. Type the name of the variable that you created into the console to learn more about the model that you just created (for instance, if your model is named “tree”) type tree to learn about your splits and y-values. Show the result.
D. Use rpart.plot to get a visual depiction of your model, and show the result.
table(g1$RESPONSE)##
## 0 1
## 300 700g1$RESPONSE<-as.factor(g1$RESPONSE)Build Classification Trees
library(adabag)## Loading required package: rpart## Loading required package: foreach## Loading required package: doParallel## Loading required package: iterators## Loading required package: parallellibrary(rpart)
library(caret)
library(rpart.plot)
class.tree<-rpart(RESPONSE~CHK_ACCT+DURATION+HISTORY+EMPLOYMENT+REAL_ESTATE+JOB,data=train.df2, method = "class")
class.tree## n=573 (1827 observations deleted due to missingness)
##
## node), split, n, loss, yval, (yprob)
## * denotes terminal node
##
## 1) root 573 180 1 (0.31413613 0.68586387)
## 2) CHK_ACCT< 1.5 311 145 1 (0.46623794 0.53376206)
## 4) DURATION>=11.5 260 124 0 (0.52307692 0.47692308)
## 8) DURATION>=22.5 135 55 0 (0.59259259 0.40740741)
## 16) JOB< 2.5 108 40 0 (0.62962963 0.37037037)
## 32) CHK_ACCT< 0.5 58 15 0 (0.74137931 0.25862069) *
## 33) CHK_ACCT>=0.5 50 25 0 (0.50000000 0.50000000)
## 66) EMPLOYMENT< 2.5 31 12 0 (0.61290323 0.38709677) *
## 67) EMPLOYMENT>=2.5 19 6 1 (0.31578947 0.68421053) *
## 17) JOB>=2.5 27 12 1 (0.44444444 0.55555556)
## 34) CHK_ACCT>=0.5 16 5 0 (0.68750000 0.31250000) *
## 35) CHK_ACCT< 0.5 11 1 1 (0.09090909 0.90909091) *
## 9) DURATION< 22.5 125 56 1 (0.44800000 0.55200000)
## 18) HISTORY< 1.5 16 4 0 (0.75000000 0.25000000) *
## 19) HISTORY>=1.5 109 44 1 (0.40366972 0.59633028) *
## 5) DURATION< 11.5 51 9 1 (0.17647059 0.82352941) *
## 3) CHK_ACCT>=1.5 262 35 1 (0.13358779 0.86641221) *prp(class.tree, type = 1, extra = 1, under = TRUE, split.font
= 1, varlen = -10, box.palette = c("green","yellow","light blue","pink"))
E. For any one terminal node on your tree, describe what it says, step-by-step, from top to bottom (For instance, with a different data set, you could say something like, “For a car with 6 or more cylinders, and horsepower of greater than 200cc, the model predicts that it will be labeled as a “muscle car.”)
For the pink terminal node in the middle of the bottom, the first split is on CHK_ACCT of 1.5, then the next split is on Duration for the Checking Account Status less than 1.5. The fowllowing split is on Duration greater than 22 months for the Duration of Credit in Months more than 12 months. The fourth split is on Job greater than or equal to 2.5 for the Duration of Credit in Months more than 22 months. Next, the slipt is on CHK_ACCT greater than 0.5 for the Nature of Job greater than or equal to 2.5. The pink terminal node will be interpreted as belonging to the group with CHK_ACCT less than 1.5, Duration greater than 12, Duration more than 22, Job greater or equal to 2.5 and CHK_ACCT less than 0.5 than Response = 1pd. The number 10 underneath the prink node means 10 people with Response of 1 (1:Credit Rating is Good). And the number 1 on the left means 1 person with Response of 0 (0:Credit Rating isn’t Good).