MJRU Machine Learning
#Code for Part I of the Coursework
library(factoextra)
library(cluster)
library(dplyr)
library(gridExtra)
setwd(
"C:/Users/mario/OneDrive/Desktop/Pgd Data Science LSE/All Modules/Machine Learning ST3189-02/Assignment"
)
rawdata <-
read.csv(
file.path(
"C:/Users/mario/OneDrive/Desktop/Pgd Data Science LSE/All Modules/Machine Learning ST3189-02/Assignment",
"EWCS2016.csv"
)
)
#Examining and preparing the data for analysis
fix(rawdata)
sum(is.na(rawdata))[1] 0PCA <- prcomp(rawdata, scale = TRUE)
PCA$rotation PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8
Gender 0.03250008 -0.1353988 0.806433781 0.55980792 -0.079270587 0.01723492 -9.778808e-02 0.01121574
Age 0.07433619 -0.2286655 -0.571101171 0.77127404 0.039682492 0.01009599 -8.934509e-05 -0.11385839
Cheerful 0.39153563 -0.2012996 -0.038289519 -0.08139296 -0.029721482 0.04231147 -1.685158e-01 -0.09686466
Relaxed 0.37789256 -0.2349038 0.076367267 -0.17083588 -0.038691987 0.06585140 1.535974e-01 -0.37141368
Active 0.39775839 -0.2056781 -0.004228871 -0.03981414 -0.014373522 0.04361610 1.144235e-01 0.14266717
Rested 0.37318465 -0.2474400 0.062722984 -0.08653645 0.003542394 0.13204170 3.688870e-01 -0.16576409
Interesting 0.36212158 -0.1250589 -0.063064281 -0.08683617 -0.042949130 -0.09205940 -7.207503e-01 0.40470810
Energy.at.Work 0.33562141 0.3044394 0.004890486 0.13487302 0.133265454 -0.25240318 4.765136e-01 0.61891947
Enthusiastic.at.Work 0.27686474 0.4407964 0.045355458 0.06943711 0.265531252 -0.60261022 -1.577092e-01 -0.48309038
Time.Flies.at.Work 0.22206255 0.5057896 0.012505515 0.09870101 0.359531100 0.72996141 -1.330233e-01 -0.06264288
I.am.good.at.Work 0.17348428 0.4143672 -0.077739182 0.08107621 -0.877592231 0.07727847 1.279804e-02 -0.08716387
PC9 PC10 PC11
Gender -0.023777600 -0.001102509 0.0074027519
Age 0.009788407 -0.075608639 -0.0267056073
Cheerful -0.603089402 0.320018154 0.5399120579
Relaxed -0.305536677 -0.587941391 -0.4007481315
Active 0.098727247 0.641330892 -0.5841863884
Rested 0.638204820 -0.046970070 0.4444878589
Interesting 0.264062221 -0.279657290 -0.0135745676
Energy.at.Work -0.194300386 -0.201698952 0.0801972500
Enthusiastic.at.Work 0.127521607 0.116074876 -0.0231568523
Time.Flies.at.Work 0.009045759 -0.005259619 -0.0336416722
I.am.good.at.Work 0.037306587 0.017094203 0.0009229801Table1 <- PCA$rotation
pdf("table1.pdf", width = 25, height = 25) # Export PDF
grid.table(Table1) #Export PDF
dev.off() #Export PDFnull device
1 summary(PCA)Importance of components:
PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10 PC11
Standard deviation 2.0866 1.1905 1.01062 0.97002 0.88699 0.75100 0.71833 0.65685 0.6025 0.57038 0.52925
Proportion of Variance 0.3958 0.1288 0.09285 0.08554 0.07152 0.05127 0.04691 0.03922 0.0330 0.02958 0.02546
Cumulative Proportion 0.3958 0.5246 0.61749 0.70303 0.77456 0.82583 0.87274 0.91196 0.9450 0.97454 1.00000plot(PCA)
biplot(PCA)
#Clustering
cleaned_data <- na.omit(rawdata)
cleaned_data <- scale(rawdata)
set.seed(220)
clustered_data <- kmeans(cleaned_data, 9, nstart = 25)did not converge in 10 iterationsdid not converge in 10 iterationsdid not converge in 10 iterationsdid not converge in 10 iterationsattributes(clustered_data)$names
[1] "cluster" "centers" "totss" "withinss" "tot.withinss" "betweenss" "size" "iter"
[9] "ifault"
$class
[1] "kmeans"wssplot <- function(clustered_data,
nc = 15,
seed = 1234) {
wss <- (nrow(clustered_data) - 1) * sum(apply(clustered_data, 2, var))
for (i in 2:nc) {
set.seed(seed)
wss[i] <- sum(kmeans(clustered_data, centers = i)$withinss)
}
plot(1:nc,
wss,
type = "b",
xlab = "Number of Clusters",
ylab = "Within groups sum of squares")
}
#choosing the value of k
wssplot(cleaned_data, nc = 10)did not converge in 10 iterations
#plotting the elbow plot
#we will choose then 4 as the numbers of clusters, and we run the cluster analysis again
distance <- dist(cleaned_data, method = "euclidean") #choosing the distance method
set.seed(221)
clustered_data <- kmeans(cleaned_data, 4, nstart = 25)
clustered_dataK-means clustering with 4 clusters of sizes 2361, 1259, 2187, 2006
Cluster means:
Gender Age Cheerful Relaxed Active Rested Interesting Energy.at.Work Enthusiastic.at.Work
1 -0.98214313 -0.0007499299 -0.003888113 -0.03134145 -0.02648324 -0.04635706 0.03038411 0.11063821 0.1765084
2 0.16041364 0.2589998645 1.470128187 1.36879220 1.48694844 1.35671790 1.29397307 1.05343842 0.7895254
3 1.01788709 -0.0295338135 -0.046381693 0.03527680 -0.01698223 0.05129799 -0.02956709 0.09765482 0.1007282
4 -0.05445658 -0.1294714829 -0.867534790 -0.86064935 -0.88354986 -0.85286517 -0.81564594 -0.89783991 -0.8130814
Time.Flies.at.Work I.am.good.at.Work
1 0.17460479 0.17225232
2 0.59290092 0.43430256
3 0.09858212 0.07665649
4 -0.68509634 -0.55888455
Clustering vector:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
1 3 3 1 3 1 1 3 3 3 3 1 1 3 1 1 1 1 4 1 2 2 1 3 3
26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
3 3 1 3 1 2 1 3 3 3 1 2 1 3 1 1 4 3 1 1 3 1 1 3 3
51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75
3 3 1 2 1 3 1 4 4 1 1 3 3 3 1 2 2 3 3 1 2 1 3 3 3
76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
1 3 3 1 1 2 1 2 3 3 3 3 1 2 1 4 1 4 4 1 4 3 1 1 1
101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125
2 1 2 1 3 3 3 2 3 1 4 1 3 4 4 3 4 3 2 3 4 4 4 2 3
126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150
4 1 1 3 3 2 1 1 2 2 3 1 2 1 1 1 1 1 4 1 4 4 4 1 2
151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175
1 2 2 3 1 1 3 2 1 1 1 4 1 4 1 1 3 1 4 2 3 1 3 1 1
176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200
2 1 1 1 1 3 3 4 1 2 3 1 3 3 3 1 3 4 3 2 1 1 2 3 3
201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225
2 1 3 1 2 2 2 1 2 3 1 4 2 4 4 1 2 1 4 1 3 3 2 1 2
226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250
2 1 2 1 1 3 1 3 3 1 1 1 1 1 3 1 1 4 1 1 1 3 3 4 2
251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275
2 3 2 1 3 1 3 2 3 3 1 3 3 3 1 1 1 1 4 3 2 1 4 1 3
276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300
1 3 2 3 4 4 4 4 4 2 1 1 4 1 1 1 4 4 4 1 4 3 4 4 3
301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325
4 3 1 1 3 2 3 1 3 2 1 1 3 4 1 3 3 3 1 1 1 1 1 2 2
326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350
4 3 1 1 4 1 1 3 1 1 3 3 1 1 1 2 1 1 1 1 1 1 1 3 3
351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375
4 3 1 3 1 3 1 1 4 3 2 3 1 4 1 1 1 1 4 3 2 1 1 3 1
376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400
1 3 1 1 3 4 1 4 1 2 1 3 2 1 3 2 1 1 3 3 1 3 1 3 2
401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425
1 1 1 4 4 3 1 3 1 3 1 3 1 3 1 1 4 2 3 4 4 1 4 4 3
426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450
4 3 2 1 2 3 1 3 3 2 3 2 1 2 2 2 2 3 3 2 3 3 3 3 2
451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475
3 1 4 3 1 3 3 2 1 2 3 3 2 4 2 3 1 3 1 3 3 1 1 1 3
476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500
4 1 2 4 1 2 2 4 2 2 4 2 2 4 1 2 4 2 3 4 4 4 1 3 1
501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525
4 2 4 4 1 1 1 3 3 1 3 1 3 3 2 1 3 3 2 1 2 3 2 1 2
526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550
3 1 4 1 4 3 3 4 3 3 4 4 2 4 3 1 2 4 4 4 4 3 1 1 1
551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575
1 1 3 2 1 3 3 3 1 3 1 1 1 4 2 3 3 2 1 4 1 4 4 4 4
576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600
1 1 3 3 3 4 1 1 1 4 3 3 4 4 4 4 1 1 4 3 3 1 2 2 2
601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625
3 2 2 1 4 2 1 1 3 2 1 2 1 1 1 1 4 4 3 3 2 4 2 3 4
626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650
1 4 1 3 1 1 1 4 3 4 3 1 3 3 3 1 3 3 1 1 4 3 1 3 4
651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675
4 4 4 3 4 2 4 4 3 3 3 2 4 3 3 4 1 1 1 4 4 1 4 1 4
676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700
4 3 1 1 1 1 1 1 1 1 3 1 1 3 1 2 3 1 3 3 1 4 4 3 4
701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725
4 4 3 4 4 3 4 3 4 4 3 4 4 2 3 4 3 2 1 2 3 2 1 2 2
726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750
3 3 2 2 1 2 1 3 2 2 1 1 2 1 2 3 2 1 1 2 2 3 3 1 3
751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775
3 1 3 1 3 4 1 3 2 2 4 1 2 2 1 4 3 1 3 4 3 3 4 3 1
776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800
3 1 1 3 2 1 3 3 3 3 2 2 2 3 1 3 2 2 4 2 3 2 3 1 2
801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825
1 2 3 1 3 4 3 1 1 3 1 3 1 3 4 3 1 1 1 3 3 1 3 4 1
826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850
4 1 1 3 2 4 3 4 1 4 3 4 4 3 3 1 3 2 3 4 1 1 1 1 4
851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875
1 4 1 4 4 3 2 2 2 2 1 1 1 1 2 1 1 4 1 3 1 1 1 3 1
876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900
2 4 4 2 2 3 2 2 3 4 2 4 4 4 2 2 2 1 2 1 3 2 3 3 4
901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925
3 3 2 3 1 3 4 1 3 1 3 3 1 2 2 1 4 1 1 1 1 1 3 4 1
926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950
1 2 2 1 3 4 1 3 3 3 3 3 3 3 3 2 1 3 1 1 3 2 1 4 4
951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975
4 4 2 4 4 2 4 2 3 3 1 1 1 1 3 3 3 1 1 1 1 1 1 3 3
976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000
1 3 2 1 2 1 3 2 3 3 4 4 4 1 1 1 3 3 4 1 2 3 1 1 4
[ reached getOption("max.print") -- omitted 6813 entries ]
Within cluster sum of squares by cluster:
[1] 14793.76 14018.34 14540.81 10511.09
(between_SS / total_SS = 37.3 %)
Available components:
[1] "cluster" "centers" "totss" "withinss" "tot.withinss" "betweenss" "size" "iter"
[9] "ifault" #hirearchical clustering
hc.complete<- hclust(dist(cleaned_data), method="average")
#plotting hierarchical clustering
plot(hc.complete)
hc <- as.dendrogram(hc.complete)
plot(hc)
cutree(hc.complete, 1) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[ reached getOption("max.print") -- omitted 6813 entries ]#Part 2 linear regression
#loading and cleaning our data (removing variables 31 and 32)
library(ISLR)
setwd( "C:/Users/mario/OneDrive/Desktop/Pgd Data Science LSE/All Modules/Machine Learning ST3189-02/Assignment")
student_mat <- read.csv("student-mat.csv", stringsAsFactors=TRUE)
fix(student_mat)
student_mat <- student_mat[-c (31:32)]
fix(student_mat)
#training and test data
data <- student_mat
dt <- sort(sample(nrow(data), nrow(data)*.7))
train_data_math <-data[dt,]
test_data_math <-data[-dt,]
#linear regression on student math
studentmat <-
glm(
G3 ~ school + sex + age + address + famsize + Pstatus + Medu + Fedu + Mjob +
Fjob + reason + guardian + traveltime + studytime + failures + schoolsup +
famsup + paid + activities + nursery + higher + internet + romantic + famrel +
freetime + goout + Dalc + Walc + health + absences,
data = train_data_math
)
summary(studentmat)
Call:
glm(formula = G3 ~ school + sex + age + address + famsize + Pstatus +
Medu + Fedu + Mjob + Fjob + reason + guardian + traveltime +
studytime + failures + schoolsup + famsup + paid + activities +
nursery + higher + internet + romantic + famrel + freetime +
goout + Dalc + Walc + health + absences, data = train_data_math)
Deviance Residuals:
Min 1Q Median 3Q Max
-12.2638 -1.9382 0.5747 2.7816 8.8798
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 12.519260 5.592784 2.238 0.026124 *
schoolMS 0.492312 0.977125 0.504 0.614846
sexM 1.381728 0.622543 2.219 0.027405 *
age -0.312930 0.267734 -1.169 0.243659
addressU 0.229502 0.774558 0.296 0.767261
famsizeLE3 0.413524 0.591686 0.699 0.485308
PstatusT -0.309014 0.854252 -0.362 0.717873
Medu 0.568449 0.409285 1.389 0.166177
Fedu -0.163780 0.340152 -0.481 0.630613
Mjobhealth 0.785001 1.459917 0.538 0.591289
Mjobother -0.757871 0.927197 -0.817 0.414537
Mjobservices -0.003451 1.011821 -0.003 0.997282
Mjobteacher -1.682537 1.321844 -1.273 0.204316
Fjobhealth 1.046985 1.828371 0.573 0.567439
Fjobother -0.222136 1.253531 -0.177 0.859497
Fjobservices -0.134095 1.282644 -0.105 0.916825
Fjobteacher 2.798164 1.554007 1.801 0.073041 .
reasonhome 0.199092 0.688918 0.289 0.772840
reasonother 0.936941 0.957937 0.978 0.329035
reasonreputation 0.552185 0.728428 0.758 0.449177
guardianmother 0.200890 0.681580 0.295 0.768450
guardianother 0.288552 1.269144 0.227 0.820341
traveltime -0.251397 0.447528 -0.562 0.574822
studytime 0.660738 0.348312 1.897 0.059052 .
failures -1.580488 0.440789 -3.586 0.000409 ***
schoolsupyes -1.596833 0.850907 -1.877 0.061803 .
famsupyes -0.717165 0.598228 -1.199 0.231802
paidyes 0.449249 0.591639 0.759 0.448413
activitiesyes -0.905042 0.548057 -1.651 0.099994 .
nurseryyes -0.547673 0.692534 -0.791 0.429841
higheryes 0.718958 1.320487 0.544 0.586636
internetyes 0.839272 0.781182 1.074 0.283758
romanticyes -1.430827 0.589982 -2.425 0.016051 *
famrel 0.447406 0.291416 1.535 0.126054
freetime 0.637623 0.304052 2.097 0.037050 *
goout -0.683421 0.278163 -2.457 0.014735 *
Dalc -0.390159 0.415094 -0.940 0.348215
Walc 0.111500 0.321152 0.347 0.728760
health -0.193789 0.194965 -0.994 0.321256
absences 0.068345 0.041793 1.635 0.103314
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for gaussian family taken to be 17.52319)
Null deviance: 5956.8 on 275 degrees of freedom
Residual deviance: 4135.5 on 236 degrees of freedom
AIC: 1612.4
Number of Fisher Scoring iterations: 2#validating in our test data (math students)
set.seed(300)
prediction_math_student <- predict.glm(studentmat, newdata=train_data_math, se.fit=TRUE, interval="confidence")
prediction_math_student_t <- predict.glm(studentmat, newdata=test_data_math, se.fit=TRUE, interval="confidence")
prediction_math_student$residual.scale[1] 4.18607prediction_math_student_t$residual.scale[1] 4.18607#LINEAR REGRESSION ON PORTUGESE STUDENT ON OUR TRAINING DATA
studentport <- read.csv("student-por.csv", stringsAsFactors=TRUE)
studentport <-studentport[-c(31:32)]
fix(studentport)
#training and data set
data <- studentport
dt <- sort(sample(nrow(data), nrow(data)*.7))
train_data_port <-data[dt,]
test_data_port <-data[-dt,]
#linear regression on portuguese students
studentport <- glm(
G3 ~ school + sex + age + address + famsize + Pstatus + Medu + Fedu + Mjob +
Fjob + reason + guardian + traveltime + studytime + failures + schoolsup +
famsup + paid + activities + nursery + higher + internet + romantic + famrel +
freetime + goout + Dalc + Walc + health + absences,
data = train_data_port
)
summary(studentport)
Call:
glm(formula = G3 ~ school + sex + age + address + famsize + Pstatus +
Medu + Fedu + Mjob + Fjob + reason + guardian + traveltime +
studytime + failures + schoolsup + famsup + paid + activities +
nursery + higher + internet + romantic + famrel + freetime +
goout + Dalc + Walc + health + absences, data = train_data_port)
Deviance Residuals:
Min 1Q Median 3Q Max
-11.720 -1.259 0.025 1.505 8.638
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 8.928826 2.437705 3.663 0.000282 ***
schoolMS -1.178771 0.326248 -3.613 0.000340 ***
sexM -0.655969 0.303323 -2.163 0.031143 *
age 0.204634 0.121853 1.679 0.093837 .
addressU 0.133383 0.314611 0.424 0.671814
famsizeLE3 0.191420 0.301737 0.634 0.526175
PstatusT -0.383306 0.430503 -0.890 0.373785
Medu -0.070484 0.185250 -0.380 0.703786
Fedu 0.343957 0.165092 2.083 0.037825 *
Mjobhealth 1.006232 0.639095 1.574 0.116144
Mjobother 0.148969 0.374025 0.398 0.690624
Mjobservices 0.658989 0.450885 1.462 0.144624
Mjobteacher 1.001839 0.593569 1.688 0.092199 .
Fjobhealth -1.233642 0.880788 -1.401 0.162079
Fjobother -1.077856 0.568139 -1.897 0.058501 .
Fjobservices -1.340193 0.595840 -2.249 0.025022 *
Fjobteacher -0.620300 0.778931 -0.796 0.426287
reasonhome 0.126423 0.344436 0.367 0.713774
reasonother -0.281983 0.463014 -0.609 0.542848
reasonreputation 0.431685 0.346268 1.247 0.213219
guardianmother -0.310488 0.323742 -0.959 0.338089
guardianother -0.043483 0.676403 -0.064 0.948774
traveltime -0.070673 0.193284 -0.366 0.714817
studytime 0.507495 0.169406 2.996 0.002902 **
failures -1.329406 0.269406 -4.935 1.17e-06 ***
schoolsupyes -1.752469 0.436211 -4.017 6.99e-05 ***
famsupyes -0.132641 0.280945 -0.472 0.637085
paidyes -0.632415 0.598788 -1.056 0.291511
activitiesyes 0.095792 0.272814 0.351 0.725673
nurseryyes -0.269798 0.336695 -0.801 0.423410
higheryes 1.999829 0.464804 4.303 2.11e-05 ***
internetyes -0.030293 0.347123 -0.087 0.930501
romanticyes -0.526521 0.280945 -1.874 0.061620 .
famrel 0.187938 0.139370 1.348 0.178240
freetime 0.000497 0.131053 0.004 0.996976
goout -0.112437 0.128650 -0.874 0.382635
Dalc -0.433413 0.189473 -2.287 0.022673 *
Walc -0.006046 0.146647 -0.041 0.967134
health -0.227855 0.091399 -2.493 0.013058 *
absences -0.008345 0.030763 -0.271 0.786314
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for gaussian family taken to be 7.076532)
Null deviance: 4800.0 on 453 degrees of freedom
Residual deviance: 2929.7 on 414 degrees of freedom
AIC: 2216.9
Number of Fisher Scoring iterations: 2#validating in our test data (portuguese students)
set.seed(250)
prediction_port_student <- predict.glm(studentport, newdata=train_data_port, se.fit=TRUE, interval="confidence")
prediction_port_student_t <- predict.glm(studentport, newdata=test_data_port, se.fit=TRUE, interval="confidence")
prediction_port_student$residual.scale[1] 2.660175prediction_port_student_t$residual.scale[1] 2.660175#WE WILL NOW TRY BOOSTED TREES
library(gbm)
student_mat <- read.csv("student-mat.csv", stringsAsFactors=TRUE)
student_mat <- student_mat[-c (31:32)]
fix(student_mat)
#set training and test data sets
data <- student_mat
dt <- sort(sample(nrow(data), nrow(data)*.7))
train_data_mat <-data[dt,]
test_data_mat <-data[-dt,]
#run the boosted tree function
set.seed(15)
treestudentmat <-
gbm(
G3 ~ school + sex + age + address + famsize + Pstatus + Medu + Fedu + Mjob +
Fjob + reason + guardian + traveltime + studytime + failures + schoolsup +
famsup + paid + activities + nursery + higher + internet + romantic + famrel +
freetime + goout + Dalc + Walc + health + absences,
data = train_data_mat, distribution="gaussian", n.trees=8000, interaction.depth=4
)
summary(treestudentmat)
#validating the data
set.seed(23)
prediction_boosted_tree<- predict(treestudentmat, newdata=train_data_math, n.trees = 10000)Number of trees not specified or exceeded number fit so far. Using 8000.prediction_boosted_tree_t <- predict(treestudentmat, newdata=test_data_math, n.trees= 10000)Number of trees not specified or exceeded number fit so far. Using 8000.mean ((prediction_boosted_tree)^2)[1] 132.039mean((prediction_boosted_tree_t)^2)[1] 114.67#our model perform slighlt worse in the validation set. lets see if changing the lambda value (shrinkage value) improves performance
#run the boosted tree function with a different lambda value
set.seed(19)
treestudentmat <-
gbm(
G3 ~ school + sex + age + address + famsize + Pstatus + Medu + Fedu + Mjob +
Fjob + reason + guardian + traveltime + studytime + failures + schoolsup +
famsup + paid + activities + nursery + higher + internet + romantic + famrel +
freetime + goout + Dalc + Walc + health + absences,
data = train_data_mat, distribution="gaussian", n.trees=8000, interaction.depth=4, shrinkage = 0.2
)
#re-test on the validation set
set.seed(60)
prediction_boosted_tree<- predict(treestudentmat, newdata=train_data_math, n.trees = 10000)Number of trees not specified or exceeded number fit so far. Using 8000.prediction_boosted_tree_t <- predict(treestudentmat, newdata=test_data_math, n.trees= 10000)Number of trees not specified or exceeded number fit so far. Using 8000.mean ((prediction_boosted_tree)^2)[1] 132.9829mean((prediction_boosted_tree_t)^2)[1] 109.8956#lets see if we can fit a Ridge Regression first and a Lasso later.
library(plyr)
library(readr)
library(dplyr)
library(caret)
library(ggplot2)
library(repr)
setwd(
"C:/Users/mario/OneDrive/Desktop/Pgd Data Science LSE/All Modules/Machine Learning ST3189-02/Assignment"
)
student_mat <- read.csv("student-mat.csv", stringsAsFactors=TRUE)
library(glmnet)
fix(student_mat)
student_mat <- student_mat[-c(31:32)]
data <- student_mat
dt <- sort(sample(nrow(data), nrow(data)*.7))
train_data_mat <-data[dt,]
test_data_mat <-data[-dt,]
#fitting a Ridge Regression
#we start preparing a grid with our x (only our predictors), and our y (our dependent variable)
x <- model.matrix(G3~.,train_data_mat)[,-1]
y=train_data_mat%>%select(G3)%>% unlist()%>% as.numeric() #here we transfrom qualitative variables into dummy variables
#we prepare the grid to cover all scenarios (from a null model to a least square fit -when lambda si really big-)
grid <-10^seq(10,-2 ,length=100)#here we are creating a grid with values from 10 to the 10th to 10 to the minuse 2, lenght=100
#ri fwe choose lambda zero a ridge will be choosen, lambda equals 1 will be a Lasso fittes
ridge_regression_student_math <- glmnet(x,y, alpha=0, lambda=grid) #remember that lambda is our shrinkage coefficient
dim(coef(ridge_regression_student_math))[1] 40 100coef(ridge_regression_student_math)40 x 100 sparse Matrix of class "dgCMatrix" [[ suppressing 56 column names 㤼㸱s0㤼㸲, 㤼㸱s1㤼㸲, 㤼㸱s2㤼㸲 ... ]]
[[ suppressing 56 column names 㤼㸱s0㤼㸲, 㤼㸱s1㤼㸲, 㤼㸱s2㤼㸲 ... ]]
(Intercept) 1.009058e+01 1.009058e+01 1.009058e+01 1.009058e+01 1.009058e+01 1.009058e+01 1.009058e+01 1.009058e+01
schoolMS -8.498804e-10 -1.123492e-09 -1.485190e-09 -1.963334e-09 -2.595412e-09 -3.430982e-09 -4.535556e-09 -5.995738e-09
sexM 4.867438e-10 6.434467e-10 8.505986e-10 1.124441e-09 1.486445e-09 1.964993e-09 2.597605e-09 3.433881e-09
age -4.225310e-10 -5.585611e-10 -7.383849e-10 -9.761013e-10 -1.290349e-09 -1.705765e-09 -2.254921e-09 -2.980872e-09
addressU 7.672038e-10 1.014198e-09 1.340710e-09 1.772340e-09 2.342929e-09 3.097215e-09 4.094336e-09 5.412471e-09
famsizeLE3 2.272078e-10 3.003554e-10 3.970521e-10 5.248795e-10 6.938598e-10 9.172419e-10 1.212540e-09 1.602906e-09
PstatusT -3.231438e-10 -4.271770e-10 -5.647029e-10 -7.465040e-10 -9.868344e-10 -1.304537e-09 -1.724521e-09 -2.279715e-09
Medu 4.115921e-10 5.441005e-10 7.192688e-10 9.508311e-10 1.256943e-09 1.661604e-09 2.196543e-09 2.903701e-09
Fedu 2.569265e-10 3.396417e-10 4.489864e-10 5.935336e-10 7.846165e-10 1.037217e-09 1.371140e-09 1.812566e-09
(Intercept) 1.009058e+01 1.009058e+01 1.009058e+01 1.009058e+01 1.009058e+01 1.009058e+01 1.009058e+01 1.009058e+01
schoolMS -7.926013e-09 -1.047772e-08 -1.385093e-08 -1.831012e-08 -2.420490e-08 -3.199745e-08 -4.229874e-08 -5.591645e-08
sexM 4.539389e-09 6.000805e-09 7.932711e-09 1.048658e-08 1.386264e-08 1.832559e-08 2.422535e-08 3.202449e-08
age -3.940538e-09 -5.209159e-09 -6.886202e-09 -9.103153e-09 -1.203383e-08 -1.590802e-08 -2.102946e-08 -2.779971e-08
addressU 7.154968e-09 9.458447e-09 1.250351e-08 1.652890e-08 2.185024e-08 2.888473e-08 3.818391e-08 5.047688e-08
famsizeLE3 2.118948e-09 2.801124e-09 3.702921e-09 4.895044e-09 6.470960e-09 8.554228e-09 1.130819e-08 1.494876e-08
PstatusT -3.013650e-09 -3.983867e-09 -5.266438e-09 -6.961921e-09 -9.203250e-09 -1.216616e-08 -1.608294e-08 -2.126070e-08
Medu 3.838521e-09 5.074299e-09 6.707925e-09 8.867482e-09 1.172229e-08 1.549618e-08 2.048503e-08 2.708001e-08
Fedu 2.396105e-09 3.167510e-09 4.187262e-09 5.535314e-09 7.317359e-09 9.673118e-09 1.278729e-08 1.690405e-08
(Intercept) 1.009058e+01 1.009058e+01 1.009058e+01 1.009058e+01 1.009058e+01 1.009058e+01 1.009058e+01 1.009058e+01
schoolMS -7.391825e-08 -9.771557e-08 -1.291742e-07 -1.707607e-07 -2.257356e-07 -2.984091e-07 -3.944792e-07 -5.214782e-07
sexM 4.233449e-08 5.596371e-08 7.398073e-08 9.779817e-08 1.292834e-07 1.709051e-07 2.259265e-07 2.986615e-07
age -3.674958e-08 -4.858079e-08 -6.422094e-08 -8.489630e-08 -1.122279e-07 -1.483587e-07 -1.961214e-07 -2.592609e-07
addressU 6.672746e-08 8.820978e-08 1.166081e-07 1.541491e-07 2.037760e-07 2.693798e-07 3.561042e-07 4.707488e-07
famsizeLE3 1.976138e-08 2.612338e-08 3.453357e-08 4.565134e-08 6.034839e-08 7.977702e-08 1.054605e-07 1.394126e-07
PstatusT -2.810540e-08 -3.715368e-08 -4.911498e-08 -6.492710e-08 -8.582981e-08 -1.134619e-07 -1.499900e-07 -1.982779e-07
Medu 3.579817e-08 4.732308e-08 6.255832e-08 8.269841e-08 1.093224e-07 1.445178e-07 1.910440e-07 2.525489e-07
Fedu 2.234615e-08 2.954030e-08 3.905053e-08 5.162250e-08 6.824190e-08 9.021176e-08 1.192546e-07 1.576475e-07
(Intercept) 1.009058e+01 1.009058e+01 1.009059e+01 1.009059e+01 1.009059e+01 1.009059e+01 1.009060e+01 1.009060e+01
schoolMS -6.893633e-07 -9.112973e-07 -1.204681e-06 -1.592516e-06 -2.105210e-06 -2.782960e-06 -3.678903e-06 -4.863282e-06
sexM 3.948129e-07 5.219195e-07 6.899469e-07 9.120692e-07 1.205702e-06 1.593867e-06 2.106999e-06 2.785329e-06
age -3.427276e-07 -4.530656e-07 -5.989258e-07 -7.917442e-07 -1.046639e-06 -1.383593e-06 -1.829027e-06 -2.417862e-06
addressU 6.223020e-07 8.226464e-07 1.087490e-06 1.437597e-06 1.900417e-06 2.512236e-06 3.321024e-06 4.390191e-06
famsizeLE3 1.842953e-07 2.436275e-07 3.220612e-07 4.257460e-07 5.628112e-07 7.440033e-07 9.835286e-07 1.300167e-06
PstatusT -2.621117e-07 -3.464962e-07 -4.580475e-07 -6.055117e-07 -8.004505e-07 -1.058148e-06 -1.398808e-06 -1.849141e-06
Medu 3.338546e-07 4.413360e-07 5.834199e-07 7.712463e-07 1.019541e-06 1.347772e-06 1.781673e-06 2.355262e-06
Fedu 2.084007e-07 2.754933e-07 3.641856e-07 4.814315e-07 6.364233e-07 8.413128e-07 1.112164e-06 1.470211e-06
(Intercept) 1.009061e+01 1.009062e+01 1.009063e+01 1.009065e+01 1.009067e+01 1.009069e+01 1.009073e+01 1.009078e+01
schoolMS -6.428953e-06 -8.498663e-06 -1.123467e-05 -1.485147e-05 -1.963259e-05 -2.595281e-05 -3.430752e-05 -4.535155e-05
sexM 3.682042e-06 4.867444e-06 6.434476e-06 8.506003e-06 1.124444e-05 1.486450e-05 1.965002e-05 2.597621e-05
age -3.196265e-06 -4.225263e-06 -5.585528e-06 -7.383705e-06 -9.760762e-06 -1.290305e-05 -1.705688e-05 -2.254787e-05
addressU 5.803562e-06 7.671944e-06 1.014182e-05 1.340682e-05 1.772290e-05 2.342842e-05 3.097062e-05 4.094069e-05
famsizeLE3 1.718744e-06 2.272079e-06 3.003555e-06 3.970524e-06 5.248800e-06 6.938607e-06 9.172433e-06 1.212542e-05
PstatusT -2.444452e-06 -3.231417e-06 -4.271735e-06 -5.646967e-06 -7.464931e-06 -9.868154e-06 -1.304504e-05 -1.724463e-05
Medu 3.113509e-06 4.115861e-06 5.440900e-06 7.192505e-06 9.507990e-06 1.256887e-05 1.661506e-05 2.196372e-05
Fedu 1.943524e-06 2.569212e-06 3.396324e-06 4.489701e-06 5.935051e-06 7.845667e-06 1.037130e-05 1.370988e-05
(Intercept) 1.009085e+01 1.009093e+01 1.009104e+01 1.009119e+01 1.009139e+01 1.009165e+01 1.009200e+01 10.0924525123
schoolMS -5.995037e-05 -7.924788e-05 -1.047558e-04 -1.384719e-04 -1.830358e-04 -2.419347e-04 -3.197749e-04 -0.0004226386
sexM 3.433908e-05 4.539436e-05 6.000888e-05 7.932856e-05 1.048683e-04 1.386308e-04 1.832636e-04 0.0002422670
age -2.980638e-05 -3.940128e-05 -5.208444e-05 -6.884951e-05 -9.100969e-05 -1.203002e-04 -1.590135e-04 -0.0002101781
addressU 5.412005e-05 7.154154e-05 9.457025e-05 1.250102e-04 1.652456e-04 2.184265e-04 2.887147e-04 0.0003816075
famsizeLE3 1.602911e-05 2.118956e-05 2.801138e-05 3.702945e-05 4.895086e-05 6.471034e-05 8.554357e-05 0.0001130841
PstatusT -2.279614e-05 -3.013472e-05 -3.983558e-05 -5.265897e-05 -6.960976e-05 -9.201597e-05 -1.216327e-04 -0.0001607789
Medu 2.903402e-05 3.837999e-05 5.073387e-05 6.706331e-05 8.864697e-05 1.171742e-04 1.548767e-04 0.0002047017
Fedu 1.812300e-05 2.395641e-05 3.166699e-05 4.185845e-05 5.532837e-05 7.313032e-05 9.665557e-05 0.0001277408
(Intercept) 10.0930551377 10.0938515441 10.0949039464 10.0962944615 10.0981314206 10.1005576427 10.1037612489 10.107989745 ......
schoolMS -0.0005585551 -0.0007381179 -0.0009752959 -0.0012884936 -0.0017019336 -0.0022474493 -0.0029667978 -0.003914615 ......
sexM 0.0003202684 0.0004233859 0.0005597086 0.0007399319 0.0009781988 0.0012932121 0.0017097077 0.002260405 ......
age -0.0002777935 -0.0003671400 -0.0004851863 -0.0006411236 -0.0008470667 -0.0011189677 -0.0014778060 -0.001951125 ......
addressU 0.0005043641 0.0006665676 0.0008808626 0.0011639239 0.0015377230 0.0020311811 0.0026823142 0.003541002 ......
famsizeLE3 0.0001494915 0.0001976206 0.0002612456 0.0003453561 0.0004565488 0.0006035449 0.0007978749 0.001054784 ......
PstatusT -0.0002125188 -0.0002808999 -0.0003712675 -0.0004906793 -0.0006484491 -0.0008568621 -0.0011321110 -0.001495519 ......
Medu 0.0002705405 0.0003575282 0.0004724385 0.0006241993 0.0008245673 0.0010890043 0.0014378118 0.001897587 ......
Fedu 0.0001688097 0.0002230584 0.0002946987 0.0003892753 0.0005140770 0.0006786688 0.0008955723 0.001181127 ......
..............................
........suppressing 44 columns and 23 rows in show(); maybe adjust 'options(max.print= *, width = *)'
.............................. [[ suppressing 56 column names 㤼㸱s0㤼㸲, 㤼㸱s1㤼㸲, 㤼㸱s2㤼㸲 ... ]]
romanticyes -5.634368e-10 -7.448303e-10 -9.846218e-10 -1.301612e-09 -1.720654e-09 -2.274604e-09 -3.006893e-09 -3.974935e-09
famrel 1.061341e-10 1.403030e-10 1.854724e-10 2.451836e-10 3.241182e-10 4.284652e-10 5.664058e-10 7.487552e-10
freetime -8.985953e-11 -1.187890e-10 -1.570321e-10 -2.075872e-10 -2.744180e-10 -3.627645e-10 -4.795533e-10 -6.339412e-10
goout -3.882777e-10 -5.132803e-10 -6.785264e-10 -8.969720e-10 -1.185744e-09 -1.567484e-09 -2.072122e-09 -2.739223e-09
Dalc -2.238065e-10 -2.958590e-10 -3.911082e-10 -5.170220e-10 -6.834726e-10 -9.035106e-10 -1.194388e-09 -1.578910e-09
Walc -1.669411e-10 -2.206863e-10 -2.917343e-10 -3.856556e-10 -5.098140e-10 -6.739442e-10 -8.909145e-10 -1.177737e-09
health -5.076823e-11 -6.711262e-11 -8.871893e-11 -1.172812e-10 -1.550388e-10 -2.049522e-10 -2.709348e-10 -3.581598e-10
absences 3.626904e-11 4.794554e-11 6.338118e-11 8.378620e-11 1.107604e-10 1.464188e-10 1.935570e-10 2.558709e-10
romanticyes -5.254630e-09 -6.946312e-09 -9.182615e-09 -1.213888e-08 -1.604688e-08 -2.121303e-08 -2.804238e-08 -3.707038e-08
famrel 9.898103e-10 1.308471e-09 1.729722e-09 2.286590e-09 3.022738e-09 3.995881e-09 5.282320e-09 6.982915e-09
freetime -8.380330e-10 -1.107830e-09 -1.464486e-09 -1.935965e-09 -2.559231e-09 -3.383153e-09 -4.472330e-09 -5.912156e-09
goout -3.621091e-09 -4.786870e-09 -6.327960e-09 -8.365190e-09 -1.105829e-08 -1.461841e-08 -1.932467e-08 -2.554608e-08
Dalc -2.087227e-09 -2.759191e-09 -3.647488e-09 -4.821764e-09 -6.374088e-09 -8.426170e-09 -1.113890e-08 -1.472497e-08
Walc -1.556898e-09 -2.058128e-09 -2.720724e-09 -3.596637e-09 -4.754543e-09 -6.285225e-09 -8.308698e-09 -1.098361e-08
health -4.734662e-10 -6.258945e-10 -8.273957e-10 -1.093768e-09 -1.445897e-09 -1.911391e-09 -2.526747e-09 -3.340211e-09
absences 3.382463e-10 4.471417e-10 5.910950e-10 7.813929e-10 1.032955e-09 1.365506e-09 1.805119e-09 2.386261e-09
romanticyes -4.900485e-08 -6.478153e-08 -8.563737e-08 -1.132076e-07 -1.496537e-07 -1.978334e-07 -2.615241e-07 -3.457194e-07
famrel 9.231003e-09 1.220284e-08 1.613144e-08 2.132481e-08 2.819015e-08 3.726571e-08 4.926307e-08 6.512288e-08
freetime -7.815522e-09 -1.033166e-08 -1.365785e-08 -1.805487e-08 -2.386747e-08 -3.155138e-08 -4.170906e-08 -5.513690e-08
goout -3.377042e-08 -4.464250e-08 -5.901476e-08 -7.801403e-08 -1.031300e-07 -1.363317e-07 -1.802225e-07 -2.382435e-07
Dalc -1.946554e-08 -2.573230e-08 -3.401659e-08 -4.496792e-08 -5.944494e-08 -7.858270e-08 -1.038817e-07 -1.373254e-07
Walc -1.451968e-08 -1.919417e-08 -2.537356e-08 -3.354235e-08 -4.434100e-08 -5.861619e-08 -7.748713e-08 -1.024334e-07
health -4.415562e-09 -5.837113e-09 -7.716320e-09 -1.020052e-08 -1.348449e-08 -1.782570e-08 -2.356452e-08 -3.115091e-08
absences 3.154496e-09 4.170059e-09 5.512572e-09 7.287296e-09 9.633377e-09 1.273476e-08 1.683460e-08 2.225435e-08
romanticyes -4.570207e-07 -6.041543e-07 -7.986562e-07 -1.055776e-06 -1.395673e-06 -1.844997e-06 -2.438976e-06 -3.224179e-06
famrel 8.608860e-08 1.138040e-07 1.504422e-07 1.988757e-07 2.629018e-07 3.475405e-07 4.594277e-07 6.073358e-07
freetime -7.288771e-08 -9.635320e-08 -1.273732e-07 -1.683797e-07 -2.225877e-07 -2.942474e-07 -3.889768e-07 -5.142029e-07
goout -3.149439e-07 -4.163372e-07 -5.503731e-07 -7.275606e-07 -9.617918e-07 -1.271431e-06 -1.680756e-06 -2.221858e-06
Dalc -1.815361e-07 -2.399799e-07 -3.172391e-07 -4.193711e-07 -5.543834e-07 -7.328612e-07 -9.687976e-07 -1.280690e-06
Walc -1.354109e-07 -1.790051e-07 -2.366341e-07 -3.128160e-07 -4.135239e-07 -5.466534e-07 -7.226421e-07 -9.552878e-07
health -4.117967e-08 -5.443710e-08 -7.196264e-08 -9.513037e-08 -1.257567e-07 -1.662430e-07 -2.197634e-07 -2.905142e-07
absences 2.941894e-08 3.889011e-08 5.141044e-08 6.796157e-08 8.984121e-08 1.187648e-07 1.570001e-07 2.075449e-07
romanticyes -4.262169e-06 -5.634327e-06 -7.448231e-06 -9.846092e-06 -1.301590e-05 -1.720616e-05 -2.274537e-05 -3.006776e-05
famrel 8.028610e-07 1.061333e-06 1.403016e-06 1.854699e-06 2.451793e-06 3.241107e-06 4.284521e-06 5.663829e-06
freetime -6.797432e-07 -8.985757e-07 -1.187856e-06 -1.570261e-06 -2.075767e-06 -2.743998e-06 -3.627326e-06 -4.794976e-06
goout -2.937162e-06 -3.882747e-06 -5.132751e-06 -6.785172e-06 -8.969559e-06 -1.185716e-05 -1.567435e-05 -2.072036e-05
Dalc -1.692992e-06 -2.238026e-06 -2.958523e-06 -3.910965e-06 -5.170016e-06 -6.834369e-06 -9.034482e-06 -1.194279e-05
Walc -1.262830e-06 -1.669379e-06 -2.206806e-06 -2.917244e-06 -3.856383e-06 -5.097837e-06 -6.738912e-06 -8.908220e-06
health -3.840425e-07 -5.076814e-07 -6.711245e-07 -8.871865e-07 -1.172807e-06 -1.550380e-06 -2.049507e-06 -2.709322e-06
absences 2.743621e-07 3.626907e-07 4.794558e-07 6.338125e-07 8.378632e-07 1.107606e-06 1.464191e-06 1.935576e-06
romanticyes -3.974731e-05 -5.254273e-05 -6.945688e-05 -9.181526e-05 -1.213697e-04 -1.604355e-04 -2.120722e-04 -2.803222e-04
famrel 7.487152e-06 9.897404e-06 1.308349e-05 1.729508e-05 2.286217e-05 3.022086e-05 3.994742e-05 5.280330e-05
freetime -6.338439e-06 -8.378629e-06 -1.107533e-05 -1.463967e-05 -1.935058e-05 -2.557646e-05 -3.380384e-05 -4.467490e-05
goout -2.739073e-05 -3.620829e-05 -4.786412e-05 -6.327160e-05 -8.363793e-05 -1.105585e-04 -1.461414e-04 -1.931722e-04
Dalc -1.578720e-05 -2.086894e-05 -2.758609e-05 -3.646471e-05 -4.819987e-05 -6.370983e-05 -8.420743e-05 -1.112942e-04
Walc -1.177575e-05 -1.556616e-05 -2.057634e-05 -2.719861e-05 -3.595129e-05 -4.751908e-05 -6.280621e-05 -8.300654e-05
health -3.581552e-06 -4.734582e-06 -6.258804e-06 -8.273711e-06 -1.093725e-05 -1.445822e-05 -1.911260e-05 -2.526518e-05
absences 2.558721e-06 3.382483e-06 4.471452e-06 5.911011e-06 7.814034e-06 1.032974e-05 1.365538e-05 1.805175e-05
romanticyes -3.705262e-04 -4.897383e-04 -6.472733e-04 -8.554269e-04 -1.130422e-03 -1.493648e-03 -0.0019732890 -0.0026064324 ......
famrel 6.979439e-05 9.224929e-05 1.219223e-04 1.611290e-04 2.129242e-04 2.813356e-04 0.0003716688 0.0004909048 ......
freetime -5.903701e-05 -7.800751e-05 -1.030586e-04 -1.361278e-04 -1.797616e-04 -2.373006e-04 -0.0003131154 -0.0004129061 ......
goout -2.553305e-04 -3.374765e-04 -4.460273e-04 -5.894529e-04 -7.789269e-04 -1.029180e-03 -0.0013596172 -0.0017957663 ......
Dalc -1.470841e-04 -1.943661e-04 -2.568176e-04 -3.392831e-04 -4.481376e-04 -5.917581e-04 -0.0007811301 -0.0010306231 ......
Walc -1.096956e-04 -1.449513e-04 -1.915129e-04 -2.529867e-04 -3.341158e-04 -4.411272e-04 -0.0005821781 -0.0007679225 ......
health -3.339810e-05 -4.414862e-05 -5.835889e-05 -7.714179e-05 -1.019678e-04 -1.347794e-04 -0.0001781425 -0.0002354448 ......
absences 2.386358e-05 3.154667e-05 4.170355e-05 5.513089e-05 7.288194e-05 9.634938e-05 0.0001273746 0.0001683928 ......plot(ridge_regression_student_math)
#choose the best lambda value
ridge_regression_student_math_cv<- cv.glmnet(x,y, alpha=0, lambda=grid)
best_lambda <- ridge_regression_student_math_cv$lambda.min
best_lambda[1] 2.656088#we now run the ridge regression again using lambda=3.51
ridge_regression_student_math <- glmnet(x,y, alpha=0, lambda=3.5)
plot(ridge_regression_student_math)
summary(ridge_regression_student_math) Length Class Mode
a0 1 -none- numeric
beta 39 dgCMatrix S4
df 1 -none- numeric
dim 2 -none- numeric
lambda 1 -none- numeric
dev.ratio 1 -none- numeric
nulldev 1 -none- numeric
npasses 1 -none- numeric
jerr 1 -none- numeric
offset 1 -none- logical
call 5 -none- call
nobs 1 -none- numericcoefficients(ridge_regression_student_math)40 x 1 sparse Matrix of class "dgCMatrix"
s0
(Intercept) 13.611831455
schoolMS -0.100443994
sexM 0.918766885
age -0.329490607
addressU 0.556802965
famsizeLE3 0.354894827
PstatusT -0.280385142
Medu 0.231295772
Fedu -0.004771552
Mjobhealth 0.624657321
Mjobother -0.198021591
Mjobservices 0.433636689
Mjobteacher -0.509818701
Fjobhealth 0.436712179
Fjobother -0.188281400
Fjobservices -0.131108888
Fjobteacher 0.706416612
reasonhome 0.142523882
reasonother 0.543637738
reasonreputation 0.484313174
guardianmother 0.151024483
guardianother -0.173285659
traveltime -0.082088629
studytime 0.361379694
failures -1.142026997
schoolsupyes -0.714707804
famsupyes -0.582411726
paidyes 0.393244592
activitiesyes -0.103623002
nurseryyes 0.037809129
higheryes 1.446946410
internetyes 0.262335815
romanticyes -0.587383718
famrel 0.088127790
freetime 0.038629095
goout -0.399807952
Dalc -0.131123111
Walc -0.048696245
health -0.069501007
absences 0.066528065#fitting a Lasso
student_mat <- read.csv("student-mat.csv", stringsAsFactors=TRUE)
fix(student_mat)
student_mat <- student_mat[-c(31:32)]
data <- student_mat
set.seed(99)
dt <- sort(sample(nrow(data), nrow(data)*.7))
train_data_mat <-data[dt,]
test_data_mat <-data[-dt,]
#we start preparing a grid with our x (only our predictors), and our y (our dependent variable)
x <- model.matrix(G3~.,train_data_mat)[,-1]
y=train_data_mat%>%select(G3)%>% unlist()%>% as.numeric() #here we transfrom qualitative variables into dummy variables
#we prepare the grid to cover all scenarios (from a null model to a least square fit -when lambda si really big-)
grid <-10^seq(10,-2 ,length=100)#here we are creating a grid with values from 10 to the 10th to 10 to the minuse 2, lenght=100
#ri fwe choose lambda zero a ridge will be choosen, lambda equals 1 will be a Lasso fittes
set.seed(33)
lasso_student_math <- glmnet(x,y, alpha=1)
lasso_student_math_best_lambda <- cv.glmnet(x,y, alpha=1, standardize=TRUE, nfolds=5)
lasso_student_math_best_lambda$lambda.min[1] 0.203589lasso_student_math <- glmnet(x,y, alpha=1,lambda=0.203589)
plot(lasso_student_math)
coefficients(lasso_student_math)40 x 1 sparse Matrix of class "dgCMatrix"
s0
(Intercept) 8.57316276
schoolMS .
sexM 0.92214464
age .
addressU .
famsizeLE3 0.03372335
PstatusT .
Medu 0.09778059
Fedu .
Mjobhealth 1.53206982
Mjobother -0.01464233
Mjobservices 0.48957106
Mjobteacher .
Fjobhealth 0.03803492
Fjobother .
Fjobservices .
Fjobteacher 1.63701332
reasonhome .
reasonother .
reasonreputation .
guardianmother -0.12263303
guardianother .
traveltime .
studytime 0.58225815
failures -1.23431556
schoolsupyes -0.47832953
famsupyes -0.09629106
paidyes .
activitiesyes .
nurseryyes .
higheryes 1.46544130
internetyes .
romanticyes -0.30137048
famrel .
freetime .
goout -0.39434155
Dalc .
Walc .
health .
absences 0.02052302prediction_lasso_math <- predict(lasso_student_math, type="coefficients")
prediction_lasso_math[prediction_lasso_math!=0]<sparse>[ <logic> ] : .M.sub.i.logical() maybe inefficient [1] 8.57316276 0.92214464 0.03372335 0.09778059 1.53206982 -0.01464233 0.48957106 0.03803492 1.63701332 -0.12263303
[11] 0.58225815 -1.23431556 -0.47832953 -0.09629106 1.46544130 -0.30137048 -0.39434155 0.02052302summary(lasso_student_math) Length Class Mode
a0 1 -none- numeric
beta 39 dgCMatrix S4
df 1 -none- numeric
dim 2 -none- numeric
lambda 1 -none- numeric
dev.ratio 1 -none- numeric
nulldev 1 -none- numeric
npasses 1 -none- numeric
jerr 1 -none- numeric
offset 1 -none- logical
call 5 -none- call
nobs 1 -none- numeric#Part 3: Classification Problems
#Assignment 3 Linear Discrminant Analysis
#LDA determines group means and computes, for each individual, the probability of belonging
#to the different groups.The individual is then affected to the group with the highest probability score.
library(MASS)
Attaching package: 㤼㸱MASS㤼㸲
The following object is masked from 㤼㸱package:dplyr㤼㸲:
selectlibrary(factoextra)
library(cluster)
library(dplyr)
library(gridExtra)
library(ISLR)
library(glmnet)
library(caret)
setwd(
"C:/Users/mario/OneDrive/Desktop/Pgd Data Science LSE/All Modules/Machine Learning ST3189-02/Assignment"
)
bank_data <- read.csv("bank.csv", stringsAsFactors = TRUE)
fix(bank_data)
set.seed(2)
data <- bank_data
dt <- sort(sample(nrow(data), nrow(data) * .7))
train_data <- data[dt, ]
test_data <- data[-dt, ]
#Now that we have our data sorted out on training and test data, we can start our discriminant analysis
disc_analysis <-
lda(
y ~ age + job + marital + education + default + balance + housing + loan +
contact + day + month + duration + campaign + pdays + previous + poutcome,
data = train_data,
)
names(disc_analysis) [1] "prior" "counts" "means" "scaling" "lev" "svd" "N" "call" "terms" "xlevels"disc_analysisCall:
lda(y ~ age + job + marital + education + default + balance +
housing + loan + contact + day + month + duration + campaign +
pdays + previous + poutcome, data = train_data, )
Prior probabilities of groups:
no yes
0.8814791 0.1185209
Group means:
age jobblue-collar jobentrepreneur jobhousemaid jobmanagement jobretired jobself-employed jobservices jobstudent
no 40.95375 0.2108283 0.04015776 0.02187164 0.2097526 0.04302617 0.04266762 0.09896020 0.01756902
yes 42.56000 0.1333333 0.03733333 0.02666667 0.2453333 0.10133333 0.04266667 0.07733333 0.02933333
jobtechnician jobunemployed jobunknown maritalmarried maritalsingle educationsecondary educationtertiary
no 0.1749731 0.02689136 0.007888132 0.6242381 0.2631768 0.5166726 0.2911438
yes 0.1573333 0.02400000 0.010666667 0.5413333 0.3173333 0.4720000 0.3706667
educationunknown defaultyes balance housingyes loanyes contacttelephone contactunknown day monthaug monthdec
no 0.03944066 0.01792757 1369.168 0.5779849 0.167085 0.06525636 0.3108641 16.01721 0.1376838 0.003585515
yes 0.03733333 0.01866667 1594.747 0.4160000 0.080000 0.09600000 0.1200000 15.48533 0.1493333 0.021333333
monthfeb monthjan monthjul monthjun monthmar monthmay monthnov monthoct monthsep duration campaign
no 0.04410183 0.03191108 0.1674435 0.1229831 0.006453926 0.3155253 0.08605235 0.01111510 0.008605235 223.7368 2.897813
yes 0.06933333 0.02933333 0.1173333 0.0960000 0.042666667 0.1893333 0.08266667 0.06933333 0.029333333 547.8907 2.362667
pdays previous poutcomeother poutcomesuccess poutcomeunknown
no 36.10577 0.4503406 0.03872356 0.0118322 0.843313
yes 56.70400 0.9920000 0.08266667 0.1493333 0.664000
Coefficients of linear discriminants:
LD1
age -1.885300e-04
jobblue-collar -2.109502e-01
jobentrepreneur -1.068415e-01
jobhousemaid -1.190944e-01
jobmanagement -6.562418e-02
jobretired 2.675079e-01
jobself-employed -1.032107e-01
jobservices -8.737002e-02
jobstudent -7.487148e-02
jobtechnician -1.268012e-01
jobunemployed -3.131836e-01
jobunknown 1.850920e-01
maritalmarried -2.397988e-01
maritalsingle -1.553266e-01
educationsecondary -4.828095e-02
educationtertiary 9.930189e-02
educationunknown -2.704915e-01
defaultyes 3.102467e-01
balance -5.140304e-07
housingyes -1.726086e-01
loanyes -2.678419e-01
contacttelephone 8.734907e-02
contactunknown -5.599634e-01
day 5.485651e-03
monthaug -3.080234e-01
monthdec 2.978553e-01
monthfeb -7.575423e-02
monthjan -5.818632e-01
monthjul -5.008905e-01
monthjun 1.537084e-01
monthmar 1.527217e+00
monthmay -1.356373e-01
monthnov -4.279541e-01
monthoct 1.423287e+00
monthsep 7.266352e-01
duration 3.507345e-03
campaign 5.070756e-05
pdays -2.940092e-03
previous -1.642272e-02
poutcomeother 5.735044e-01
poutcomesuccess 2.581519e+00
poutcomeunknown -6.546518e-01plot(disc_analysis) 
#here we have found both the coefficients of our LDA (the ones that we will use for predicition)
disc_analysis$prior no yes
0.8814791 0.1185209 #here we are told that prior to our prediciton, 89% of our data belong to no's and 11% to yes.
set.seed(4)
disc_analysis_prediction <- predict(disc_analysis, data=train_data)
names(disc_analysis_prediction)[1] "class" "posterior" "x" disc_analysis_prediction$class [1] no no no no no no no no no no no no no no no no no no no no no no no no no no no no yes
[30] no no no no no no yes yes yes no yes no no no no no no no no no no yes no no no no no no yes
[59] no no no no no no no no no no no no no yes yes no no no no no no no no no no no no no no
[88] no yes no no no no no no no no no no no no no no no no no no no no no no no no no yes no
[117] no no no no yes no no no no no no no no no no no yes no no no no no no no yes yes no yes no
[146] no no no no no no no no no no no no no no no no no yes no no no no no no no no no no no
[175] no no no no no no no yes no no no no no no no no no no no no yes no no no no no no no no
[204] no no yes no no no no yes no yes yes no no no no no no no no no no no no no no no no no yes
[233] no no no yes no no no yes no no no yes no no no no no no no no no no no no no no no no no
[262] no no no no no yes no no no no no no no no no no no no no no no no no no no no no no no
[291] no no no no no no no no no no no no no no no yes no no no no no no no no no no no no no
[320] no no no no no no no no no no no no no yes no no no no no no no yes no no no no no no no
[349] no no no no no yes no no no no no no no no no no no yes no no no no no yes no no no no no
[378] no no no no no no no no no yes no no no no no no no no no no no no no no no no no no no
[407] no no no no no no no no no no no no no no no no no no no no no no yes no no no no no no
[436] no no no no no no yes no no no no no no no no no yes no no no no no no no no no yes no no
[465] no no no no no no yes no no no no no no no no no no no no no no no no yes no no no no no
[494] no no no no no no no no yes no no no no no no no no no no no no no no no no no no no no
[523] no no no no no no no no no no no no no no no no no no no no no no no no no no no no no
[552] no no no no no no no no no no no no no no no no no no no no no yes no no no no no no no
[581] no no no no no no yes yes no no no no no no no no no no no no no no no no no no no yes no
[610] no no no no no no no no no no no no no no no no no no no no no yes no no no yes no no no
[639] no no no no no no no no no no no no no no no no no no no no no no no no no no no no no
[668] no no no no yes no no no yes no no no no no no no no no no no no yes no no no no no no no
[697] no no no no no no no no no yes no no no no no no no no no no no no no no no no no no no
[726] no no no no no no no no no no no no no no no no no no no no no yes yes no no no no yes no
[755] no yes no no no no no no no no no no no yes no no no yes no no no no no no no no no no no
[784] no no no no no no yes no no no no no no no no yes yes no no no no no no no no no no no no
[813] no no no no no no no no yes no no no no no yes no no no yes no yes no no no no no no yes no
[842] no no no no yes no no no no no no no no no no no no no no no no no no no no no no no no
[871] no no no no no no no no no no no no no no no no no no no no no no no no no no no no yes
[900] no no no no no no no no no no no no no no no no no no no no no no no no yes no yes no no
[929] no no yes no no no no no no yes no no no no no no no no no yes no no no no no no no no no
[958] no no no no no no no no yes no no no no no no no no no no no no no no no no yes no no no
[987] no no no yes no no no no no no no no no no
[ reached getOption("max.print") -- omitted 2164 entries ]
Levels: no yes#class will give us the prediction about the movement of the market
table(disc_analysis_prediction$class)#here we are trying to have the same result in a more ordered way
no yes
2906 258 #here 92% of the predicitons belonged to the NO, and 8% to the YES
#Here we would change the threshold of how we aggroup our observations between yes and no.
set.seed(45)
sum(disc_analysis_prediction$posterior[,1] >=0.5) #here we check that the no values are the same [1] 2906sum(disc_analysis_prediction$posterior[,1] <=0.5) #here we chec that the yes values are the same[1] 258#lets see if we change the threshold
sum(disc_analysis_prediction$posterior[,1] >=0.7)[1] 2791sum(disc_analysis_prediction$posterior[,1] <=0.7)[1] 373#even changing the threshold, the numbers does not change radically (but still have more on the yes side)
#LETS NOW TRY THE MODEL IN OUR TEST DATA
disc_analysis <-
lda(
y ~ age + job + marital + education + default + balance + housing + loan +
contact + day + month + duration + campaign + pdays + previous + poutcome,
data = test_data,
)
disc_analysisCall:
lda(y ~ age + job + marital + education + default + balance +
housing + loan + contact + day + month + duration + campaign +
pdays + previous + poutcome, data = test_data, )
Prior probabilities of groups:
no yes
0.8924097 0.1075903
Group means:
age jobblue-collar jobentrepreneur jobhousemaid jobmanagement jobretired jobself-employed jobservices jobstudent
no 41.09992 0.2386457 0.033856317 0.03055326 0.2089182 0.04624277 0.03633361 0.08505367 0.01321222
yes 42.31507 0.1301370 0.006849315 0.02739726 0.2671233 0.10958904 0.02739726 0.06164384 0.05479452
jobtechnician jobunemployed jobunknown maritalmarried maritalsingle educationsecondary educationtertiary
no 0.1626755 0.03303055 0.007431874 0.6432700 0.2436003 0.5119736 0.2848885
yes 0.1643836 0.02739726 0.020547945 0.5068493 0.3287671 0.4657534 0.3698630
educationunknown defaultyes balance housingyes loanyes contacttelephone contactunknown day monthaug
no 0.04789430 0.01403799 1481.617 0.6003303 0.1502890 0.06193229 0.3270025 15.79108 0.1403799
yes 0.03424658 0.01369863 1513.418 0.4383562 0.0890411 0.05479452 0.1095890 16.10274 0.1575342
monthdec monthfeb monthjan monthjul monthjun monthmar monthmay monthnov monthoct monthsep duration
no 0.0008257638 0.05037159 0.03550784 0.1469860 0.1098266 0.008257638 0.3509496 0.09083402 0.009909166 0.009083402 232.3600
yes 0.0068493151 0.08219178 0.03424658 0.1164384 0.1301370 0.034246575 0.1506849 0.05479452 0.075342466 0.041095890 565.2055
campaign pdays previous poutcomeother poutcomesuccess poutcomeunknown
no 2.780347 35.77622 0.5194055 0.04211396 0.01073493 0.8389761
yes 2.020548 99.29452 1.3424658 0.04794521 0.18493151 0.6027397
Coefficients of linear discriminants:
LD1
age 5.047134e-03
jobblue-collar -1.476100e-01
jobentrepreneur -3.180219e-01
jobhousemaid -4.188431e-01
jobmanagement -2.215757e-02
jobretired 5.895759e-01
jobself-employed 4.901701e-02
jobservices -1.238964e-01
jobstudent 1.452642e+00
jobtechnician -8.872657e-02
jobunemployed -4.124137e-01
jobunknown 1.860828e-01
maritalmarried -3.114669e-01
maritalsingle -1.758568e-01
educationsecondary 1.022972e-01
educationtertiary 1.823787e-01
educationunknown -5.357584e-02
defaultyes 4.359624e-01
balance -1.634923e-05
housingyes -1.137493e-02
loanyes -1.383595e-01
contacttelephone -1.015590e-01
contactunknown -4.206849e-01
day 2.124224e-02
monthaug -1.807145e-01
monthdec -2.110531e-01
monthfeb 3.589018e-01
monthjan -9.150854e-01
monthjul -3.945153e-01
monthjun 2.429369e-01
monthmar 1.610931e+00
monthmay -5.115734e-01
monthnov -7.092281e-01
monthoct 1.728788e+00
monthsep 7.880860e-01
duration 2.903858e-03
campaign -3.151815e-02
pdays 3.551347e-03
previous 2.182345e-02
poutcomeother -2.189500e-01
poutcomesuccess 3.250864e+00
poutcomeunknown 5.204431e-01disc_analysis$prior no yes
0.8924097 0.1075903 #here we are told that prior to our prediciton, 88% of our data belong to no's and 12% to yes.
disc_analysis_prediction <- predict(disc_analysis, data=test_data)
disc_analysis_prediction$class
[1] no no no no no yes yes no no no no no no no no no yes no no no no no no no no no no no no
[30] no yes no no no no no no no no no no no no no no no no no no no no no no no no no no no
[59] no no no no no no no no no no no no no no no no no no no no no no no no no no no no no
[88] no no no no no no no no no yes no yes no no no no no no no no yes no no no no yes no no yes
[117] no no no yes no no no no no no no no no no no no yes no no no no no no yes no no yes no no
[146] no no yes yes no no no no no no no no no no yes no no no no no yes no no no no no no no no
[175] no no no no no no no no no no no no no yes no no no no no no no no no no no no no yes no
[204] no no no no no no no no no no no no no no no no no no no no no no no no no no yes no yes
[233] no no no no no no no no no no no yes no no no no no no no no no no no no no no no no no
[262] no no no yes no no no no no no no no no no no no no yes no no no no no no no no no no no
[291] no no no no no no no no no no no no no no no no no no no no no no no yes no no no no no
[320] no no no no yes no no no no no no no no no no no no no no no no no yes no yes no no no no
[349] no no no no no no yes no no no no no no no no no no no no no no no no no no no no no no
[378] no no no no no no no no no no yes yes no no no no no no no no no no no no no no no no no
[407] no no no yes no no no yes no no no yes no no no no no no no no no no no no no no no no no
[436] no no no no no no no no no no no no yes no no no no no no no no no no no no no no no no
[465] no no no no no no no no no no no no yes no no no no no no yes no no no no no no no no yes
[494] no no no yes no no no yes no no yes no yes no no no no yes yes no no no no no no no no no no
[523] no no no no no no no no no no no no no no no no no no no no no no no yes yes yes no no no
[552] no no no yes no no no no yes no no no no no no no no no no no no no no yes no yes no no no
[581] no no no no no no no no no no no no no no no yes no no no no no no no no no no no no no
[610] no no no no no no no no no no no no no no no no no no no no no no no no no no no no no
[639] no no no no no no no no no no no no no no no yes no no no no no no no no no no no no no
[668] no no no no no no no no no no no no no no no no no no no no no no no no no no no no no
[697] no no no no no no no no yes yes no no no no no no no no no no no no no no no no no no no
[726] no no no no no no no no no no no no no no no no no yes no no no no no no no no no no no
[755] no no no no no no no no no no no no no no no no no no no no no no no no no no no no yes
[784] no no no no no no no no no no no no no no no no no no no no yes no no no no no no no no
[813] no no no no no no no no no no no no no no no no no no no no no no no no yes no no no yes
[842] no no no no no no no no no no no no no no no no no no no no no no no no no no no no no
[871] no no no yes no no no no no no no no no no no no no no no no no no no no no no no yes no
[900] no no no no no yes no no no no no no no no yes no no no yes no no no no yes no no no no no
[929] no no no no no no no no no no no no no no no no no yes no yes no no no no no no no no no
[958] no no no no no yes no no no no no no no no no no no no no no no no yes no no no no no no
[987] yes no no no no no no no yes no yes no no no
[ reached getOption("max.print") -- omitted 357 entries ]
Levels: no yes
$posterior
no yes
1 8.857304e-01 0.1142695505
3 9.027358e-01 0.0972641511
4 9.964407e-01 0.0035593331
6 9.265291e-01 0.0734709130
19 9.972843e-01 0.0027157158
31 1.712512e-01 0.8287488414
34 2.692284e-01 0.7307716231
35 9.741875e-01 0.0258125211
39 6.208994e-01 0.3791006091
42 9.930927e-01 0.0069073140
46 9.990459e-01 0.0009540507
47 9.991879e-01 0.0008120910
48 9.942108e-01 0.0057891670
49 9.777149e-01 0.0222850791
58 9.888907e-01 0.0111093008
59 9.736922e-01 0.0263077601
62 1.266427e-01 0.8733572960
63 9.883103e-01 0.0116897465
66 9.937716e-01 0.0062283914
67 9.980326e-01 0.0019673655
74 9.968441e-01 0.0031558515
83 9.978914e-01 0.0021085946
91 9.979171e-01 0.0020829216
95 9.955013e-01 0.0044986724
96 9.854648e-01 0.0145352490
97 9.987330e-01 0.0012670238
101 9.977889e-01 0.0022110826
104 9.987588e-01 0.0012412061
106 9.650005e-01 0.0349994989
108 9.596219e-01 0.0403781228
111 2.256211e-04 0.9997743789
113 9.917066e-01 0.0082934234
119 9.975471e-01 0.0024528833
120 7.467861e-01 0.2532139418
121 8.254918e-01 0.1745082151
122 9.964339e-01 0.0035660621
125 8.919784e-01 0.1080215812
139 8.241592e-01 0.1758407650
141 9.806411e-01 0.0193588952
150 9.995153e-01 0.0004846851
151 9.989977e-01 0.0010022971
154 9.889941e-01 0.0110059020
163 9.995453e-01 0.0004547316
164 9.991971e-01 0.0008029337
166 9.619567e-01 0.0380432738
167 8.893017e-01 0.1106982880
168 9.449497e-01 0.0550502765
169 9.990751e-01 0.0009248658
174 9.969035e-01 0.0030965320
175 9.977776e-01 0.0022223676
177 9.981660e-01 0.0018340285
178 9.890117e-01 0.0109882610
180 9.986150e-01 0.0013850376
185 9.960265e-01 0.0039734832
188 9.812134e-01 0.0187865561
189 9.893316e-01 0.0106684124
190 6.868772e-01 0.3131227514
191 9.987006e-01 0.0012994315
193 9.929640e-01 0.0070360395
203 5.811795e-01 0.4188205206
208 9.989973e-01 0.0010027194
209 9.764243e-01 0.0235757043
211 9.954794e-01 0.0045206259
212 9.940195e-01 0.0059805100
216 8.776546e-01 0.1223453758
220 9.920413e-01 0.0079586591
221 9.790710e-01 0.0209289569
222 9.984839e-01 0.0015160958
223 9.992021e-01 0.0007978728
224 9.966444e-01 0.0033556497
232 9.955698e-01 0.0044301867
235 9.372136e-01 0.0627863877
240 9.968371e-01 0.0031629459
243 9.937881e-01 0.0062119490
244 9.898394e-01 0.0101606425
245 9.682806e-01 0.0317193811
246 9.974667e-01 0.0025333307
254 9.221324e-01 0.0778676274
261 9.981492e-01 0.0018507954
264 9.967815e-01 0.0032184939
266 9.927643e-01 0.0072357032
270 9.917556e-01 0.0082444126
283 9.974755e-01 0.0025244884
289 9.862355e-01 0.0137645460
295 9.942700e-01 0.0057300171
301 8.061192e-01 0.1938807771
302 5.912948e-01 0.4087052066
304 9.906993e-01 0.0093007002
307 6.919367e-01 0.3080633369
308 9.996867e-01 0.0003132534
314 9.321267e-01 0.0678732874
322 9.890666e-01 0.0109334290
325 9.969627e-01 0.0030373108
330 9.846698e-01 0.0153302067
338 9.724351e-01 0.0275649402
345 8.584745e-01 0.1415255004
348 7.120573e-03 0.9928794273
350 9.431674e-01 0.0568325519
355 6.968086e-03 0.9930319138
361 9.986942e-01 0.0013057879
364 9.953863e-01 0.0046136526
365 9.930273e-01 0.0069727491
367 9.886598e-01 0.0113401742
371 9.973455e-01 0.0026544843
372 9.323554e-01 0.0676445546
376 9.776726e-01 0.0223274428
380 9.977193e-01 0.0022806829
383 1.745890e-01 0.8254109615
385 9.972730e-01 0.0027270423
387 9.917385e-01 0.0082615128
389 9.967488e-01 0.0032511840
390 9.888706e-01 0.0111294372
393 4.652707e-01 0.5347293271
394 9.931151e-01 0.0068849065
396 9.984697e-01 0.0015303454
398 4.783827e-01 0.5216172874
409 9.967603e-01 0.0032397049
411 9.967777e-01 0.0032223460
415 9.940754e-01 0.0059246129
416 3.626186e-02 0.9637381424
418 9.972340e-01 0.0027659538
419 9.856297e-01 0.0143702507
421 9.957914e-01 0.0042085937
423 8.996308e-01 0.1003692172
433 9.672696e-01 0.0327304256
434 9.899516e-01 0.0100484485
439 9.987818e-01 0.0012182057
442 9.978720e-01 0.0021280324
447 9.983107e-01 0.0016893000
452 9.868800e-01 0.0131199847
453 9.973513e-01 0.0026486536
457 8.089812e-01 0.1910188295
465 1.393614e-02 0.9860638616
467 9.006006e-01 0.0993993778
474 5.843243e-01 0.4156757062
476 9.993347e-01 0.0006653332
477 9.995016e-01 0.0004984367
487 7.582727e-01 0.2417272566
492 9.964984e-01 0.0035015720
495 3.979806e-03 0.9960201945
502 9.922733e-01 0.0077267460
503 9.907973e-01 0.0092027399
505 4.672486e-01 0.5327514236
508 9.801903e-01 0.0198096552
511 9.808208e-01 0.0191791549
512 8.060138e-01 0.1939861608
513 9.693978e-01 0.0306022259
518 4.743357e-01 0.5256642750
527 3.260878e-02 0.9673912164
530 9.232972e-01 0.0767027539
532 9.986306e-01 0.0013693618
535 9.930189e-01 0.0069811313
538 9.948093e-01 0.0051907260
540 9.966559e-01 0.0033440915
542 8.348489e-01 0.1651511258
543 9.972505e-01 0.0027494914
545 9.903167e-01 0.0096833317
551 9.913507e-01 0.0086493248
554 9.997251e-01 0.0002748601
556 8.284035e-03 0.9917159653
558 9.261679e-01 0.0738321140
561 9.941802e-01 0.0058198282
562 8.677268e-01 0.1322732428
563 9.989063e-01 0.0010936575
566 9.943284e-01 0.0056716073
569 4.247223e-06 0.9999957528
571 9.987863e-01 0.0012136632
575 9.958460e-01 0.0041539515
580 9.620790e-01 0.0379210471
584 9.157052e-01 0.0842948112
586 9.817009e-01 0.0182990500
587 9.981996e-01 0.0018003960
589 9.969758e-01 0.0030241868
591 9.955726e-01 0.0044274116
604 9.910799e-01 0.0089201207
606 9.954550e-01 0.0045449749
607 9.968083e-01 0.0031917119
618 9.880828e-01 0.0119172361
622 9.890657e-01 0.0109342904
632 9.978367e-01 0.0021633289
635 5.602874e-01 0.4397126388
636 9.876244e-01 0.0123755640
637 9.945198e-01 0.0054801806
642 9.016349e-01 0.0983650709
648 9.938591e-01 0.0061409063
651 9.956099e-01 0.0043901269
655 9.847941e-01 0.0152059321
659 2.575572e-02 0.9742442840
661 9.942151e-01 0.0057848549
664 9.018660e-01 0.0981340391
665 9.944203e-01 0.0055797008
666 6.628655e-01 0.3371345142
669 9.293966e-01 0.0706034163
673 9.989880e-01 0.0010120029
680 9.967305e-01 0.0032694606
682 9.915878e-01 0.0084121793
684 9.764703e-01 0.0235296669
688 9.992440e-01 0.0007560099
695 9.945147e-01 0.0054852869
697 9.934930e-01 0.0065070290
698 9.963666e-01 0.0036333564
705 3.969681e-02 0.9603031863
708 9.633854e-01 0.0366146298
715 9.810831e-01 0.0189168980
718 9.945695e-01 0.0054304805
722 9.758555e-01 0.0241445426
724 9.992135e-01 0.0007864993
727 9.967670e-01 0.0032329907
728 9.109882e-01 0.0890117998
729 9.991934e-01 0.0008066238
732 9.985663e-01 0.0014337273
740 9.967454e-01 0.0032546203
742 9.679688e-01 0.0320312112
746 9.978255e-01 0.0021744781
750 9.990752e-01 0.0009247663
754 9.942414e-01 0.0057586172
756 9.978191e-01 0.0021808713
757 9.801249e-01 0.0198751144
758 9.828985e-01 0.0171015273
761 9.691832e-01 0.0308167667
762 9.942797e-01 0.0057203187
764 9.980015e-01 0.0019984927
765 9.784801e-01 0.0215199451
766 9.812919e-01 0.0187081266
769 9.912455e-01 0.0087545456
770 9.013034e-01 0.0986965574
785 9.981591e-01 0.0018408663
793 8.825028e-01 0.1174972356
794 9.934794e-01 0.0065206239
795 4.854748e-03 0.9951452520
801 9.856221e-01 0.0143779322
804 9.183676e-02 0.9081632357
806 9.963355e-01 0.0036644870
815 9.887300e-01 0.0112700086
818 9.986898e-01 0.0013102212
819 9.953169e-01 0.0046830887
832 8.322997e-01 0.1677002960
837 9.978259e-01 0.0021741035
840 9.991613e-01 0.0008386719
844 9.839250e-01 0.0160749528
845 9.986256e-01 0.0013743869
848 9.856451e-01 0.0143549110
851 9.200834e-01 0.0799166323
856 5.809905e-04 0.9994190095
859 6.062562e-01 0.3937438010
866 8.881953e-01 0.1118046861
869 9.813503e-01 0.0186496969
873 9.941278e-01 0.0058722094
876 9.611471e-01 0.0388528773
878 9.961379e-01 0.0038621431
884 9.943640e-01 0.0056359776
885 9.026664e-01 0.0973336322
888 9.993524e-01 0.0006475916
892 9.963916e-01 0.0036084026
896 9.987717e-01 0.0012283076
897 8.377000e-01 0.1622999779
908 9.919478e-01 0.0080521759
917 9.922758e-01 0.0077242444
920 9.988044e-01 0.0011956008
921 9.926010e-01 0.0073990120
926 9.974316e-01 0.0025683817
928 9.954592e-01 0.0045407892
930 9.970015e-01 0.0029985387
931 9.960769e-01 0.0039230666
935 3.423773e-01 0.6576226930
939 9.980869e-01 0.0019131029
943 9.893013e-01 0.0106987221
947 9.941296e-01 0.0058704492
948 9.986846e-01 0.0013154163
949 9.972266e-01 0.0027734222
953 9.978202e-01 0.0021797759
968 9.965881e-01 0.0034118553
970 9.875866e-01 0.0124133795
971 8.772353e-01 0.1227646721
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[ reached getOption("max.print") -- omitted 857 rows ]
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1927 0.196457824
1928 0.572143637
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1936 0.070027999
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1947 1.828865997
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2005 1.092859569
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2016 1.082366396
2018 1.566946871
2019 2.098858993
2020 -0.421620526
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2701 1.397606632
2702 0.427849552
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2747 1.219532198
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2750 0.519425471
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2761 2.171611693
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2774 2.234371698
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2781 1.179754590
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2805 0.644599795
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2810 0.458837427
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2824 1.072918202
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2853 1.118052648
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2871 0.055860173
2872 0.663842729
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2905 1.483023820
2907 0.113520802
2908 0.250567012
2914 0.404204984
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2919 0.909562496
2923 1.460685036
2925 0.067334273
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2945 1.582813051
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2954 1.932358296
2955 0.907234458
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2964 1.635167019
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2993 1.833486542
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3089 3.230426001
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3092 2.619756881
3095 1.264766009
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3118 1.003236448
3122 0.396112299
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3136 0.841790143
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3158 2.344429064
3162 0.477734736
3164 0.322416370
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3172 1.535645114
3173 0.146671868
3175 -1.091756596
3179 0.056915460
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3188 0.703991194
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3194 0.772547873
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3196 -1.299040956
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3200 -0.337994188
3203 3.730452097
3207 -1.065445504
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3218 -0.660325768
3219 -0.726239313
3225 1.876514126
3227 -0.790981314
3233 -0.868904773
3234 1.764088243
3240 1.470633402
3241 -0.551347878
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3243 -0.600508230
3244 5.205632670
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3251 6.950621932
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[ reached getOption("max.print") -- omitted 357 rows ]#here 91% belongs to the no group and 8% to the yes.
#MODEL VADILITY CONFUSION MATRIX
table_1 <- table(list(predicted=disc_analysis_prediction$class, observed = test_data$y))
table_1 observed
predicted no yes
no 1171 77
yes 40 69#OUr model predicted 1357 cases
#109 were predicted as YES, and 1248 as NO
#Out of the 109 predicted YES, just 69 were corrected predicted (0.63%) and
#out of the 1357 predicted NO, just 1171 were corrected predicted (0.94%)
#then our model fitted in our test data correctly predicted 63% of the yes cases using the coefficients for
#each variable that we have found WHICH IS OUR VARIABLE OF INTEREST.
#OVERALL OUR MODEL SEEMS TO CORRECTLY PREDICT 91% OF THE TIME, BUT JUST A 63% FOR POSITITVE RESPONSES.
#We now try fitting a logistic regression model
set.seed(77)
logistic_model <- glm(y~., data=train_data, family=binomial)
summary(logistic_model)
Call:
glm(formula = y ~ ., family = binomial, data = train_data)
Deviance Residuals:
Min 1Q Median 3Q Max
-3.0864 -0.3867 -0.2617 -0.1716 2.9939
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -1.582e+00 7.155e-01 -2.211 0.02703 *
age -5.088e-03 8.549e-03 -0.595 0.55177
jobblue-collar -3.980e-01 2.856e-01 -1.394 0.16346
jobentrepreneur -1.500e-01 4.226e-01 -0.355 0.72268
jobhousemaid -2.460e-01 4.988e-01 -0.493 0.62184
jobmanagement -7.416e-02 2.877e-01 -0.258 0.79655
jobretired 4.899e-01 3.808e-01 1.287 0.19824
jobself-employed -3.029e-01 4.098e-01 -0.739 0.45977
jobservices -1.548e-01 3.188e-01 -0.486 0.62723
jobstudent -1.351e-01 4.694e-01 -0.288 0.77348
jobtechnician -1.859e-01 2.707e-01 -0.687 0.49228
jobunemployed -5.674e-01 4.908e-01 -1.156 0.24763
jobunknown 2.681e-01 7.244e-01 0.370 0.71124
maritalmarried -3.978e-01 2.079e-01 -1.913 0.05569 .
maritalsingle -2.912e-01 2.419e-01 -1.204 0.22872
educationsecondary 2.626e-02 2.403e-01 0.109 0.91298
educationtertiary 3.017e-01 2.781e-01 1.085 0.27802
educationunknown -3.940e-01 4.241e-01 -0.929 0.35284
defaultyes 4.780e-01 5.022e-01 0.952 0.34117
balance 2.791e-06 2.379e-05 0.117 0.90660
housingyes -3.238e-01 1.644e-01 -1.969 0.04890 *
loanyes -7.468e-01 2.392e-01 -3.122 0.00180 **
contacttelephone 5.021e-02 2.643e-01 0.190 0.84934
contactunknown -1.324e+00 2.564e-01 -5.162 2.44e-07 ***
day 6.634e-03 9.725e-03 0.682 0.49514
monthaug -5.319e-01 3.017e-01 -1.763 0.07791 .
monthdec 4.078e-02 7.376e-01 0.055 0.95591
monthfeb -1.722e-01 3.609e-01 -0.477 0.63327
monthjan -9.582e-01 4.441e-01 -2.158 0.03096 *
monthjul -9.358e-01 2.989e-01 -3.131 0.00174 **
monthjun 2.852e-01 3.545e-01 0.804 0.42121
monthmar 1.374e+00 4.700e-01 2.924 0.00346 **
monthmay -2.992e-01 2.787e-01 -1.074 0.28300
monthnov -7.287e-01 3.204e-01 -2.275 0.02292 *
monthoct 1.173e+00 4.002e-01 2.931 0.00338 **
monthsep 7.030e-01 4.996e-01 1.407 0.15934
duration 4.409e-03 2.440e-04 18.070 < 2e-16 ***
campaign -3.685e-02 3.050e-02 -1.208 0.22693
pdays -4.263e-03 1.360e-03 -3.135 0.00172 **
previous -2.967e-02 4.953e-02 -0.599 0.54916
poutcomeother 7.980e-01 3.268e-01 2.442 0.01461 *
poutcomesuccess 2.262e+00 3.406e-01 6.642 3.09e-11 ***
poutcomeunknown -7.751e-01 3.864e-01 -2.006 0.04487 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 2303.2 on 3163 degrees of freedom
Residual deviance: 1561.7 on 3121 degrees of freedom
AIC: 1647.7
Number of Fisher Scoring iterations: 6#here we have which ones are statistically significants. (variables)
coef(logistic_model) (Intercept) age jobblue-collar jobentrepreneur jobhousemaid jobmanagement
-1.582040e+00 -5.087841e-03 -3.980106e-01 -1.499611e-01 -2.460282e-01 -7.416213e-02
jobretired jobself-employed jobservices jobstudent jobtechnician jobunemployed
4.899010e-01 -3.029036e-01 -1.548270e-01 -1.350934e-01 -1.858827e-01 -5.673663e-01
jobunknown maritalmarried maritalsingle educationsecondary educationtertiary educationunknown
2.681494e-01 -3.977668e-01 -2.911892e-01 2.625751e-02 3.016832e-01 -3.940005e-01
defaultyes balance housingyes loanyes contacttelephone contactunknown
4.780139e-01 2.790719e-06 -3.237508e-01 -7.467830e-01 5.020524e-02 -1.323694e+00
day monthaug monthdec monthfeb monthjan monthjul
6.634354e-03 -5.318875e-01 4.077920e-02 -1.722098e-01 -9.582297e-01 -9.357987e-01
monthjun monthmar monthmay monthnov monthoct monthsep
2.851564e-01 1.374085e+00 -2.992175e-01 -7.287046e-01 1.173213e+00 7.030135e-01
duration campaign pdays previous poutcomeother poutcomesuccess
4.408803e-03 -3.684972e-02 -4.263041e-03 -2.966890e-02 7.979738e-01 2.262209e+00
poutcomeunknown
-7.750752e-01 #here we have the coefficient models
logistic_model_probability <- predict(logistic_model, type="response")
#here the predict function give us the PROBABILITY THAT THE ANSWER WILL BE YES GIVEN THE VALUES OF THE PREDICTORS
# TO INTERPRET THESE VALUES WE NEED TO CONVERT THEM WITH E(^VALUE)
logistic_model_probability 2 5 7 8 9 10 11 12 13
0.0149137835 0.0124131864 0.1306713885 0.0431323367 0.0111725478 0.0657241292 0.0241582275 0.0612909510 0.1314568115
14 15 16 17 18 20 21 22 23
0.1764836984 0.0063927752 0.0450975972 0.0649427644 0.1010183882 0.0817267675 0.0266528637 0.0805465277 0.0279702484
24 25 26 27 28 29 30 32 33
0.0290322687 0.0497179390 0.0702669162 0.0135453160 0.0684397575 0.0146243482 0.0202226681 0.0401680571 0.0279641383
36 37 38 40 41 43 44 45 50
0.0226532042 0.3777790081 0.0242730690 0.0070086430 0.1216052566 0.0872104668 0.0731018143 0.0241992438 0.2363823459
51 52 53 54 55 56 57 60 61
0.5974343504 0.9798340056 0.0484300334 0.6142540908 0.0303592368 0.0309916388 0.0338896223 0.0540073102 0.0687503766
64 65 68 69 70 71 72 73 75
0.0289782154 0.3108333005 0.0229541463 0.1217170418 0.0663997642 0.4341358450 0.0986963051 0.0210721945 0.0314296188
76 77 78 79 80 81 82 84 85
0.0685998221 0.1617203176 0.0174836127 0.4776426288 0.0240560625 0.3146609527 0.0617273390 0.0279335390 0.2187835826
86 87 88 89 90 92 93 94 98
0.0269103512 0.0106780777 0.0604460928 0.1262779702 0.0136141743 0.0465117626 0.1509608711 0.0867092587 0.3517852814
99 100 102 103 105 107 109 110 112
0.7830554048 0.4241790215 0.1469581291 0.0966812784 0.0096607592 0.0211720139 0.0816879814 0.0806388714 0.0182657293
114 115 116 117 118 123 124 126 127
0.0213992572 0.0700291817 0.0651277895 0.0377569759 0.0260551527 0.0078513383 0.1782150848 0.9930029719 0.0255784980
128 129 130 131 132 133 134 135 136
0.0110166327 0.0442072321 0.2361000260 0.0272280435 0.0064187862 0.0077816147 0.0259435215 0.0292566868 0.0946132644
137 138 140 142 143 144 145 146 147
0.0095133830 0.0792654271 0.0131165786 0.1467128109 0.0100838553 0.0606044532 0.0119293302 0.1997443915 0.0129600778
148 149 152 153 155 156 157 158 159
0.0237753507 0.0251078410 0.0167372994 0.0035882929 0.0348780944 0.0567944494 0.7680245878 0.0160251891 0.0422928534
160 161 162 165 170 171 172 173 176
0.1609572789 0.0416232376 0.0243774275 0.8510505489 0.0343623377 0.0244415060 0.0882326858 0.0649853943 0.0162517871
179 181 182 183 184 186 187 192 194
0.0219262192 0.0423673154 0.0410678884 0.0317599985 0.0514039391 0.0212266132 0.7191930861 0.0903035858 0.0209457265
195 196 197 198 199 200 201 202 204
0.3721501363 0.1497015698 0.0456014014 0.0216205944 0.1670384656 0.6283272474 0.6442469854 0.0749948664 0.9373022678
205 206 207 210 213 214 215 217 218
0.2774347453 0.0410476967 0.0142363792 0.0354775995 0.0313401846 0.0451418036 0.1378514711 0.0337368278 0.0282252534
219 225 226 227 228 229 230 231 233
0.1214871468 0.0380015414 0.0202886564 0.1111004796 0.1333399767 0.0212032623 0.1908613834 0.0565870146 0.0210991404
234 236 237 238 239 241 242 247 248
0.8141488501 0.1088388612 0.0529251331 0.0090879885 0.0167582702 0.1157960045 0.3393567083 0.0205422538 0.0474499203
249 250 251 252 253 255 256 257 258
0.0335419848 0.0138333553 0.0728876994 0.0622789493 0.0232367856 0.0260450368 0.0066720651 0.0625592421 0.0322145625
259 260 262 263 265 267 268 269 271
0.1280593697 0.4869210909 0.0690369317 0.0682407971 0.3534677187 0.0214355114 0.0114651702 0.0173677540 0.2187402270
272 273 274 275 276 277 278 279 280
0.0930025411 0.0200927158 0.1061628403 0.0460464719 0.1064100499 0.5295684504 0.1138071056 0.0200218433 0.1110155870
281 282 284 285 286 287 288 290 291
0.0123879267 0.0485022343 0.0200358406 0.0348692812 0.0419325005 0.0175045951 0.0120722036 0.3532894136 0.1239630852
292 293 294 296 297 298 299 300 303
0.0138639408 0.0294511464 0.0136804806 0.6345109611 0.1838715759 0.4327749572 0.6781223561 0.0883649358 0.1371410958
305 306 309 310 311 312 313 315 316
0.0128785156 0.0547024431 0.0456916538 0.0644360033 0.0174784152 0.0411530045 0.2729316484 0.1536056873 0.0311543261
317 318 319 320 321 323 324 326 327
0.0358627676 0.1118648134 0.1735788191 0.0137840130 0.0096481248 0.0142124630 0.6291486504 0.0422924647 0.0145092321
328 329 331 332 333 334 335 336 337
0.4106724279 0.9914110409 0.0213270470 0.1253852940 0.0208147798 0.5186926191 0.2149404875 0.0152500284 0.0218334670
339 340 341 342 343 344 346 347 349
0.8532599947 0.0600568618 0.0238402137 0.1201665621 0.0260104325 0.0141900082 0.0160388322 0.1026609836 0.0076045736
351 352 353 354 356 357 358 359 360
0.1196693124 0.0847517965 0.0168968198 0.1048121676 0.0083844726 0.0108830678 0.0328383465 0.2953566922 0.3162256131
362 363 366 368 369 370 373 374 375
0.0210848673 0.0347739227 0.2853131405 0.1614921604 0.1114548085 0.8125682731 0.1144844856 0.0531813149 0.0211617343
377 378 379 381 382 384 386 388 391
0.0148872406 0.2024104778 0.0198796210 0.0199759869 0.0135166263 0.0199956226 0.0559707902 0.0159643408 0.3853479931
392 395 397 399 400 401 402 403 404
0.0230733489 0.0375102439 0.0696654439 0.0229620845 0.1833987847 0.0487734840 0.1393411200 0.0437528848 0.0616981132
405 406 407 408 410 412 413 414 417
0.0440155088 0.0313870449 0.0150550251 0.0401500878 0.0570594889 0.1328210817 0.1419404655 0.1390423499 0.1266023519
420 422 424 425 426 427 428 429 430
0.0701422477 0.1612091962 0.0456830822 0.0138456759 0.0173261635 0.0098050749 0.0150390637 0.0098895644 0.9869350164
431 432 435 436 437 438 440 441 443
0.0782676178 0.1965630078 0.0200179283 0.0440558572 0.0350600555 0.0483013755 0.0781249344 0.0349705197 0.0283571891
444 445 446 448 449 450 451 454 455
0.0670349282 0.1432893206 0.1367989638 0.1830155148 0.0299619856 0.0483259618 0.4303294082 0.0735524715 0.0282284142
456 458 459 460 461 462 463 464 466
0.0098396842 0.0320540693 0.0332988834 0.1530730787 0.0299883423 0.0355941160 0.0322644599 0.0376072386 0.5009318496
468 469 470 471 472 473 475 478 479
0.0196817918 0.1664617087 0.0082900250 0.0472654902 0.0137962121 0.0360478209 0.0284069477 0.8640377735 0.0184583804
480 481 482 483 484 485 486 488 489
0.0081023553 0.0163481252 0.0379513399 0.0289143228 0.0328066391 0.0829497641 0.0080444226 0.0053259681 0.0200280437
490 491 493 494 496 497 498 499 500
0.1189465102 0.0250278658 0.9161328982 0.1384506974 0.0565209505 0.0207183148 0.0148628825 0.1057743580 0.1946514850
501 504 506 507 509 510 514 515 516
0.1313164199 0.0335641796 0.0239716118 0.0153046905 0.0323643712 0.9688269304 0.0214972958 0.0090348890 0.0345406699
517 519 520 521 522 523 524 525 526
0.0096613603 0.0682051559 0.7014796432 0.0417531899 0.0641561430 0.2338317698 0.0638828002 0.0098690480 0.0443834289
528 529 531 533 534 536 537 539 541
0.0403645820 0.0175213707 0.0513853573 0.0739556481 0.1025714217 0.0601514848 0.1686762567 0.0436454651 0.3701558675
544 546 547 548 549 550 552 553 555
0.0067730134 0.0140451283 0.1233984282 0.0358639356 0.0474341605 0.1656670127 0.0760979972 0.2870219431 0.0170778124
557 559 560 564 565 567 568 570 572
0.0291147178 0.1763860668 0.1021853832 0.0186607601 0.0278235437 0.0515312454 0.0984238523 0.1784422109 0.0422712566
573 574 576 577 578 579 581 582 583
0.2574475459 0.0497325406 0.0573566371 0.0235026385 0.1787001482 0.0584015032 0.2709223090 0.1739820153 0.0337407338
585 588 590 592 593 594 595 596 597
0.0165285756 0.0104522199 0.1066410699 0.0521392200 0.0037333677 0.1029516213 0.0331222835 0.0232337151 0.0085796981
598 599 600 601 602 603 605 608 609
0.0407741349 0.0369294538 0.0284489520 0.1660853841 0.0166972719 0.3270875776 0.0143025868 0.0503081632 0.0810221944
610 611 612 613 614 615 616 617 619
0.0204122914 0.0171459851 0.0195103380 0.0849981019 0.1227067294 0.0583235058 0.0207372174 0.1225706980 0.1067756028
620 621 623 624 625 626 627 628 629
0.4389434702 0.0611320822 0.1315263543 0.2749607452 0.0874345554 0.0108946604 0.2179206419 0.0316768805 0.0526091471
630 631 633 634 638 639 640 641 643
0.1450159764 0.4603469812 0.0041763858 0.2860771913 0.0432343211 0.0168314505 0.1993435843 0.0172007196 0.0291872611
644 645 646 647 649 650 652 653 654
0.1397339433 0.0131413200 0.7936952789 0.0522542230 0.0606462034 0.0268593725 0.1087708389 0.0155578536 0.0218638697
656 657 658 660 662 663 667 668 670
0.0157583387 0.1118041619 0.8760166906 0.3652556237 0.3740041924 0.1413252330 0.0458944801 0.0244012043 0.0095542871
671 672 674 675 676 677 678 679 681
0.0218990914 0.0438603270 0.0233705864 0.0231740736 0.0823344097 0.0703539480 0.0240676703 0.0572273319 0.1799228113
683 685 686 687 689 690 691 692 693
0.0090751646 0.7637503516 0.0499056478 0.0412524978 0.2044333528 0.0153243674 0.0150339813 0.0791594062 0.0072131234
694 696 699 700 701 702 703 704 706
0.0207922958 0.0234658016 0.0742472139 0.0563767748 0.0307696882 0.2524226536 0.9366128228 0.0109996178 0.2402588699
707 709 710 711 712 713 714 716 717
0.1219002577 0.0155000067 0.0138164342 0.0139398396 0.0522767892 0.1089649644 0.0756855121 0.0775020953 0.0458313223
719 720 721 723 725 726 730 731 733
0.0128198945 0.0113738614 0.1008457791 0.0825227261 0.1068155252 0.1341681927 0.0564940033 0.0100441885 0.1456370088
734 735 736 737 738 739 741 743 744
0.0454958180 0.0824435761 0.0682055641 0.0603785747 0.2923615737 0.0271215191 0.0691668332 0.2053376072 0.4179274709
745 747 748 749 751 752 753 755 759
0.0703688835 0.0316484101 0.0227013734 0.0267071084 0.0114324670 0.0356452761 0.0064965064 0.0203759165 0.0080499567
760 763 767 768 771 772 773 774 775
0.2647357587 0.0787228436 0.0160026613 0.0151853026 0.0060105509 0.0117825561 0.1359468292 0.0168252105 0.0035388904
776 777 778 779 780 781 782 783 784
0.0642672262 0.0164772545 0.0977099008 0.0178078454 0.0346659117 0.0215709395 0.0253988812 0.0895463968 0.0053257183
786 787 788 789 790 791 792 796 797
0.1598899643 0.0666314640 0.0423319131 0.1169016872 0.0359452218 0.1303844673 0.0253871789 0.0238917599 0.1403549412
798 799 800 802 803 805 807 808 809
0.2095262822 0.0933837338 0.0545638083 0.0408614361 0.0352687315 0.7389880260 0.0763111920 0.0129980555 0.0543470712
810 811 812 813 814 816 817 820 821
0.1893818661 0.0595133978 0.0512029687 0.0463090535 0.0573869139 0.0471151154 0.0297387251 0.0448400240 0.0370761887
822 823 824 825 826 827 828 829 830
0.0550201872 0.4203705339 0.8083247320 0.1020902841 0.0826392076 0.0202202018 0.0096158470 0.0213832102 0.0295621429
831 833 834 835 836 838 839 841 842
0.1852562050 0.2138407734 0.0159232854 0.0286436210 0.0679169590 0.3347509678 0.0679207681 0.1673179168 0.0490253698
843 846 847 849 850 852 853 854 855
0.0135168645 0.2918776869 0.0356805122 0.0206088090 0.5394605097 0.0274810710 0.0460792887 0.0200967881 0.0295535137
857 858 860 861 862 863 864 865 867
0.0126426578 0.0373041053 0.0370960676 0.0378833854 0.0492311151 0.3116463198 0.0077980277 0.0119799148 0.0362749771
868 870 871 872 874 875 877 879 880
0.0268070773 0.0066294856 0.0101578252 0.4941097616 0.0321489603 0.1435785146 0.0381516440 0.0245121078 0.0068391690
881 882 883 886 887 889 890 891 893
0.8899231498 0.1271061369 0.0354758408 0.0145724190 0.3384982363 0.0177951690 0.0187886262 0.0151709805 0.1036710312
894 895 898 899 900 901 902 903 904
0.0266929544 0.0304687296 0.0169946484 0.0429025353 0.0094624122 0.0370560929 0.0411578100 0.1271762122 0.2774183519
905 906 907 909 910 911 912 913 914
0.2446552137 0.0346726027 0.0708684056 0.0743225756 0.0302781511 0.0115602609 0.0505699592 0.0291582322 0.0216037726
915 916 918 919 922 923 924 925 927
0.0603460886 0.0667356616 0.0425984737 0.0458035729 0.0977413574 0.2394281777 0.0148192692 0.2040287680 0.0490296260
929 932 933 934 936 937 938 940 941
0.0145566008 0.0124366936 0.0370643845 0.1201329270 0.1096481614 0.4644405709 0.0281217980 0.0360343287 0.1007254520
942 944 945 946 950 951 952 954 955
0.5410614044 0.0448879653 0.1567605712 0.0549355555 0.0905803871 0.0467339059 0.0193737774 0.1484605066 0.0720852929
956 957 958 959 960 961 962 963 964
0.0378112802 0.0877759330 0.0105662992 0.0089153381 0.6388179372 0.0138541784 0.1337312304 0.1633543479 0.0072249743
965 966 967 969 972 977 978 979 980
0.0584172667 0.4217267812 0.0250844265 0.0919944315 0.0206750898 0.0649358583 0.0435342138 0.2025250343 0.0968618086
982 983 984 985 986 989 992 994 997
0.0236008147 0.0152004820 0.0634617701 0.5773126650 0.0297593041 0.0699038665 0.0944008061 0.1302252325 0.0281681256
998 999 1000 1001 1002 1004 1006 1007 1008
0.0415069843 0.1721539974 0.0318326790 0.0744331551 0.0492040849 0.0293818166 0.1823134739 0.0570730944 0.2692832208
1009 1011 1012 1013 1015 1016 1018 1019 1020
0.0261809250 0.0698282472 0.0250921102 0.0137373039 0.0250330559 0.0092057782 0.1854624013 0.0894135213 0.2463659579
1021 1027 1028 1029 1031 1033 1034 1035 1036
0.0477064100 0.0087987386 0.0244471936 0.0068641507 0.1483065567 0.0302715873 0.1411270126 0.0301363490 0.1001228573
1038 1039 1040 1041 1042 1044 1046 1047 1048
0.0310186325 0.0052557585 0.0433632363 0.0755193985 0.0377239228 0.1132268221 0.0367792129 0.0490400916 0.8026786485
1049 1050 1051 1053 1056 1057 1058 1059 1061
0.7086699017 0.0550881255 0.0542584217 0.0588769576 0.1320461814 0.3931451592 0.1026234530 0.0612402402 0.7532820500
1062 1064 1065 1067 1069 1071 1073 1074 1075
0.0457775707 0.0341376691 0.0262809733 0.0720489445 0.0034317437 0.0477648839 0.0212430381 0.0314990657 0.0142032418
1076 1077 1078 1079 1083 1085 1086 1089 1090
0.0019694645 0.1341423939 0.4312162824 0.1121824983 0.0317637790 0.0153475033 0.4507388272 0.2335293934 0.0098678263
1091 1092 1093 1094 1095 1096 1098 1099 1101
0.0084276708 0.0234593776 0.0268265453 0.0231643026 0.1361749862 0.0550484152 0.1062549357 0.0367293277 0.1163324507
1103 1105 1106 1107 1109 1113 1114 1115 1116
0.1248773319 0.0201944203 0.0396655849 0.0007346745 0.1089059830 0.2176585584 0.3954394962 0.0557789753 0.1020526254
1117 1118 1119 1121 1122 1124 1125 1127 1128
0.0103335921 0.0243684027 0.1517158213 0.0132989867 0.0242755726 0.1208352286 0.7670280243 0.5489504125 0.0246859243
1129 1130 1131 1132 1133 1134 1136 1140 1142
0.0819283464 0.0323983630 0.0998230238 0.0540131824 0.0220771681 0.0110514181 0.1260141170 0.1535181707 0.0114774928
1146 1147 1148 1149 1151 1152 1153 1154 1155
0.0175786872 0.0534392710 0.0070473981 0.2105446534 0.0440518223 0.0817231457 0.0372426968 0.0446488664 0.0226057663
1156 1157 1160 1161 1163 1165 1166 1167 1168
0.1378589157 0.2527277046 0.0488214092 0.0593929627 0.0084377619 0.0896629754 0.0449669558 0.7440886234 0.0558590310
1169 1170 1172 1173 1174 1175 1177 1178 1179
0.2636024128 0.1889723985 0.5258016711 0.0155053508 0.9639897198 0.0200223123 0.2254031925 0.1274095949 0.0258873964
1181 1186 1187 1188 1189 1190 1191 1192 1193
0.1210315392 0.0854254038 0.8686654985 0.0713590946 0.0268006750 0.0625866516 0.3351717662 0.0316996476 0.3755420112
1194 1195 1196 1198 1201 1203 1204 1205 1206
0.0643476947 0.0151933503 0.1333751360 0.1028432497 0.0077891516 0.0638167484 0.0255760361 0.0318466714 0.2983905988
1207 1208 1211 1213 1214 1215 1216 1218 1219
0.4669831671 0.0077153971 0.0502225081 0.1188619914 0.0233902409 0.1516977816 0.1166054475 0.0035832470 0.0148475286
1222 1224 1230 1231 1232 1233 1235 1236 1237
0.0539995504 0.0163382828 0.0318566201 0.3816296877 0.0538599545 0.0376486353 0.0121268001 0.0165204159 0.0353605407
1238 1239 1240 1241 1242 1243 1244 1245 1246
0.0432655232 0.0082488391 0.0252605458 0.0186087903 0.1272886311 0.0146731247 0.1118487188 0.0541099944 0.0360565037
1247 1248 1249 1250 1251 1252 1254 1256 1257
0.0611798226 0.0443339342 0.0458779091 0.2584413117 0.0213008053 0.0349637498 0.0299057816 0.0162002905 0.0239662853
1258 1259 1261 1263 1264 1265 1266 1267 1268
0.0066896958 0.0679779491 0.0145357007 0.0152958909 0.0113436541 0.0417687997 0.1048474826 0.3801377514 0.0159929147
1269 1272 1274 1275 1276 1277 1279 1280 1281
0.0343032183 0.0778852034 0.0259242861 0.1645712565 0.0726629164 0.3194857901 0.1401367995 0.2820338821 0.0243862972
1282 1283 1284 1285 1286 1288 1289 1292 1293
0.0403266991 0.0191387709 0.0296308435 0.0072360016 0.0327498334 0.1182118387 0.0091983759 0.0210196200 0.0239031347
1294 1295 1296 1298 1299 1301 1302 1304 1307
0.0363460650 0.0072570909 0.0379661818 0.4671491538 0.2360589329 0.9065932471 0.0190315740 0.8114348665 0.0520843659
1308 1309 1311 1313 1314 1315 1316 1317 1318
0.0178525480 0.0490313850 0.0195139400 0.7351528522 0.0179442806 0.0152167808 0.3170811632 0.0354372750 0.0356556529
1319 1320 1321 1322 1323 1324 1325 1327 1328
0.0440391063 0.6731606123 0.0938294024 0.0784262587 0.0618454133 0.0091869573 0.0469341700 0.0088135837 0.0185687206
1330 1331 1334 1335 1336 1337 1339 1340 1341
0.0916993119 0.1649885976 0.4686280342 0.2977577777 0.0170569771 0.0088503927 0.0317516253 0.0527705357 0.0944585276
1342 1344 1345 1346 1347 1348 1349 1351 1353
0.0095043888 0.0711016174 0.2649628595 0.2226892027 0.0460878871 0.0143210962 0.1256886834 0.0141794070 0.0840164259
1354 1355 1356 1357 1358 1359 1360 1361 1362
0.0450589005 0.0238357157 0.5438129265 0.1953110164 0.0562883922 0.2203988040 0.0495974430 0.0288512246 0.0983867886
1364 1365 1366 1367 1368 1369 1371 1372 1373
0.0023682849 0.0248875663 0.0079567273 0.0547057198 0.0217250147 0.0497529434 0.0371215725 0.3591579327 0.1300763690
1374 1375 1378 1379 1380 1381 1382 1383 1384
0.0217389722 0.3700568431 0.1660494848 0.0268143640 0.2620753817 0.0339683067 0.0587016561 0.0402524189 0.3997739880
1385 1386 1387 1388 1391 1392 1393 1395 1396
0.0177899165 0.0465778712 0.0850201740 0.0474175687 0.1007458998 0.5094638181 0.0304909214 0.0910063964 0.2781154352
1399
0.0126086698
[ reached getOption("max.print") -- omitted 2164 entries ]#ee are now running a prediction function
set.seed(88)
logistic_model_prediction <- rep("No", 3164)
logistic_model_prediction[logistic_model_probability> 0.5]<-"Yes"
table(logistic_model_prediction, logistic_model$y)
logistic_model_prediction 0 1
No 2725 253
Yes 64 122#here the interpretation is as follows,
#2978 were predicted as No, and 186 as YES, out of 3164
#but just 2725 out of 2978 were correctly predicted as NO (91%)
#and just 122 out of 186 were correctly predicted as YES (65%)
#finally we run our model using our test data.
set.seed(77)
logistic_model <- glm(y~., data=test_data, family=binomial)
summary(logistic_model)
Call:
glm(formula = y ~ ., family = binomial, data = test_data)
Deviance Residuals:
Min 1Q Median 3Q Max
-3.8000 -0.3266 -0.1891 -0.0840 2.8295
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -4.059e+00 1.243e+00 -3.265 0.001094 **
age -2.906e-03 1.488e-02 -0.195 0.845169
jobblue-collar -3.887e-01 4.955e-01 -0.784 0.432771
jobentrepreneur -9.920e-01 1.149e+00 -0.864 0.387833
jobhousemaid -5.099e-01 8.506e-01 -0.599 0.548849
jobmanagement 4.576e-02 4.730e-01 0.097 0.922933
jobretired 9.037e-01 6.018e-01 1.502 0.133176
jobself-employed 4.354e-01 7.433e-01 0.586 0.558013
jobservices -3.484e-01 5.726e-01 -0.608 0.542903
jobstudent 1.910e+00 7.288e-01 2.621 0.008774 **
jobtechnician -2.222e-02 4.712e-01 -0.047 0.962380
jobunemployed -1.223e+00 8.977e-01 -1.362 0.173181
jobunknown 2.466e-01 1.179e+00 0.209 0.834292
maritalmarried -6.652e-01 3.570e-01 -1.863 0.062404 .
maritalsingle -4.614e-01 4.230e-01 -1.091 0.275379
educationsecondary 1.969e-01 4.090e-01 0.481 0.630235
educationtertiary 2.046e-01 4.714e-01 0.434 0.664266
educationunknown -6.887e-01 7.194e-01 -0.957 0.338404
defaultyes 9.602e-01 8.711e-01 1.102 0.270365
balance -1.759e-05 2.992e-05 -0.588 0.556632
housingyes -1.681e-01 2.761e-01 -0.609 0.542592
loanyes -4.221e-01 4.144e-01 -1.019 0.308339
contacttelephone -5.199e-01 5.447e-01 -0.954 0.339857
contactunknown -2.169e+00 5.487e-01 -3.954 7.70e-05 ***
day 4.539e-02 1.696e-02 2.676 0.007460 **
monthaug -9.840e-02 4.837e-01 -0.203 0.838811
monthdec -9.126e-01 1.580e+00 -0.578 0.563430
monthfeb 9.004e-01 5.484e-01 1.642 0.100626
monthjan -1.802e+00 7.962e-01 -2.263 0.023606 *
monthjul -5.563e-01 4.975e-01 -1.118 0.263454
monthjun 1.343e+00 6.298e-01 2.132 0.033014 *
monthmar 2.281e+00 7.352e-01 3.103 0.001918 **
monthmay -1.170e+00 4.842e-01 -2.417 0.015638 *
monthnov -1.432e+00 5.767e-01 -2.482 0.013059 *
monthoct 1.818e+00 6.500e-01 2.797 0.005154 **
monthsep 1.022e+00 7.815e-01 1.308 0.190912
duration 4.365e-03 4.077e-04 10.706 < 2e-16 ***
campaign -2.037e-01 7.467e-02 -2.728 0.006374 **
pdays 6.072e-03 1.735e-03 3.500 0.000466 ***
previous 5.285e-02 5.761e-02 0.917 0.358956
poutcomeother -4.624e-01 5.740e-01 -0.806 0.420469
poutcomesuccess 2.978e+00 5.370e-01 5.546 2.92e-08 ***
poutcomeunknown 9.863e-01 6.292e-01 1.567 0.117006
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 926.69 on 1356 degrees of freedom
Residual deviance: 540.32 on 1314 degrees of freedom
AIC: 626.32
Number of Fisher Scoring iterations: 7#here we have which ones are statistically significants. (variables)
coef(logistic_model) (Intercept) age jobblue-collar jobentrepreneur jobhousemaid jobmanagement
-4.0585260115 -0.0029058795 -0.3887379990 -0.9919776570 -0.5099348286 0.0457614486
jobretired jobself-employed jobservices jobstudent jobtechnician jobunemployed
0.9036807117 0.4354300308 -0.3484000081 1.9100598967 -0.0222236797 -1.2226812783
jobunknown maritalmarried maritalsingle educationsecondary educationtertiary educationunknown
0.2465683914 -0.6651871142 -0.4614029532 0.1968938299 0.2045828644 -0.6886820319
defaultyes balance housingyes loanyes contacttelephone contactunknown
0.9601571911 -0.0000175867 -0.1681194794 -0.4221052310 -0.5199038480 -2.1694838173
day monthaug monthdec monthfeb monthjan monthjul
0.0453891762 -0.0984014541 -0.9125762962 0.9004353488 -1.8021860828 -0.5563402873
monthjun monthmar monthmay monthnov monthoct monthsep
1.3426546518 2.2810050805 -1.1703382534 -1.4315058417 1.8182958891 1.0220701134
duration campaign pdays previous poutcomeother poutcomesuccess
0.0043651722 -0.2036852409 0.0060720579 0.0528485504 -0.4624268693 2.9783174578
poutcomeunknown
0.9862868404 #here we have the coefficient models
logistic_model_probability <- predict(logistic_model, type="response")
#here the predict function give us the PROBABILITY THAT THE ANSWER WILL BE YES GIVEN THE VALUES OF THE PREDICTORS
# TO INTERPRET THESE VALUES WE NEED TO CONVERT THEM WITH E(^VALUE)
logistic_model_probability 1 3 4 6 19 31 34 35 39
9.423998e-02 2.356954e-01 7.897764e-03 2.680194e-01 3.782444e-03 6.938937e-01 6.097742e-01 9.117484e-02 4.026908e-01
42 46 47 48 49 58 59 62 63
4.985529e-02 1.438449e-03 4.138006e-03 5.993638e-03 7.791532e-02 6.853948e-02 1.585206e-02 5.844027e-01 6.531501e-02
66 67 74 83 91 95 96 97 101
2.413305e-02 1.452112e-02 5.385350e-03 1.138020e-02 1.222479e-02 1.874291e-02 5.298436e-02 1.687303e-03 2.452522e-03
104 106 108 111 113 119 120 121 122
4.021339e-03 1.049744e-01 1.787980e-01 9.859879e-01 3.528506e-02 2.515282e-02 2.763372e-01 3.981955e-01 2.036739e-02
125 139 141 150 151 154 163 164 166
1.759059e-01 3.137934e-01 1.183411e-01 4.658016e-04 4.373939e-04 4.125920e-02 6.962129e-04 1.072691e-03 7.268097e-02
167 168 169 174 175 177 178 180 185
9.362354e-02 1.102541e-01 1.678881e-03 3.084114e-02 1.605683e-02 7.749833e-03 3.373894e-02 8.139385e-03 1.216818e-02
188 189 190 191 193 203 208 209 211
7.928814e-02 3.866400e-02 5.820160e-01 3.348689e-03 3.611977e-02 5.174030e-01 1.337072e-02 9.986585e-02 3.548263e-02
212 216 220 221 222 223 224 232 235
1.897619e-02 2.133844e-01 4.142470e-02 6.723201e-02 1.803054e-03 1.371370e-03 2.022503e-02 8.407030e-03 1.343280e-01
240 243 244 245 246 254 261 264 266
8.613078e-03 1.197065e-02 2.271023e-02 1.173475e-02 1.613135e-02 1.532297e-01 1.782388e-02 8.576111e-03 8.874644e-03
270 283 289 295 301 302 304 307 308
2.964735e-02 1.013302e-02 3.832799e-02 4.213177e-02 2.549766e-01 6.642378e-01 4.247007e-02 2.842803e-01 1.849562e-04
314 322 325 330 338 345 348 350 355
1.710967e-01 7.117219e-02 8.565046e-03 1.231081e-02 1.426769e-01 1.791785e-01 7.309699e-01 1.129212e-01 9.585387e-01
361 364 365 367 371 372 376 380 383
6.217213e-03 1.681978e-02 4.557402e-02 5.326905e-02 6.897242e-03 3.119495e-01 3.730734e-02 1.400565e-02 6.510910e-01
385 387 389 390 393 394 396 398 409
1.753426e-02 2.363417e-02 1.913630e-02 5.276081e-03 3.497652e-01 5.237843e-02 1.708932e-03 6.075391e-02 9.296936e-03
411 415 416 418 419 421 423 433 434
1.856532e-02 1.243585e-02 9.123713e-01 1.513350e-02 8.583626e-02 5.659274e-03 2.238803e-01 9.017649e-02 3.543156e-02
439 442 447 452 453 457 465 467 474
1.024110e-02 1.031289e-02 3.192231e-03 8.506447e-02 3.756868e-03 4.851180e-01 6.750747e-01 6.316407e-02 4.359793e-01
476 477 487 492 495 502 503 505 508
5.918384e-04 8.489660e-04 3.616948e-01 5.578654e-03 9.717989e-01 7.774442e-03 4.977307e-02 4.069502e-01 4.695188e-02
511 512 513 518 527 530 532 535 538
7.426653e-02 2.803017e-01 1.479435e-01 5.019267e-01 6.297596e-01 1.069855e-01 4.119102e-03 1.042307e-01 4.140167e-02
540 542 543 545 551 554 556 558 561
3.884483e-03 1.731960e-01 4.331174e-03 5.474931e-02 2.206101e-02 8.121080e-06 6.902459e-01 1.848630e-01 7.897811e-03
562 563 566 569 571 575 580 584 586
2.286500e-01 6.740032e-03 2.801548e-02 9.992681e-01 4.904696e-04 1.774982e-02 1.665658e-01 1.701886e-01 5.188279e-02
587 589 591 604 606 607 618 622 632
8.095474e-03 9.244375e-03 2.048012e-02 4.973076e-02 2.802862e-02 4.587979e-03 9.888321e-02 3.045751e-02 2.212493e-02
635 636 637 642 648 651 655 659 661
4.507761e-01 7.362343e-02 1.014127e-02 6.794069e-02 1.641534e-02 3.469980e-02 3.606644e-02 5.935110e-01 3.135469e-02
664 665 666 669 673 680 682 684 688
7.068182e-02 2.572480e-03 3.021234e-01 2.255631e-01 3.059288e-03 1.476798e-02 6.952887e-02 1.312012e-01 6.818545e-04
695 697 698 705 708 715 718 722 724
2.474182e-02 4.078967e-02 3.604242e-02 7.279991e-01 7.285658e-02 5.012253e-02 2.094585e-02 7.509337e-02 9.104911e-04
727 728 729 732 740 742 746 750 754
1.638160e-02 1.347388e-01 3.806010e-03 9.018676e-03 2.380622e-02 3.013653e-01 1.237717e-02 1.563177e-03 5.136567e-02
756 757 758 761 762 764 765 766 769
1.268622e-02 1.293610e-01 4.667217e-02 9.969752e-02 1.645348e-02 1.549317e-02 5.294533e-02 8.707558e-02 3.215097e-02
770 785 793 794 795 801 804 806 815
1.609579e-01 2.083028e-03 1.263511e-01 2.830853e-02 9.583788e-01 5.176156e-02 7.121242e-01 1.440965e-02 6.691469e-02
818 819 832 837 840 844 845 848 851
2.986126e-03 2.981675e-02 1.427812e-01 1.396830e-02 8.672174e-04 4.104646e-02 6.614879e-03 5.043962e-02 4.320859e-02
856 859 866 869 873 876 878 884 885
9.567021e-01 3.089906e-01 3.520258e-02 1.016226e-01 2.758637e-02 1.122553e-01 2.745796e-02 8.194216e-03 9.744699e-02
888 892 896 897 908 917 920 921 926
1.161552e-03 2.372173e-02 6.014836e-03 4.888144e-01 1.503317e-02 2.424927e-02 1.458374e-03 5.076303e-02 2.808635e-03
928 930 931 935 939 943 947 948 949
6.146284e-03 3.787750e-03 2.063006e-02 2.271791e-01 2.568034e-03 3.435469e-02 2.555039e-02 1.568603e-03 7.139805e-03
953 968 970 971 973 974 975 976 981
1.041397e-02 1.772348e-02 4.063971e-02 3.330834e-01 2.115367e-03 3.539088e-03 1.449835e-02 3.774908e-01 9.307439e-01
987 988 990 991 993 995 996 1003 1005
2.166308e-02 1.270366e-02 3.608405e-01 5.250420e-02 1.426690e-03 5.450631e-03 3.711025e-02 3.237625e-03 3.110730e-02
1010 1014 1017 1022 1023 1024 1025 1026 1030
8.964706e-03 6.705747e-02 1.522428e-03 4.120864e-02 1.271795e-03 1.480061e-03 2.373346e-02 6.719766e-02 6.038993e-02
1032 1037 1043 1045 1052 1054 1055 1060 1063
4.389142e-02 3.716841e-03 8.805291e-03 1.114857e-02 3.897109e-03 1.304038e-01 3.079697e-02 5.809577e-02 4.668132e-02
1066 1068 1070 1072 1080 1081 1082 1084 1087
7.344012e-02 2.911776e-03 4.232494e-03 7.888569e-03 2.484600e-02 1.029102e-03 3.289075e-02 3.802634e-01 3.120283e-02
1088 1097 1100 1102 1104 1108 1110 1111 1112
2.207748e-02 3.820468e-02 5.666294e-02 2.409255e-02 8.633258e-03 2.737356e-02 2.143006e-01 2.302042e-02 5.772710e-01
1120 1123 1126 1135 1137 1138 1139 1141 1143
2.933556e-02 2.358183e-02 2.330683e-02 2.753615e-02 1.022638e-02 1.566259e-03 1.586097e-02 1.265121e-03 7.015998e-01
1144 1145 1150 1158 1159 1162 1164 1171 1176
7.043326e-03 1.228425e-02 3.473755e-02 1.261787e-02 2.885642e-01 2.178528e-01 5.695680e-04 4.300236e-02 4.531577e-01
1180 1182 1183 1184 1185 1197 1199 1200 1202
1.873416e-01 3.190228e-01 2.865781e-03 6.494833e-03 6.301431e-02 9.880992e-02 6.593367e-02 4.437572e-02 1.358419e-01
1209 1210 1212 1217 1220 1221 1223 1225 1226
1.265928e-02 1.203064e-01 1.359460e-02 4.451493e-01 2.902200e-02 1.269028e-01 5.325866e-02 1.415869e-02 3.033616e-02
1227 1228 1229 1234 1253 1255 1260 1262 1270
8.756039e-02 1.891414e-03 1.561067e-02 9.539501e-04 2.602556e-02 1.312119e-02 2.685905e-01 7.065128e-03 2.420425e-02
1271 1273 1278 1287 1290 1291 1297 1300 1303
2.119924e-03 9.600023e-02 2.245498e-01 8.793592e-03 1.640736e-02 2.737029e-02 1.165342e-01 1.649190e-02 3.080394e-02
1305 1306 1310 1312 1326 1329 1332 1333 1338
1.483588e-02 6.352374e-04 1.307224e-01 8.586762e-02 8.276405e-02 5.233735e-03 3.649833e-02 1.418722e-01 3.956754e-01
1343 1350 1352 1363 1370 1376 1377 1389 1390
8.392774e-01 9.093988e-01 1.894939e-02 3.495759e-03 8.294444e-02 1.790771e-02 4.673831e-02 9.883338e-03 9.430228e-02
1394 1397 1398 1402 1403 1405 1406 1407 1411
3.014362e-02 8.433697e-04 1.960309e-03 7.923381e-04 3.464101e-01 2.311302e-02 1.117191e-02 3.471526e-02 2.375864e-03
1413 1417 1418 1420 1422 1433 1444 1449 1450
3.237785e-01 1.787074e-03 1.289874e-03 3.489445e-02 3.386969e-01 6.814315e-02 8.856502e-02 1.283799e-03 9.021068e-01
1453 1454 1457 1460 1462 1466 1472 1473 1475
1.553239e-02 1.382243e-02 1.199391e-03 9.567269e-01 1.051176e-01 1.811459e-02 9.868516e-02 1.304853e-02 1.489591e-01
1482 1483 1491 1493 1498 1499 1500 1501 1509
2.947772e-04 1.957395e-02 5.390038e-02 6.837160e-04 7.585426e-02 2.730671e-02 2.589934e-02 4.608001e-02 8.539044e-02
1511 1514 1522 1524 1525 1528 1530 1532 1539
5.361595e-02 6.254131e-03 9.460256e-02 2.447795e-02 5.148304e-02 4.075438e-03 2.566483e-01 1.990439e-02 1.502109e-02
1543 1544 1545 1548 1551 1554 1558 1563 1568
1.554015e-02 4.256914e-02 1.242915e-02 9.049175e-03 2.793716e-02 8.301456e-02 8.918013e-01 5.357080e-04 1.074714e-01
1570 1575 1576 1577 1579 1580 1585 1592 1594
5.563936e-03 1.036746e-01 2.855994e-02 3.737701e-01 1.865146e-02 5.902854e-02 7.482283e-03 1.978639e-01 2.231278e-02
1595 1599 1609 1613 1621 1624 1628 1629 1633
3.820550e-02 2.026664e-03 1.437067e-03 1.173396e-02 4.123990e-02 6.110201e-03 9.719497e-04 1.466132e-02 2.435631e-02
1636 1637 1638 1640 1644 1647 1648 1653 1654
2.874540e-02 2.070537e-02 7.333213e-04 6.926296e-03 1.821270e-03 1.053755e-01 2.804236e-02 2.412660e-02 6.582605e-01
1655 1657 1658 1659 1663 1664 1673 1676 1678
7.715374e-03 1.757655e-02 3.751173e-02 5.960096e-02 8.036191e-04 3.389909e-02 3.119892e-01 4.821819e-02 1.661489e-02
1681 1682 1689 1691 1694 1695 1696 1698 1700
2.766266e-01 4.574703e-03 3.233338e-02 1.724705e-03 1.088375e-01 3.876106e-03 8.868277e-01 3.049450e-02 3.635048e-03
1704 1705 1706 1716 1719 1720 1721 1724 1726
1.171174e-01 5.867187e-01 2.845882e-01 6.493748e-03 6.912399e-03 6.494701e-01 3.807303e-03 1.734548e-02 7.161927e-01
1732 1737 1741 1745 1748 1749 1755 1761 1762
1.072545e-01 9.155321e-01 2.061633e-02 5.835609e-02 4.514424e-03 9.362359e-02 8.553972e-01 5.168115e-01 9.129450e-04
1763 1766 1770 1771 1773 1774 1775 1777 1781
1.868544e-01 1.450078e-03 7.929347e-04 9.853042e-04 3.162807e-03 3.798012e-02 2.527272e-02 3.528688e-03 4.103534e-03
1782 1785 1787 1789 1790 1795 1797 1801 1802
1.507161e-01 5.911127e-05 4.360570e-02 1.120317e-02 1.524548e-03 5.498878e-03 3.968897e-02 2.379871e-03 8.162288e-03
1808 1813 1814 1816 1822 1828 1831 1835 1838
3.549229e-02 1.796265e-02 2.307640e-02 2.395519e-02 4.128810e-03 1.487336e-02 1.551614e-01 1.453634e-02 2.648986e-01
1844 1850 1854 1857 1859 1863 1864 1867 1872
6.000483e-02 1.049853e-02 4.697382e-03 6.284642e-02 2.085653e-03 8.546938e-01 4.518726e-01 2.672787e-01 4.453462e-02
1875 1876 1877 1886 1895 1900 1901 1902 1907
9.437988e-03 5.605796e-02 2.129505e-01 8.333583e-02 6.481361e-03 9.097653e-01 2.596149e-01 2.434927e-02 7.267226e-03
1909 1915 1920 1921 1922 1923 1924 1927 1928
9.467156e-04 9.502834e-01 1.195515e-01 4.947225e-03 1.260017e-03 5.490051e-02 6.157369e-02 1.288666e-01 1.077590e-01
1933 1934 1936 1937 1939 1942 1943 1947 1950
3.127987e-03 2.615677e-02 2.343689e-02 4.200719e-02 1.007173e-02 1.593904e-02 5.047852e-02 4.040055e-01 1.544409e-02
1960 1962 1963 1964 1965 1967 1969 1972 1974
2.122785e-01 1.809135e-02 1.410661e-01 5.924158e-02 1.011788e-02 2.761947e-02 3.543548e-02 6.923140e-03 5.878797e-03
1990 1991 1997 2000 2002 2005 2009 2011 2016
1.926872e-02 3.282564e-03 3.696606e-02 1.433456e-03 2.691062e-05 2.527100e-01 5.958971e-03 1.539998e-02 3.544676e-01
2018 2019 2020 2024 2025 2026 2028 2030 2031
4.602687e-01 6.142401e-01 1.790278e-02 1.274441e-02 2.869384e-02 7.591942e-02 2.731005e-03 2.367671e-02 7.241521e-03
2033 2035 2037 2039 2044 2048 2053 2055 2058
1.433249e-01 1.504607e-02 9.055138e-03 9.464601e-03 9.710351e-03 1.257694e-01 9.301276e-03 6.603768e-02 3.921789e-02
2060 2062 2063 2066 2072 2092 2093 2102 2109
1.522995e-03 1.392095e-03 4.458917e-02 2.337138e-02 1.250356e-02 1.149679e-02 7.746603e-02 2.132698e-03 8.845166e-04
2111 2113 2115 2120 2121 2125 2128 2129 2133
8.067044e-02 6.679365e-02 3.571234e-02 6.400337e-03 8.255445e-02 1.538730e-03 6.730783e-02 1.884706e-02 6.633179e-02
2140 2141 2144 2145 2146 2151 2152 2154 2158
1.844613e-02 2.284926e-01 1.024739e-01 6.127801e-02 1.371318e-02 1.105560e-02 9.078919e-02 2.576911e-02 3.708094e-02
2163 2164 2166 2168 2173 2187 2201 2207 2208
4.124268e-02 4.448225e-02 3.369217e-02 1.498155e-02 5.760880e-03 1.248265e-02 2.202484e-03 3.978750e-02 1.275914e-03
2209 2211 2213 2216 2217 2218 2223 2227 2231
2.093977e-02 3.803208e-03 6.491758e-01 3.067556e-02 3.808520e-03 7.038234e-01 9.877890e-03 1.170745e-02 1.083193e-02
2235 2240 2246 2250 2253 2257 2261 2262 2266
1.571773e-02 1.105040e-02 1.098711e-02 3.859656e-01 1.873115e-02 2.797520e-01 1.012135e-01 9.071630e-02 1.644549e-04
2268 2270 2272 2274 2277 2280 2285 2289 2290
2.143083e-02 1.239253e-03 5.097842e-02 5.493208e-04 2.068655e-03 1.792697e-01 1.937927e-03 2.648746e-02 4.550516e-02
2291 2292 2293 2298 2299 2300 2303 2304 2305
3.132821e-02 9.782240e-02 6.483812e-03 8.821514e-02 1.675149e-03 1.850971e-02 9.320196e-02 1.288570e-02 5.467203e-02
2310 2311 2315 2321 2327 2328 2330 2335 2336
1.694177e-02 2.872864e-02 2.807219e-02 1.654312e-05 1.896500e-03 1.289184e-03 1.882870e-02 3.660731e-03 3.919953e-02
2338 2339 2340 2344 2345 2349 2351 2354 2356
5.835231e-03 2.972239e-02 3.549004e-02 1.683250e-02 2.401725e-03 4.908372e-02 5.087138e-02 6.017883e-02 9.896499e-02
2360 2363 2373 2376 2380 2382 2387 2389 2391
1.293700e-02 5.421098e-02 6.084067e-01 6.776978e-01 5.456577e-02 4.479280e-03 2.242258e-03 1.047505e-02 7.125403e-03
2394 2401 2404 2407 2409 2412 2414 2416 2420
6.083243e-03 1.142933e-01 2.842829e-02 2.247962e-01 1.339587e-02 7.088291e-02 7.924113e-03 1.954800e-01 1.244357e-01
2425 2431 2432 2436 2440 2441 2442 2444 2446
3.366380e-02 1.086723e-02 5.378037e-02 3.277241e-02 1.060088e-03 2.391118e-01 3.961058e-03 7.344886e-02 5.057013e-02
2447 2454 2457 2458 2460 2463 2465 2466 2471
8.426400e-02 2.489165e-02 3.894918e-03 3.411881e-02 3.177803e-02 3.410295e-03 8.576735e-02 1.367961e-02 2.051554e-01
2472 2473 2480 2484 2487 2489 2490 2491 2494
1.493556e-01 1.165264e-02 2.546327e-02 1.048788e-02 6.936607e-01 4.043615e-03 2.437894e-02 8.621314e-02 4.282102e-02
2496 2497 2502 2503 2508 2513 2518 2519 2525
1.036417e-02 2.044897e-02 4.772853e-03 1.519161e-02 1.036544e-02 7.076732e-02 5.118440e-04 7.552744e-02 1.055378e-01
2526 2529 2530 2531 2533 2538 2539 2542 2544
1.882868e-03 1.089360e-03 2.012239e-03 3.899082e-02 1.936907e-02 2.762866e-02 5.034315e-02 1.243136e-02 8.641286e-02
2547 2549 2552 2554 2555 2557 2560 2566 2575
2.304982e-03 4.657883e-04 1.490799e-02 1.084553e-01 7.222965e-03 4.185321e-01 3.173854e-03 7.490810e-03 3.580093e-04
2576 2578 2580 2581 2583 2586 2589 2590 2592
1.451520e-03 8.803519e-04 1.008038e-03 5.447295e-04 8.514613e-02 3.864637e-02 1.168671e-01 9.123393e-03 5.577226e-01
2596 2599 2600 2606 2607 2608 2609 2612 2621
4.079853e-02 1.312229e-01 1.269439e-02 1.220959e-03 5.562231e-03 5.906796e-02 1.921861e-01 3.190208e-02 6.281541e-02
2622 2623 2624 2628 2632 2633 2635 2641 2646
5.385882e-04 3.912593e-02 5.519781e-02 3.509140e-02 7.205288e-02 3.293000e-02 6.962000e-03 7.998825e-02 1.056065e-01
2647 2651 2654 2657 2661 2665 2679 2680 2684
1.780998e-02 2.376780e-03 9.774352e-01 2.637543e-02 1.198068e-03 2.703850e-02 1.760281e-02 1.772037e-02 2.082288e-02
2685 2690 2691 2694 2696 2699 2701 2702 2704
5.067062e-03 6.854882e-02 1.670242e-01 7.631390e-03 3.523942e-02 4.951324e-02 2.921431e-01 1.098314e-01 6.109439e-03
2717 2718 2720 2722 2726 2730 2733 2735 2736
6.608014e-02 1.043930e-01 2.314632e-01 3.064805e-03 4.850052e-02 1.246613e-03 2.333118e-02 3.195701e-02 1.673397e-02
2738 2740 2746 2747 2748 2750 2753 2760 2761
4.844605e-03 3.085025e-02 3.348347e-01 3.142218e-01 1.571585e-03 2.183616e-01 1.829145e-02 1.054082e-02 5.392962e-01
2764 2769 2772 2774 2780 2781 2783 2784 2788
1.833465e-02 1.751282e-03 1.462672e-02 5.149069e-01 2.127605e-02 3.470069e-01 1.173357e-03 2.495402e-02 7.242068e-02
2791 2797 2798 2800 2804 2805 2807 2808 2810
6.089787e-03 7.013433e-03 5.411606e-04 3.253761e-02 4.750935e-03 1.546108e-01 2.479675e-02 1.290335e-02 1.510286e-01
2811 2812 2818 2824 2831 2832 2836 2840 2843
8.479612e-03 2.110663e-02 1.747282e-03 3.093137e-01 5.938409e-03 3.936504e-02 2.456325e-02 1.667767e-02 8.056117e-03
2845 2851 2853 2855 2858 2860 2871 2872 2875
1.652125e-04 4.952833e-03 2.518140e-01 5.156249e-02 3.984146e-02 4.322980e-02 7.297162e-02 7.375229e-02 8.859354e-03
2876 2879 2880 2881 2885 2887 2893 2895 2897
9.838757e-01 2.286211e-02 2.616960e-01 6.098506e-03 9.895165e-03 3.037893e-03 3.675752e-03 3.206650e-02 1.314639e-01
2905 2907 2908 2914 2916 2917 2919 2923 2925
4.125994e-01 1.084163e-01 9.169585e-02 9.482715e-02 3.988669e-02 1.614767e-02 2.490049e-01 3.998561e-01 3.686095e-02
2928 2930 2936 2945 2952 2953 2954 2955 2958
3.740337e-03 3.288664e-02 2.371257e-03 5.230266e-01 3.944778e-02 3.121878e-03 6.305513e-01 9.476850e-02 1.900664e-02
2962 2964 2965 2968 2970 2971 2972 2975 2976
2.004332e-02 4.979746e-01 1.143879e-02 3.493254e-02 5.535797e-01 3.496607e-02 2.778177e-01 6.794041e-02 1.798011e-02
2977 2978 2979 2980 2981 2984 2987 2992 2993
2.038537e-03 3.780801e-03 1.218634e-02 1.319170e-02 8.375562e-01 3.788959e-02 1.651423e-01 1.713194e-02 9.370672e-02
2995 3000 3004 3005 3006 3012 3014 3020 3023
8.923712e-03 2.003428e-02 9.582799e-02 6.912961e-03 6.318882e-01 3.280976e-02 2.301373e-01 2.236171e-02 2.581538e-02
3025 3029 3031 3032 3035 3040 3041 3044 3046
1.942900e-02 2.593474e-03 1.538809e-03 1.037444e-01 1.765781e-03 2.331650e-01 1.825974e-02 9.563225e-03 2.897029e-02
3047 3051 3055 3061 3069 3077 3079 3082 3087
5.595799e-03 1.876174e-02 4.836113e-02 1.227289e-01 3.964117e-02 1.794079e-01 4.496931e-02 9.250071e-02 1.694487e-02
3089 3091 3092 3095 3099 3106 3109 3112 3116
6.888773e-01 2.797516e-02 3.085613e-01 3.032644e-01 6.010646e-03 2.879690e-02 3.582151e-04 4.782340e-02 2.351073e-02
3118 3122 3123 3131 3135 3136 3144 3156 3158
1.663387e-01 4.516835e-02 2.251189e-03 9.197174e-03 5.475543e-04 2.918912e-01 2.942462e-03 1.041232e-02 6.758596e-01
3162 3164 3166 3172 3173 3175 3179 3180 3182
1.828354e-01 1.120866e-01 1.653075e-02 4.503634e-02 3.663657e-02 5.884613e-03 9.079641e-02 1.675327e-02 1.273027e-02
3188 3189 3194 3195 3196 3199 3200 3203 3207
1.348191e-01 4.179612e-03 2.114356e-01 1.219157e-02 5.155215e-03 4.938252e-02 3.880330e-02 5.115321e-01 1.005104e-02
3209 3212 3213 3218 3219 3225 3227 3233 3234
8.872802e-04 1.852435e-02 1.305915e-02 3.179991e-02 6.950205e-03 5.756234e-01 1.538102e-02 8.849140e-03 5.382976e-02
3240 3241 3242 3243 3244 3250 3251 3255 3260
4.825063e-01 3.618485e-02 6.273671e-03 3.382692e-02 9.473031e-01 6.104223e-03 9.951075e-01 1.483713e-03 4.765594e-03
3263
3.728299e-02
[ reached getOption("max.print") -- omitted 357 entries ]#ee are now running a prediction function
set.seed(102)
logistic_model_prediction <- rep("No", 1357)
logistic_model_prediction[logistic_model_probability> 0.5]<-"Yes"
table(predicted=logistic_model_prediction, observed=logistic_model$y) observed
predicted 0 1
No 1187 82
Yes 24 64#here the interpretation is as follows,
#1269 were predicted as NO, 88 were predicted as YES
#of which 93% of the NO were correctly predicted
#and 72% of the yes cases were correctly predicted as YES.
#and this is our result when running the logistic regression in our test data.
#we now fit a boosted tree to our bank data
library(tidyverse)package 㤼㸱tidyverse㤼㸲 was built under R version 3.6.3Registered S3 methods overwritten by 'dbplyr':
method from
print.tbl_lazy
print.tbl_sql
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library(caret)
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autoplotlibrary(psych)
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%+%, alphalibrary(Amelia)package 㤼㸱Amelia㤼㸲 was built under R version 3.6.3Loading required package: Rcpp
package 㤼㸱Rcpp㤼㸲 was built under R version 3.6.3##
## Amelia II: Multiple Imputation
## (Version 1.7.6, built: 2019-11-24)
## Copyright (C) 2005-2021 James Honaker, Gary King and Matthew Blackwell
## Refer to http://gking.harvard.edu/amelia/ for more information
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print.tree cli library(gbm)
setwd( "C:/Users/mario/OneDrive/Desktop/Pgd Data Science LSE/All Modules/Machine Learning ST3189-02/Assignment")
bank_data <- read.csv("bank.csv")
describe(bank_data)str(bank_data)'data.frame': 4521 obs. of 17 variables:
$ age : int 30 33 35 30 59 35 36 39 41 43 ...
$ job : Factor w/ 12 levels "admin.","blue-collar",..: 11 8 5 5 2 5 7 10 3 8 ...
$ marital : Factor w/ 3 levels "divorced","married",..: 2 2 3 2 2 3 2 2 2 2 ...
$ education: Factor w/ 4 levels "primary","secondary",..: 1 2 3 3 2 3 3 2 3 1 ...
$ default : Factor w/ 2 levels "no","yes": 1 1 1 1 1 1 1 1 1 1 ...
$ balance : int 1787 4789 1350 1476 0 747 307 147 221 -88 ...
$ housing : Factor w/ 2 levels "no","yes": 1 2 2 2 2 1 2 2 2 2 ...
$ loan : Factor w/ 2 levels "no","yes": 1 2 1 2 1 1 1 1 1 2 ...
$ contact : Factor w/ 3 levels "cellular","telephone",..: 1 1 1 3 3 1 1 1 3 1 ...
$ day : int 19 11 16 3 5 23 14 6 14 17 ...
$ month : Factor w/ 12 levels "apr","aug","dec",..: 11 9 1 7 9 4 9 9 9 1 ...
$ duration : int 79 220 185 199 226 141 341 151 57 313 ...
$ campaign : int 1 1 1 4 1 2 1 2 2 1 ...
$ pdays : int -1 339 330 -1 -1 176 330 -1 -1 147 ...
$ previous : int 0 4 1 0 0 3 2 0 0 2 ...
$ poutcome : Factor w/ 4 levels "failure","other",..: 4 1 1 4 4 1 2 4 4 1 ...
$ y : Factor w/ 2 levels "no","yes": 1 1 1 1 1 1 1 1 1 1 ...data <-bank_data
dt <- sort(sample(nrow(data), nrow(data)*.7))
train_data <-data[dt,]
test_data <-data[-dt,]
#We will fit a boosted tree with the bernoulli dsitrbution for binary classification problems
set.seed(2340)
#lets encode Yes=1 and No=0
train_data$y <-ifelse(train_data$y=="yes",1,0)
table(train_data$y)
0 1
2808 356 #lets run the regression
bosteed_tree_bank <- gbm(y~.,data=train_data, distribution = "bernoulli", n.trees = 5000, interaction.depth = 4)
bosteed_tree_bank gbm(formula = y ~ ., distribution = "bernoulli", data = train_data,
n.trees = 5000, interaction.depth = 4)
A gradient boosted model with bernoulli loss function.
5000 iterations were performed.
There were 16 predictors of which 15 had non-zero influence.summary(bosteed_tree_bank)
#we now use the boosted model to predict y on the test set #
prediction_bank_tree <- predict(bosteed_tree_bank, newdata = test_data, n.trees = 5000)
#we try now but this time we delete the duration variable
setwd( "C:/Users/mario/OneDrive/Desktop/Pgd Data Science LSE/All Modules/Machine Learning ST3189-02/Assignment")
bank_data <- read.csv("bank.csv")
data <-bank_data
data <-bank_data[-c(12)]
dt <- sort(sample(nrow(data), nrow(data)*.7))
train_data <-data[dt,]
test_data <-data[-dt,]
set.seed(240)
#lets encode Yes=1 and No=0
train_data$y <-ifelse(train_data$y=="yes",1,0)
table(train_data$y)
0 1
2788 376 #lets run the regression
bosteed_tree_bank <- gbm(y~.,data=train_data, distribution = "bernoulli", n.trees = 5000, interaction.depth = 4)
bosteed_tree_bank gbm(formula = y ~ ., distribution = "bernoulli", data = train_data,
n.trees = 5000, interaction.depth = 4)
A gradient boosted model with bernoulli loss function.
5000 iterations were performed.
There were 15 predictors of which 15 had non-zero influence.summary(bosteed_tree_bank)
#we now use the boosted model to predict y on the test set #
prediction_bank_tree <- predict(bosteed_tree_bank, newdata = test_data, n.trees = 5000)
---
title: "MJRU Machine Learning"
output: html_notebook
---
```{r}
#Code for Part I of the Coursework
library(factoextra)
library(cluster)
library(dplyr)
library(gridExtra)
setwd(
  "C:/Users/mario/OneDrive/Desktop/Pgd Data Science LSE/All Modules/Machine Learning ST3189-02/Assignment"
)
rawdata <-
  read.csv(
    file.path(
      "C:/Users/mario/OneDrive/Desktop/Pgd Data Science LSE/All Modules/Machine Learning ST3189-02/Assignment",
      "EWCS2016.csv"
    )
  )
#Examining and preparing the data for analysis 
fix(rawdata)
sum(is.na(rawdata))
PCA <- prcomp(rawdata, scale = TRUE)
PCA$rotation
Table1 <- PCA$rotation
pdf("table1.pdf", width = 25, height = 25)       # Export PDF
grid.table(Table1) #Export PDF 
dev.off()         #Export PDF
summary(PCA)
plot(PCA)
biplot(PCA)

#Clustering 
cleaned_data <- na.omit(rawdata)
cleaned_data <- scale(rawdata)
set.seed(220)
clustered_data <- kmeans(cleaned_data, 9, nstart = 25)
attributes(clustered_data)
wssplot <- function(clustered_data,
                    nc = 15,
                    seed = 1234) {
  wss <- (nrow(clustered_data) - 1) * sum(apply(clustered_data, 2, var))
  for (i in 2:nc) {
    set.seed(seed)
    wss[i] <- sum(kmeans(clustered_data, centers = i)$withinss)
  }
  plot(1:nc,
       wss,
       type = "b",
       xlab = "Number of Clusters",
       ylab = "Within groups sum of squares")
}
#choosing the value of k
wssplot(cleaned_data, nc = 10)
#plotting the elbow plot
#we will choose then 4 as the numbers of clusters, and we run the cluster analysis again
distance <- dist(cleaned_data, method = "euclidean") #choosing the distance method 
set.seed(221)
clustered_data <- kmeans(cleaned_data, 4, nstart = 25)
clustered_data
#hirearchical clustering 
hc.complete<- hclust(dist(cleaned_data), method="average")
#plotting hierarchical clustering 
plot(hc.complete)
hc <- as.dendrogram(hc.complete)
plot(hc)
cutree(hc.complete, 1)

#Part 2 linear regression 
#loading and cleaning our data (removing variables 31 and 32)
library(ISLR)
setwd( "C:/Users/mario/OneDrive/Desktop/Pgd Data Science LSE/All Modules/Machine Learning ST3189-02/Assignment")
student_mat <- read.csv("student-mat.csv", stringsAsFactors=TRUE)
fix(student_mat)
student_mat <- student_mat[-c (31:32)]
fix(student_mat)
#training and test data 
data <- student_mat
dt <- sort(sample(nrow(data), nrow(data)*.7))
train_data_math <-data[dt,]
test_data_math <-data[-dt,]
#linear regression on student math
studentmat <-
  glm(
    G3 ~ school + sex + age + address + famsize + Pstatus + Medu + Fedu + Mjob +
      Fjob + reason + guardian + traveltime + studytime + failures + schoolsup +
      famsup + paid + activities + nursery + higher + internet + romantic + famrel +
      freetime + goout + Dalc + Walc + health + absences,
    data = train_data_math
  )
summary(studentmat)
#validating in our test data (math students)
set.seed(300)
prediction_math_student <- predict.glm(studentmat, newdata=train_data_math, se.fit=TRUE, interval="confidence")
prediction_math_student_t <- predict.glm(studentmat, newdata=test_data_math, se.fit=TRUE, interval="confidence")
prediction_math_student$residual.scale
prediction_math_student_t$residual.scale
#LINEAR REGRESSION ON PORTUGESE STUDENT ON OUR TRAINING DATA 
studentport <- read.csv("student-por.csv", stringsAsFactors=TRUE)
studentport <-studentport[-c(31:32)]
fix(studentport)
#training and data set 
data <- studentport
dt <- sort(sample(nrow(data), nrow(data)*.7))
train_data_port <-data[dt,]
test_data_port <-data[-dt,]
#linear regression on portuguese students 
studentport <- glm(
  G3 ~ school + sex + age + address + famsize + Pstatus + Medu + Fedu + Mjob +
    Fjob + reason + guardian + traveltime + studytime + failures + schoolsup +
    famsup + paid + activities + nursery + higher + internet + romantic + famrel +
    freetime + goout + Dalc + Walc + health + absences,
  data = train_data_port
)
summary(studentport)
#validating in our test data (portuguese students)
set.seed(250)
prediction_port_student <- predict.glm(studentport, newdata=train_data_port, se.fit=TRUE, interval="confidence")
prediction_port_student_t <- predict.glm(studentport, newdata=test_data_port, se.fit=TRUE, interval="confidence")
prediction_port_student$residual.scale
prediction_port_student_t$residual.scale

#WE WILL NOW TRY BOOSTED TREES 
library(gbm)
student_mat <- read.csv("student-mat.csv", stringsAsFactors=TRUE)
student_mat <- student_mat[-c (31:32)]
fix(student_mat)
#set training and test data sets 
data <- student_mat
dt <- sort(sample(nrow(data), nrow(data)*.7))
train_data_mat <-data[dt,]
test_data_mat <-data[-dt,]
#run the boosted tree function
set.seed(15)
treestudentmat <-
  gbm(
    G3 ~ school + sex + age + address + famsize + Pstatus + Medu + Fedu + Mjob +
      Fjob + reason + guardian + traveltime + studytime + failures + schoolsup +
      famsup + paid + activities + nursery + higher + internet + romantic + famrel +
      freetime + goout + Dalc + Walc + health + absences,
    data = train_data_mat, distribution="gaussian", n.trees=8000, interaction.depth=4
  )
summary(treestudentmat)
#validating the data 
set.seed(23)
prediction_boosted_tree<- predict(treestudentmat, newdata=train_data_math, n.trees = 10000)
prediction_boosted_tree_t <- predict(treestudentmat, newdata=test_data_math, n.trees= 10000)
mean ((prediction_boosted_tree)^2)
mean((prediction_boosted_tree_t)^2)
#our model perform slighlt worse in the validation set. lets see if changing the lambda value (shrinkage value) improves performance
#run the boosted tree function with a different lambda value 
set.seed(19)
treestudentmat <-
  gbm(
    G3 ~ school + sex + age + address + famsize + Pstatus + Medu + Fedu + Mjob +
      Fjob + reason + guardian + traveltime + studytime + failures + schoolsup +
      famsup + paid + activities + nursery + higher + internet + romantic + famrel +
      freetime + goout + Dalc + Walc + health + absences,
    data = train_data_mat, distribution="gaussian", n.trees=8000, interaction.depth=4, shrinkage = 0.2
  )
#re-test on the validation set 
set.seed(60)
prediction_boosted_tree<- predict(treestudentmat, newdata=train_data_math, n.trees = 10000)
prediction_boosted_tree_t <- predict(treestudentmat, newdata=test_data_math, n.trees= 10000)
mean ((prediction_boosted_tree)^2)
mean((prediction_boosted_tree_t)^2)

#lets see if we can fit a Ridge Regression first and a Lasso later. 
library(plyr)
library(readr)
library(dplyr)
library(caret)
library(ggplot2)
library(repr)
setwd(
  "C:/Users/mario/OneDrive/Desktop/Pgd Data Science LSE/All Modules/Machine Learning ST3189-02/Assignment"
)
student_mat <- read.csv("student-mat.csv", stringsAsFactors=TRUE)
library(glmnet)
fix(student_mat)
student_mat <- student_mat[-c(31:32)]
data <- student_mat
dt <- sort(sample(nrow(data), nrow(data)*.7))
train_data_mat <-data[dt,]
test_data_mat <-data[-dt,]
#fitting a Ridge Regression 
#we start preparing a grid with our x (only our predictors), and our y (our dependent variable)
x <- model.matrix(G3~.,train_data_mat)[,-1]
y=train_data_mat%>%select(G3)%>% unlist()%>% as.numeric() #here we transfrom qualitative variables into dummy variables 
#we prepare the grid to cover all scenarios (from a null model to a least square fit -when lambda si really big-)
grid <-10^seq(10,-2 ,length=100)#here we are creating a grid with values from 10 to the 10th to 10 to the minuse 2, lenght=100
#ri fwe choose lambda zero a ridge will be choosen, lambda equals 1 will be a Lasso fittes 
ridge_regression_student_math <- glmnet(x,y, alpha=0, lambda=grid) #remember that lambda is our shrinkage coefficient 
dim(coef(ridge_regression_student_math))
coef(ridge_regression_student_math)
plot(ridge_regression_student_math)
#choose the best lambda value 
ridge_regression_student_math_cv<- cv.glmnet(x,y, alpha=0, lambda=grid)
best_lambda <- ridge_regression_student_math_cv$lambda.min
best_lambda
#we now run the ridge regression again using lambda=3.51
ridge_regression_student_math <- glmnet(x,y, alpha=0, lambda=3.5)
plot(ridge_regression_student_math)
summary(ridge_regression_student_math)
coefficients(ridge_regression_student_math)
#fitting a Lasso 
student_mat <- read.csv("student-mat.csv", stringsAsFactors=TRUE)
fix(student_mat)
student_mat <- student_mat[-c(31:32)]
data <- student_mat
set.seed(99)
dt <- sort(sample(nrow(data), nrow(data)*.7))
train_data_mat <-data[dt,]
test_data_mat <-data[-dt,]
#we start preparing a grid with our x (only our predictors), and our y (our dependent variable)
x <- model.matrix(G3~.,train_data_mat)[,-1]
y=train_data_mat%>%select(G3)%>% unlist()%>% as.numeric() #here we transfrom qualitative variables into dummy variables 
#we prepare the grid to cover all scenarios (from a null model to a least square fit -when lambda si really big-)
grid <-10^seq(10,-2 ,length=100)#here we are creating a grid with values from 10 to the 10th to 10 to the minuse 2, lenght=100
#ri fwe choose lambda zero a ridge will be choosen, lambda equals 1 will be a Lasso fittes 
set.seed(33)
lasso_student_math <- glmnet(x,y, alpha=1)
lasso_student_math_best_lambda <- cv.glmnet(x,y, alpha=1, standardize=TRUE, nfolds=5)
lasso_student_math_best_lambda$lambda.min
lasso_student_math <- glmnet(x,y, alpha=1,lambda=0.203589)
plot(lasso_student_math)
coefficients(lasso_student_math)
prediction_lasso_math <- predict(lasso_student_math, type="coefficients")
prediction_lasso_math[prediction_lasso_math!=0]
summary(lasso_student_math)





#Part 3: Classification Problems 

#Assignment 3 Linear Discrminant Analysis 
#LDA determines group means and computes, for each individual, the probability of belonging 
#to the different groups.The individual is then affected to the group with the highest probability score.
library(MASS)
library(factoextra)
library(cluster)
library(dplyr)
library(gridExtra)
library(ISLR)
library(glmnet)
library(caret)
setwd(
  "C:/Users/mario/OneDrive/Desktop/Pgd Data Science LSE/All Modules/Machine Learning ST3189-02/Assignment"
)
bank_data <- read.csv("bank.csv", stringsAsFactors = TRUE)
fix(bank_data)
set.seed(2)
data <- bank_data
dt <- sort(sample(nrow(data), nrow(data) * .7))
train_data <- data[dt, ]
test_data <- data[-dt, ]
#Now that we have our data sorted out on training and test data, we can start our discriminant analysis 
disc_analysis <-
  lda(
    y ~ age + job + marital + education + default + balance + housing + loan +
      contact + day + month + duration + campaign + pdays + previous + poutcome,
    data = train_data,
    
  )
names(disc_analysis)
disc_analysis
plot(disc_analysis) 
#here we have found both the coefficients of our LDA (the ones that we will use for predicition)
disc_analysis$prior
#here we are told that prior to our prediciton, 89% of our data belong to no's and 11% to yes. 
set.seed(4)
disc_analysis_prediction <- predict(disc_analysis, data=train_data)
names(disc_analysis_prediction)
disc_analysis_prediction$class
#class will give us the prediction about the movement of the market
table(disc_analysis_prediction$class)#here we are trying to have the same result in a more ordered way 
#here 92% of the predicitons belonged to the NO, and 8% to the YES
#Here we would change the threshold of how we aggroup our observations between yes and no. 
set.seed(45)
sum(disc_analysis_prediction$posterior[,1] >=0.5) #here we check that the no values are the same 
sum(disc_analysis_prediction$posterior[,1] <=0.5) #here we chec that the yes values are the same
#lets see if we change the threshold 
sum(disc_analysis_prediction$posterior[,1] >=0.7)
sum(disc_analysis_prediction$posterior[,1] <=0.7)
#even changing the threshold, the numbers does not change radically (but still have more on the yes side)

#LETS NOW TRY THE MODEL IN OUR TEST DATA 
disc_analysis <-
  lda(
    y ~ age + job + marital + education + default + balance + housing + loan +
      contact + day + month + duration + campaign + pdays + previous + poutcome,
    data = test_data,
    
  )
disc_analysis
disc_analysis$prior
#here we are told that prior to our prediciton, 88% of our data belong to no's and 12% to yes.
disc_analysis_prediction <- predict(disc_analysis, data=test_data)
disc_analysis_prediction
#here 91% belongs to the no group and 8% to the yes.

#MODEL VADILITY CONFUSION MATRIX 
table_1 <- table(list(predicted=disc_analysis_prediction$class, observed = test_data$y))
table_1
#OUr model predicted 1357 cases
#109 were predicted as YES, and 1248 as NO
#Out of the 109 predicted YES, just 69 were corrected predicted (0.63%) and 
#out of the 1357  predicted NO, just 1171 were corrected predicted (0.94%)
#then our model fitted in our test data correctly predicted 63% of the yes cases using the coefficients for 
#each variable that we have found WHICH IS OUR VARIABLE OF INTEREST. 
#OVERALL OUR MODEL SEEMS TO CORRECTLY PREDICT 91% OF THE TIME, BUT JUST A 63% FOR POSITITVE RESPONSES. 

#We now try fitting a logistic regression model 
set.seed(77)
logistic_model <- glm(y~., data=train_data, family=binomial)
summary(logistic_model)
#here we have which ones are statistically significants. (variables) 
coef(logistic_model)
#here we have the coefficient models 
logistic_model_probability  <- predict(logistic_model, type="response")
#here the predict function give us the PROBABILITY THAT THE ANSWER WILL BE YES GIVEN THE VALUES OF THE PREDICTORS
# TO INTERPRET THESE  VALUES WE NEED TO CONVERT THEM WITH E(^VALUE) 
logistic_model_probability
#ee are now running a prediction function 
set.seed(88)
logistic_model_prediction <- rep("No", 3164)
logistic_model_prediction[logistic_model_probability> 0.5]<-"Yes"
table(logistic_model_prediction, logistic_model$y)
#here the interpretation is as follows, 
#2978 were predicted as No, and 186 as YES, out of 3164
#but just 2725 out of 2978 were correctly predicted as NO (91%)
#and just 122 out of 186 were correctly predicted as YES (65%)

#finally we run our model using our test data.
set.seed(77)
logistic_model <- glm(y~., data=test_data, family=binomial)
summary(logistic_model)
#here we have which ones are statistically significants. (variables) 
coef(logistic_model)
#here we have the coefficient models 
logistic_model_probability  <- predict(logistic_model, type="response")
#here the predict function give us the PROBABILITY THAT THE ANSWER WILL BE YES GIVEN THE VALUES OF THE PREDICTORS
# TO INTERPRET THESE  VALUES WE NEED TO CONVERT THEM WITH E(^VALUE) 
logistic_model_probability
#ee are now running a prediction function 
set.seed(102)
logistic_model_prediction <- rep("No", 1357)
logistic_model_prediction[logistic_model_probability> 0.5]<-"Yes"
table(predicted=logistic_model_prediction, observed=logistic_model$y)
#here the interpretation is as follows, 
#1269 were predicted as NO, 88 were predicted as YES 
#of which 93% of the NO were correctly predicted 
#and 72% of the yes cases were correctly predicted as YES. 
#and this is our result when running the logistic regression in our test data.

#we now fit a boosted tree to our bank data 
library(tidyverse)
library(ggplot2)
library(caret)
library(caretEnsemble)
library(psych)
library(Amelia)
library(mice)
library(GGally)
library(rpart)
library(randomForest)
library(e1071)
library(klaR)
library(tree)
library(gbm)
setwd( "C:/Users/mario/OneDrive/Desktop/Pgd Data Science LSE/All Modules/Machine Learning ST3189-02/Assignment")
bank_data <- read.csv("bank.csv")
describe(bank_data)
str(bank_data)
data <-bank_data
dt <- sort(sample(nrow(data), nrow(data)*.7))
train_data <-data[dt,]
test_data <-data[-dt,]
#We will fit a boosted tree with the bernoulli dsitrbution for binary classification problems 
set.seed(2340)
#lets encode Yes=1 and No=0 
train_data$y <-ifelse(train_data$y=="yes",1,0)
table(train_data$y)
#lets run the regression 
bosteed_tree_bank <- gbm(y~.,data=train_data, distribution = "bernoulli", n.trees = 5000, interaction.depth = 4)
bosteed_tree_bank 
summary(bosteed_tree_bank)
#we now use the boosted model to predict y on the test set #

prediction_bank_tree <- predict(bosteed_tree_bank, newdata = test_data, n.trees = 5000)

#we try now but this time we  delete the duration variable 
setwd( "C:/Users/mario/OneDrive/Desktop/Pgd Data Science LSE/All Modules/Machine Learning ST3189-02/Assignment")
bank_data <- read.csv("bank.csv")
data <-bank_data
data <-bank_data[-c(12)]
dt <- sort(sample(nrow(data), nrow(data)*.7))
train_data <-data[dt,]
test_data <-data[-dt,]
set.seed(240)
#lets encode Yes=1 and No=0 
train_data$y <-ifelse(train_data$y=="yes",1,0)
table(train_data$y)
#lets run the regression 
bosteed_tree_bank <- gbm(y~.,data=train_data, distribution = "bernoulli", n.trees = 5000, interaction.depth = 4)
bosteed_tree_bank 
summary(bosteed_tree_bank)
#we now use the boosted model to predict y on the test set #

prediction_bank_tree <- predict(bosteed_tree_bank, newdata = test_data, n.trees = 5000)





```

