case study 3 v5
Chance Jones
2025-03-31
library(MASS)
library(tidyr)
library(dplyr)##
## Attaching package: 'dplyr'## The following object is masked from 'package:MASS':
##
## select## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(caret)## Loading required package: ggplot2## Loading required package: latticelibrary(lattice)
library(ggplot2)
library(gam)## Loading required package: splines## Loading required package: foreach## Loaded gam 1.22-5library(readr)
library(ROCR)
library(readxl)
library(e1071)
library(car)## Loading required package: carData##
## Attaching package: 'car'## The following object is masked from 'package:dplyr':
##
## recodecancer_data = read.csv("CancerData.csv")
head(cancer_data)## id diagnosis radius_mean texture_mean perimeter_mean area_mean
## 1 842302 M 17.99 10.38 122.80 1001.0
## 2 842517 M 20.57 17.77 132.90 1326.0
## 3 84300903 M 19.69 21.25 130.00 1203.0
## 4 84348301 M 11.42 20.38 77.58 386.1
## 5 84358402 M 20.29 14.34 135.10 1297.0
## 6 843786 M 12.45 15.70 82.57 477.1
## smoothness_mean compactness_mean concavity_mean concave.points_mean
## 1 0.11840 0.27760 0.3001 0.14710
## 2 0.08474 0.07864 0.0869 0.07017
## 3 0.10960 0.15990 0.1974 0.12790
## 4 0.14250 0.28390 0.2414 0.10520
## 5 0.10030 0.13280 0.1980 0.10430
## 6 0.12780 0.17000 0.1578 0.08089
## symmetry_mean fractal_dimension_mean radius_se texture_se perimeter_se
## 1 0.2419 0.07871 1.0950 0.9053 8.589
## 2 0.1812 0.05667 0.5435 0.7339 3.398
## 3 0.2069 0.05999 0.7456 0.7869 4.585
## 4 0.2597 0.09744 0.4956 1.1560 3.445
## 5 0.1809 0.05883 0.7572 0.7813 5.438
## 6 0.2087 0.07613 0.3345 0.8902 2.217
## area_se smoothness_se compactness_se concavity_se concave.points_se
## 1 153.40 0.006399 0.04904 0.05373 0.01587
## 2 74.08 0.005225 0.01308 0.01860 0.01340
## 3 94.03 0.006150 0.04006 0.03832 0.02058
## 4 27.23 0.009110 0.07458 0.05661 0.01867
## 5 94.44 0.011490 0.02461 0.05688 0.01885
## 6 27.19 0.007510 0.03345 0.03672 0.01137
## symmetry_se fractal_dimension_se radius_worst texture_worst perimeter_worst
## 1 0.03003 0.006193 25.38 17.33 184.60
## 2 0.01389 0.003532 24.99 23.41 158.80
## 3 0.02250 0.004571 23.57 25.53 152.50
## 4 0.05963 0.009208 14.91 26.50 98.87
## 5 0.01756 0.005115 22.54 16.67 152.20
## 6 0.02165 0.005082 15.47 23.75 103.40
## area_worst smoothness_worst compactness_worst concavity_worst
## 1 2019.0 0.1622 0.6656 0.7119
## 2 1956.0 0.1238 0.1866 0.2416
## 3 1709.0 0.1444 0.4245 0.4504
## 4 567.7 0.2098 0.8663 0.6869
## 5 1575.0 0.1374 0.2050 0.4000
## 6 741.6 0.1791 0.5249 0.5355
## concave.points_worst symmetry_worst fractal_dimension_worst
## 1 0.2654 0.4601 0.11890
## 2 0.1860 0.2750 0.08902
## 3 0.2430 0.3613 0.08758
## 4 0.2575 0.6638 0.17300
## 5 0.1625 0.2364 0.07678
## 6 0.1741 0.3985 0.12440Only one character variable, diagnosis, if the cancer
is M/malignent or B/benign
str(cancer_data)## 'data.frame': 569 obs. of 32 variables:
## $ id : int 842302 842517 84300903 84348301 84358402 843786 844359 84458202 844981 84501001 ...
## $ diagnosis : chr "M" "M" "M" "M" ...
## $ radius_mean : num 18 20.6 19.7 11.4 20.3 ...
## $ texture_mean : num 10.4 17.8 21.2 20.4 14.3 ...
## $ perimeter_mean : num 122.8 132.9 130 77.6 135.1 ...
## $ area_mean : num 1001 1326 1203 386 1297 ...
## $ smoothness_mean : num 0.1184 0.0847 0.1096 0.1425 0.1003 ...
## $ compactness_mean : num 0.2776 0.0786 0.1599 0.2839 0.1328 ...
## $ concavity_mean : num 0.3001 0.0869 0.1974 0.2414 0.198 ...
## $ concave.points_mean : num 0.1471 0.0702 0.1279 0.1052 0.1043 ...
## $ symmetry_mean : num 0.242 0.181 0.207 0.26 0.181 ...
## $ fractal_dimension_mean : num 0.0787 0.0567 0.06 0.0974 0.0588 ...
## $ radius_se : num 1.095 0.543 0.746 0.496 0.757 ...
## $ texture_se : num 0.905 0.734 0.787 1.156 0.781 ...
## $ perimeter_se : num 8.59 3.4 4.58 3.44 5.44 ...
## $ area_se : num 153.4 74.1 94 27.2 94.4 ...
## $ smoothness_se : num 0.0064 0.00522 0.00615 0.00911 0.01149 ...
## $ compactness_se : num 0.049 0.0131 0.0401 0.0746 0.0246 ...
## $ concavity_se : num 0.0537 0.0186 0.0383 0.0566 0.0569 ...
## $ concave.points_se : num 0.0159 0.0134 0.0206 0.0187 0.0188 ...
## $ symmetry_se : num 0.03 0.0139 0.0225 0.0596 0.0176 ...
## $ fractal_dimension_se : num 0.00619 0.00353 0.00457 0.00921 0.00511 ...
## $ radius_worst : num 25.4 25 23.6 14.9 22.5 ...
## $ texture_worst : num 17.3 23.4 25.5 26.5 16.7 ...
## $ perimeter_worst : num 184.6 158.8 152.5 98.9 152.2 ...
## $ area_worst : num 2019 1956 1709 568 1575 ...
## $ smoothness_worst : num 0.162 0.124 0.144 0.21 0.137 ...
## $ compactness_worst : num 0.666 0.187 0.424 0.866 0.205 ...
## $ concavity_worst : num 0.712 0.242 0.45 0.687 0.4 ...
## $ concave.points_worst : num 0.265 0.186 0.243 0.258 0.163 ...
## $ symmetry_worst : num 0.46 0.275 0.361 0.664 0.236 ...
## $ fractal_dimension_worst: num 0.1189 0.089 0.0876 0.173 0.0768 ...summary(cancer_data)## id diagnosis radius_mean texture_mean
## Min. : 8670 Length:569 Min. : 6.981 Min. : 9.71
## 1st Qu.: 869218 Class :character 1st Qu.:11.700 1st Qu.:16.17
## Median : 906024 Mode :character Median :13.370 Median :18.84
## Mean : 30371831 Mean :14.127 Mean :19.29
## 3rd Qu.: 8813129 3rd Qu.:15.780 3rd Qu.:21.80
## Max. :911320502 Max. :28.110 Max. :39.28
## perimeter_mean area_mean smoothness_mean compactness_mean
## Min. : 43.79 Min. : 143.5 Min. :0.05263 Min. :0.01938
## 1st Qu.: 75.17 1st Qu.: 420.3 1st Qu.:0.08637 1st Qu.:0.06492
## Median : 86.24 Median : 551.1 Median :0.09587 Median :0.09263
## Mean : 91.97 Mean : 654.9 Mean :0.09636 Mean :0.10434
## 3rd Qu.:104.10 3rd Qu.: 782.7 3rd Qu.:0.10530 3rd Qu.:0.13040
## Max. :188.50 Max. :2501.0 Max. :0.16340 Max. :0.34540
## concavity_mean concave.points_mean symmetry_mean fractal_dimension_mean
## Min. :0.00000 Min. :0.00000 Min. :0.1060 Min. :0.04996
## 1st Qu.:0.02956 1st Qu.:0.02031 1st Qu.:0.1619 1st Qu.:0.05770
## Median :0.06154 Median :0.03350 Median :0.1792 Median :0.06154
## Mean :0.08880 Mean :0.04892 Mean :0.1812 Mean :0.06280
## 3rd Qu.:0.13070 3rd Qu.:0.07400 3rd Qu.:0.1957 3rd Qu.:0.06612
## Max. :0.42680 Max. :0.20120 Max. :0.3040 Max. :0.09744
## radius_se texture_se perimeter_se area_se
## Min. :0.1115 Min. :0.3602 Min. : 0.757 Min. : 6.802
## 1st Qu.:0.2324 1st Qu.:0.8339 1st Qu.: 1.606 1st Qu.: 17.850
## Median :0.3242 Median :1.1080 Median : 2.287 Median : 24.530
## Mean :0.4052 Mean :1.2169 Mean : 2.866 Mean : 40.337
## 3rd Qu.:0.4789 3rd Qu.:1.4740 3rd Qu.: 3.357 3rd Qu.: 45.190
## Max. :2.8730 Max. :4.8850 Max. :21.980 Max. :542.200
## smoothness_se compactness_se concavity_se concave.points_se
## Min. :0.001713 Min. :0.002252 Min. :0.00000 Min. :0.000000
## 1st Qu.:0.005169 1st Qu.:0.013080 1st Qu.:0.01509 1st Qu.:0.007638
## Median :0.006380 Median :0.020450 Median :0.02589 Median :0.010930
## Mean :0.007041 Mean :0.025478 Mean :0.03189 Mean :0.011796
## 3rd Qu.:0.008146 3rd Qu.:0.032450 3rd Qu.:0.04205 3rd Qu.:0.014710
## Max. :0.031130 Max. :0.135400 Max. :0.39600 Max. :0.052790
## symmetry_se fractal_dimension_se radius_worst texture_worst
## Min. :0.007882 Min. :0.0008948 Min. : 7.93 Min. :12.02
## 1st Qu.:0.015160 1st Qu.:0.0022480 1st Qu.:13.01 1st Qu.:21.08
## Median :0.018730 Median :0.0031870 Median :14.97 Median :25.41
## Mean :0.020542 Mean :0.0037949 Mean :16.27 Mean :25.68
## 3rd Qu.:0.023480 3rd Qu.:0.0045580 3rd Qu.:18.79 3rd Qu.:29.72
## Max. :0.078950 Max. :0.0298400 Max. :36.04 Max. :49.54
## perimeter_worst area_worst smoothness_worst compactness_worst
## Min. : 50.41 Min. : 185.2 Min. :0.07117 Min. :0.02729
## 1st Qu.: 84.11 1st Qu.: 515.3 1st Qu.:0.11660 1st Qu.:0.14720
## Median : 97.66 Median : 686.5 Median :0.13130 Median :0.21190
## Mean :107.26 Mean : 880.6 Mean :0.13237 Mean :0.25427
## 3rd Qu.:125.40 3rd Qu.:1084.0 3rd Qu.:0.14600 3rd Qu.:0.33910
## Max. :251.20 Max. :4254.0 Max. :0.22260 Max. :1.05800
## concavity_worst concave.points_worst symmetry_worst fractal_dimension_worst
## Min. :0.0000 Min. :0.00000 Min. :0.1565 Min. :0.05504
## 1st Qu.:0.1145 1st Qu.:0.06493 1st Qu.:0.2504 1st Qu.:0.07146
## Median :0.2267 Median :0.09993 Median :0.2822 Median :0.08004
## Mean :0.2722 Mean :0.11461 Mean :0.2901 Mean :0.08395
## 3rd Qu.:0.3829 3rd Qu.:0.16140 3rd Qu.:0.3179 3rd Qu.:0.09208
## Max. :1.2520 Max. :0.29100 Max. :0.6638 Max. :0.20750Shows no missing or NA values
colSums(is.na(cancer_data)) #the code book says there are no missing, but double checking## id diagnosis radius_mean
## 0 0 0
## texture_mean perimeter_mean area_mean
## 0 0 0
## smoothness_mean compactness_mean concavity_mean
## 0 0 0
## concave.points_mean symmetry_mean fractal_dimension_mean
## 0 0 0
## radius_se texture_se perimeter_se
## 0 0 0
## area_se smoothness_se compactness_se
## 0 0 0
## concavity_se concave.points_se symmetry_se
## 0 0 0
## fractal_dimension_se radius_worst texture_worst
## 0 0 0
## perimeter_worst area_worst smoothness_worst
## 0 0 0
## compactness_worst concavity_worst concave.points_worst
## 0 0 0
## symmetry_worst fractal_dimension_worst
## 0 0Visually we can see the distribution of diagnosis
levels
ggplot(cancer_data, aes(x = diagnosis, fill = diagnosis)) +
geom_bar() +
scale_fill_manual(values = c("B" = "blue", "M" = "red")) + # Swaps default colors
labs(title = "Distribution of Diagnosis", x = "Diagnosis", y = "Frequency") +
theme_minimal()
table(cancer_data$diagnosis)##
## B M
## 357 212We can see that there are 357 benign observations, and 212 Malignent obvservations (the goal of this study is to see if we can classify certain results, so early detection can catch it, but we ultimatley want benign, we will focus mostly of malignent, so we can see the data that causes the malignent results)
cancer_data_copy = cancer_data
cancer_data_copy <- dplyr::select(cancer_data_copy, -id, -diagnosis)
corr_matrix <- cor(cancer_data_copy)
print(corr_matrix)## radius_mean texture_mean perimeter_mean area_mean
## radius_mean 1.000000000 0.323781891 0.997855281 0.987357170
## texture_mean 0.323781891 1.000000000 0.329533059 0.321085696
## perimeter_mean 0.997855281 0.329533059 1.000000000 0.986506804
## area_mean 0.987357170 0.321085696 0.986506804 1.000000000
## smoothness_mean 0.170581187 -0.023388516 0.207278164 0.177028377
## compactness_mean 0.506123578 0.236702222 0.556936211 0.498501682
## concavity_mean 0.676763550 0.302417828 0.716135650 0.685982829
## concave.points_mean 0.822528522 0.293464051 0.850977041 0.823268869
## symmetry_mean 0.147741242 0.071400980 0.183027212 0.151293079
## fractal_dimension_mean -0.311630826 -0.076437183 -0.261476908 -0.283109812
## radius_se 0.679090388 0.275868676 0.691765014 0.732562227
## texture_se -0.097317443 0.386357623 -0.086761078 -0.066280214
## perimeter_se 0.674171616 0.281673115 0.693134890 0.726628328
## area_se 0.735863663 0.259844987 0.744982694 0.800085921
## smoothness_se -0.222600125 0.006613777 -0.202694026 -0.166776667
## compactness_se 0.205999980 0.191974611 0.250743681 0.212582551
## concavity_se 0.194203623 0.143293077 0.228082345 0.207660060
## concave.points_se 0.376168956 0.163851025 0.407216916 0.372320282
## symmetry_se -0.104320881 0.009127168 -0.081629327 -0.072496588
## fractal_dimension_se -0.042641269 0.054457520 -0.005523391 -0.019886963
## radius_worst 0.969538973 0.352572947 0.969476363 0.962746086
## texture_worst 0.297007644 0.912044589 0.303038372 0.287488627
## perimeter_worst 0.965136514 0.358039575 0.970386887 0.959119574
## area_worst 0.941082460 0.343545947 0.941549808 0.959213326
## smoothness_worst 0.119616140 0.077503359 0.150549404 0.123522939
## compactness_worst 0.413462823 0.277829592 0.455774228 0.390410309
## concavity_worst 0.526911462 0.301025224 0.563879263 0.512605920
## concave.points_worst 0.744214198 0.295315843 0.771240789 0.722016626
## symmetry_worst 0.163953335 0.105007910 0.189115040 0.143569914
## fractal_dimension_worst 0.007065886 0.119205351 0.051018530 0.003737597
## smoothness_mean compactness_mean concavity_mean
## radius_mean 0.17058119 0.50612358 0.67676355
## texture_mean -0.02338852 0.23670222 0.30241783
## perimeter_mean 0.20727816 0.55693621 0.71613565
## area_mean 0.17702838 0.49850168 0.68598283
## smoothness_mean 1.00000000 0.65912322 0.52198377
## compactness_mean 0.65912322 1.00000000 0.88312067
## concavity_mean 0.52198377 0.88312067 1.00000000
## concave.points_mean 0.55369517 0.83113504 0.92139103
## symmetry_mean 0.55777479 0.60264105 0.50066662
## fractal_dimension_mean 0.58479200 0.56536866 0.33678336
## radius_se 0.30146710 0.49747345 0.63192482
## texture_se 0.06840645 0.04620483 0.07621835
## perimeter_se 0.29609193 0.54890526 0.66039079
## area_se 0.24655243 0.45565285 0.61742681
## smoothness_se 0.33237544 0.13529927 0.09856375
## compactness_se 0.31894330 0.73872179 0.67027882
## concavity_se 0.24839568 0.57051687 0.69127021
## concave.points_se 0.38067569 0.64226185 0.68325992
## symmetry_se 0.20077438 0.22997659 0.17800921
## fractal_dimension_se 0.28360670 0.50731813 0.44930075
## radius_worst 0.21312014 0.53531540 0.68823641
## texture_worst 0.03607180 0.24813283 0.29987889
## perimeter_worst 0.23885263 0.59021043 0.72956492
## area_worst 0.20671836 0.50960381 0.67598723
## smoothness_worst 0.80532420 0.56554117 0.44882204
## compactness_worst 0.47246844 0.86580904 0.75496802
## concavity_worst 0.43492571 0.81627525 0.88410264
## concave.points_worst 0.50305335 0.81557322 0.86132303
## symmetry_worst 0.39430948 0.51022343 0.40946413
## fractal_dimension_worst 0.49931637 0.68738232 0.51492989
## concave.points_mean symmetry_mean
## radius_mean 0.82252852 0.14774124
## texture_mean 0.29346405 0.07140098
## perimeter_mean 0.85097704 0.18302721
## area_mean 0.82326887 0.15129308
## smoothness_mean 0.55369517 0.55777479
## compactness_mean 0.83113504 0.60264105
## concavity_mean 0.92139103 0.50066662
## concave.points_mean 1.00000000 0.46249739
## symmetry_mean 0.46249739 1.00000000
## fractal_dimension_mean 0.16691738 0.47992133
## radius_se 0.69804983 0.30337926
## texture_se 0.02147958 0.12805293
## perimeter_se 0.71064987 0.31389276
## area_se 0.69029854 0.22397022
## smoothness_se 0.02765331 0.18732117
## compactness_se 0.49042425 0.42165915
## concavity_se 0.43916707 0.34262702
## concave.points_se 0.61563413 0.39329787
## symmetry_se 0.09535079 0.44913654
## fractal_dimension_se 0.25758375 0.33178615
## radius_worst 0.83031763 0.18572775
## texture_worst 0.29275171 0.09065069
## perimeter_worst 0.85592313 0.21916856
## area_worst 0.80962962 0.17719338
## smoothness_worst 0.45275305 0.42667503
## compactness_worst 0.66745368 0.47320001
## concavity_worst 0.75239950 0.43372101
## concave.points_worst 0.91015531 0.43029661
## symmetry_worst 0.37574415 0.69982580
## fractal_dimension_worst 0.36866113 0.43841350
## fractal_dimension_mean radius_se texture_se
## radius_mean -0.3116308263 0.6790903880 -0.09731744
## texture_mean -0.0764371834 0.2758686762 0.38635762
## perimeter_mean -0.2614769081 0.6917650135 -0.08676108
## area_mean -0.2831098117 0.7325622270 -0.06628021
## smoothness_mean 0.5847920019 0.3014670983 0.06840645
## compactness_mean 0.5653686634 0.4974734461 0.04620483
## concavity_mean 0.3367833594 0.6319248221 0.07621835
## concave.points_mean 0.1669173832 0.6980498336 0.02147958
## symmetry_mean 0.4799213301 0.3033792632 0.12805293
## fractal_dimension_mean 1.0000000000 0.0001109951 0.16417397
## radius_se 0.0001109951 1.0000000000 0.21324734
## texture_se 0.1641739659 0.2132473373 1.00000000
## perimeter_se 0.0398299316 0.9727936770 0.22317073
## area_se -0.0901702475 0.9518301121 0.11156725
## smoothness_se 0.4019644254 0.1645142198 0.39724285
## compactness_se 0.5598366906 0.3560645755 0.23169970
## concavity_se 0.4466303217 0.3323575376 0.19499846
## concave.points_se 0.3411980444 0.5133464414 0.23028340
## symmetry_se 0.3450073971 0.2405673625 0.41162068
## fractal_dimension_se 0.6881315775 0.2277535327 0.27972275
## radius_worst -0.2536914949 0.7150651951 -0.11169031
## texture_worst -0.0512692020 0.1947985568 0.40900277
## perimeter_worst -0.2051512113 0.7196838037 -0.10224192
## area_worst -0.2318544512 0.7515484761 -0.08319499
## smoothness_worst 0.5049420754 0.1419185529 -0.07365766
## compactness_worst 0.4587981567 0.2871031656 -0.09243935
## concavity_worst 0.3462338763 0.3805846346 -0.06895622
## concave.points_worst 0.1753254492 0.5310623278 -0.11963752
## symmetry_worst 0.3340186839 0.0945428304 -0.12821476
## fractal_dimension_worst 0.7672967792 0.0495594325 -0.04565457
## perimeter_se area_se smoothness_se compactness_se
## radius_mean 0.67417162 0.73586366 -0.222600125 0.2060000
## texture_mean 0.28167311 0.25984499 0.006613777 0.1919746
## perimeter_mean 0.69313489 0.74498269 -0.202694026 0.2507437
## area_mean 0.72662833 0.80008592 -0.166776667 0.2125826
## smoothness_mean 0.29609193 0.24655243 0.332375443 0.3189433
## compactness_mean 0.54890526 0.45565285 0.135299268 0.7387218
## concavity_mean 0.66039079 0.61742681 0.098563746 0.6702788
## concave.points_mean 0.71064987 0.69029854 0.027653308 0.4904242
## symmetry_mean 0.31389276 0.22397022 0.187321165 0.4216591
## fractal_dimension_mean 0.03982993 -0.09017025 0.401964425 0.5598367
## radius_se 0.97279368 0.95183011 0.164514220 0.3560646
## texture_se 0.22317073 0.11156725 0.397242853 0.2316997
## perimeter_se 1.00000000 0.93765541 0.151075331 0.4163224
## area_se 0.93765541 1.00000000 0.075150338 0.2848401
## smoothness_se 0.15107533 0.07515034 1.000000000 0.3366961
## compactness_se 0.41632237 0.28484006 0.336696081 1.0000000
## concavity_se 0.36248158 0.27089473 0.268684760 0.8012683
## concave.points_se 0.55626408 0.41572957 0.328429499 0.7440827
## symmetry_se 0.26648709 0.13410898 0.413506125 0.3947128
## fractal_dimension_se 0.24414277 0.12707090 0.427374207 0.8032688
## radius_worst 0.69720059 0.75737319 -0.230690710 0.2046072
## texture_worst 0.20037085 0.19649665 -0.074742965 0.1430026
## perimeter_worst 0.72103131 0.76121264 -0.217303755 0.2605158
## area_worst 0.73071297 0.81140796 -0.182195478 0.1993713
## smoothness_worst 0.13005439 0.12538943 0.314457456 0.2273942
## compactness_worst 0.34191945 0.28325654 -0.055558139 0.6787804
## concavity_worst 0.41889882 0.38510014 -0.058298387 0.6391467
## concave.points_worst 0.55489723 0.53816631 -0.102006796 0.4832083
## symmetry_worst 0.10993043 0.07412629 -0.107342098 0.2778784
## fractal_dimension_worst 0.08543257 0.01753930 0.101480315 0.5909728
## concavity_se concave.points_se symmetry_se
## radius_mean 0.1942036 0.37616896 -0.104320881
## texture_mean 0.1432931 0.16385103 0.009127168
## perimeter_mean 0.2280823 0.40721692 -0.081629327
## area_mean 0.2076601 0.37232028 -0.072496588
## smoothness_mean 0.2483957 0.38067569 0.200774376
## compactness_mean 0.5705169 0.64226185 0.229976591
## concavity_mean 0.6912702 0.68325992 0.178009208
## concave.points_mean 0.4391671 0.61563413 0.095350787
## symmetry_mean 0.3426270 0.39329787 0.449136542
## fractal_dimension_mean 0.4466303 0.34119804 0.345007397
## radius_se 0.3323575 0.51334644 0.240567362
## texture_se 0.1949985 0.23028340 0.411620680
## perimeter_se 0.3624816 0.55626408 0.266487092
## area_se 0.2708947 0.41572957 0.134108980
## smoothness_se 0.2686848 0.32842950 0.413506125
## compactness_se 0.8012683 0.74408267 0.394712835
## concavity_se 1.0000000 0.77180399 0.309428578
## concave.points_se 0.7718040 1.00000000 0.312780223
## symmetry_se 0.3094286 0.31278022 1.000000000
## fractal_dimension_se 0.7273722 0.61104414 0.369078083
## radius_worst 0.1869035 0.35812667 -0.128120769
## texture_worst 0.1002410 0.08674121 -0.077473420
## perimeter_worst 0.2266804 0.39499925 -0.103753044
## area_worst 0.1883527 0.34227116 -0.110342743
## smoothness_worst 0.1684813 0.21535060 -0.012661800
## compactness_worst 0.4848578 0.45288838 0.060254879
## concavity_worst 0.6625641 0.54959238 0.037119049
## concave.points_worst 0.4404723 0.60244961 -0.030413396
## symmetry_worst 0.1977878 0.14311567 0.389402485
## fractal_dimension_worst 0.4393293 0.31065455 0.078079476
## fractal_dimension_se radius_worst texture_worst
## radius_mean -0.042641269 0.96953897 0.297007644
## texture_mean 0.054457520 0.35257295 0.912044589
## perimeter_mean -0.005523391 0.96947636 0.303038372
## area_mean -0.019886963 0.96274609 0.287488627
## smoothness_mean 0.283606699 0.21312014 0.036071799
## compactness_mean 0.507318127 0.53531540 0.248132833
## concavity_mean 0.449300749 0.68823641 0.299878889
## concave.points_mean 0.257583746 0.83031763 0.292751713
## symmetry_mean 0.331786146 0.18572775 0.090650688
## fractal_dimension_mean 0.688131577 -0.25369149 -0.051269202
## radius_se 0.227753533 0.71506520 0.194798557
## texture_se 0.279722748 -0.11169031 0.409002766
## perimeter_se 0.244142773 0.69720059 0.200370854
## area_se 0.127070903 0.75737319 0.196496649
## smoothness_se 0.427374207 -0.23069071 -0.074742965
## compactness_se 0.803268818 0.20460717 0.143002583
## concavity_se 0.727372184 0.18690352 0.100240984
## concave.points_se 0.611044139 0.35812667 0.086741210
## symmetry_se 0.369078083 -0.12812077 -0.077473420
## fractal_dimension_se 1.000000000 -0.03748762 -0.003195029
## radius_worst -0.037487618 1.00000000 0.359920754
## texture_worst -0.003195029 0.35992075 1.000000000
## perimeter_worst -0.001000398 0.99370792 0.365098245
## area_worst -0.022736147 0.98401456 0.345842283
## smoothness_worst 0.170568316 0.21657443 0.225429415
## compactness_worst 0.390158842 0.47582004 0.360832339
## concavity_worst 0.379974661 0.57397471 0.368365607
## concave.points_worst 0.215204013 0.78742385 0.359754610
## symmetry_worst 0.111093956 0.24352920 0.233027461
## fractal_dimension_worst 0.591328066 0.09349198 0.219122425
## perimeter_worst area_worst smoothness_worst
## radius_mean 0.965136514 0.94108246 0.11961614
## texture_mean 0.358039575 0.34354595 0.07750336
## perimeter_mean 0.970386887 0.94154981 0.15054940
## area_mean 0.959119574 0.95921333 0.12352294
## smoothness_mean 0.238852626 0.20671836 0.80532420
## compactness_mean 0.590210428 0.50960381 0.56554117
## concavity_mean 0.729564917 0.67598723 0.44882204
## concave.points_mean 0.855923128 0.80962962 0.45275305
## symmetry_mean 0.219168559 0.17719338 0.42667503
## fractal_dimension_mean -0.205151211 -0.23185445 0.50494208
## radius_se 0.719683804 0.75154848 0.14191855
## texture_se -0.102241922 -0.08319499 -0.07365766
## perimeter_se 0.721031310 0.73071297 0.13005439
## area_se 0.761212636 0.81140796 0.12538943
## smoothness_se -0.217303755 -0.18219548 0.31445746
## compactness_se 0.260515840 0.19937133 0.22739423
## concavity_se 0.226680426 0.18835265 0.16848132
## concave.points_se 0.394999252 0.34227116 0.21535060
## symmetry_se -0.103753044 -0.11034274 -0.01266180
## fractal_dimension_se -0.001000398 -0.02273615 0.17056832
## radius_worst 0.993707916 0.98401456 0.21657443
## texture_worst 0.365098245 0.34584228 0.22542941
## perimeter_worst 1.000000000 0.97757809 0.23677460
## area_worst 0.977578091 1.00000000 0.20914533
## smoothness_worst 0.236774604 0.20914533 1.00000000
## compactness_worst 0.529407690 0.43829628 0.56818652
## concavity_worst 0.618344080 0.54333053 0.51852329
## concave.points_worst 0.816322102 0.74741880 0.54769090
## symmetry_worst 0.269492769 0.20914551 0.49383833
## fractal_dimension_worst 0.138956862 0.07964703 0.61762419
## compactness_worst concavity_worst concave.points_worst
## radius_mean 0.41346282 0.52691146 0.7442142
## texture_mean 0.27782959 0.30102522 0.2953158
## perimeter_mean 0.45577423 0.56387926 0.7712408
## area_mean 0.39041031 0.51260592 0.7220166
## smoothness_mean 0.47246844 0.43492571 0.5030534
## compactness_mean 0.86580904 0.81627525 0.8155732
## concavity_mean 0.75496802 0.88410264 0.8613230
## concave.points_mean 0.66745368 0.75239950 0.9101553
## symmetry_mean 0.47320001 0.43372101 0.4302966
## fractal_dimension_mean 0.45879816 0.34623388 0.1753254
## radius_se 0.28710317 0.38058463 0.5310623
## texture_se -0.09243935 -0.06895622 -0.1196375
## perimeter_se 0.34191945 0.41889882 0.5548972
## area_se 0.28325654 0.38510014 0.5381663
## smoothness_se -0.05555814 -0.05829839 -0.1020068
## compactness_se 0.67878035 0.63914670 0.4832083
## concavity_se 0.48485780 0.66256413 0.4404723
## concave.points_se 0.45288838 0.54959238 0.6024496
## symmetry_se 0.06025488 0.03711905 -0.0304134
## fractal_dimension_se 0.39015884 0.37997466 0.2152040
## radius_worst 0.47582004 0.57397471 0.7874239
## texture_worst 0.36083234 0.36836561 0.3597546
## perimeter_worst 0.52940769 0.61834408 0.8163221
## area_worst 0.43829628 0.54333053 0.7474188
## smoothness_worst 0.56818652 0.51852329 0.5476909
## compactness_worst 1.00000000 0.89226090 0.8010804
## concavity_worst 0.89226090 1.00000000 0.8554339
## concave.points_worst 0.80108036 0.85543386 1.0000000
## symmetry_worst 0.61444050 0.53251973 0.5025285
## fractal_dimension_worst 0.81045486 0.68651092 0.5111141
## symmetry_worst fractal_dimension_worst
## radius_mean 0.16395333 0.007065886
## texture_mean 0.10500791 0.119205351
## perimeter_mean 0.18911504 0.051018530
## area_mean 0.14356991 0.003737597
## smoothness_mean 0.39430948 0.499316369
## compactness_mean 0.51022343 0.687382323
## concavity_mean 0.40946413 0.514929891
## concave.points_mean 0.37574415 0.368661134
## symmetry_mean 0.69982580 0.438413498
## fractal_dimension_mean 0.33401868 0.767296779
## radius_se 0.09454283 0.049559432
## texture_se -0.12821476 -0.045654569
## perimeter_se 0.10993043 0.085432572
## area_se 0.07412629 0.017539295
## smoothness_se -0.10734210 0.101480315
## compactness_se 0.27787843 0.590972763
## concavity_se 0.19778782 0.439329269
## concave.points_se 0.14311567 0.310654551
## symmetry_se 0.38940248 0.078079476
## fractal_dimension_se 0.11109396 0.591328066
## radius_worst 0.24352920 0.093491979
## texture_worst 0.23302746 0.219122425
## perimeter_worst 0.26949277 0.138956862
## area_worst 0.20914551 0.079647034
## smoothness_worst 0.49383833 0.617624192
## compactness_worst 0.61444050 0.810454856
## concavity_worst 0.53251973 0.686510921
## concave.points_worst 0.50252849 0.511114146
## symmetry_worst 1.00000000 0.537848206
## fractal_dimension_worst 0.53784821 1.000000000Hard to see, so will make visual plot
library(corrplot)## Warning: package 'corrplot' was built under R version 4.3.3## corrplot 0.95 loaded# Adjust margins to give labels more space
par(mar = c(5, 5, 5, 5))
# Plot correlation matrix with larger text and better spacing
corrplot(corr_matrix, method="circle", type="upper", order="hclust",
tl.col="black", tl.srt=45, tl.cex=0.6) # Adjust tl.cex for text size
Almost all variables are correlated, very heavily, creating a dataset that is hard to navigate and properly process, as indicated by the VIF function, these high values skews and implodes the results, giving false results.
We can now see a majority of values that fall below 0.8
library(corrplot)
# Adjust margins to give labels more space
par(mar = c(5, 5, 5, 5))
# Plot correlation matrix with larger text and better spacing
corrplot(corr_matrix_2, method="circle", type="upper", order="hclust",
tl.col="black", tl.srt=45, tl.cex=0.6) # Adjust tl.cex for text size
cancer_data$diagnosis <- as.factor(cancer_data$diagnosis)cols_to_remove <- c("id", "radius_mean", "perimeter_mean", "area_mean", "compactness_mean",
"concave.points_mean", "area_worst", "smoothness_worst", "concavity_worst",
"fractal_dimension_se", "concave.points_worst", "perimeter_worst",
"radius_worst", "compactness_se", "texture_worst", "symmetry_worst",
"radius_se", "concavity_se", "fractal_dimension_worst")
cancer_data <- dplyr::select(cancer_data, -all_of(cols_to_remove))# sample.split used instead of just sample, to keep an even split between benign and malignant values
library(caTools)
set.seed(2025)
split <- sample.split(cancer_data$diagnosis, SplitRatio = 0.8)
cancer_train <- subset(cancer_data, split == TRUE)
cancer_test <- subset(cancer_data, split == FALSE)glm_model <- glm(diagnosis ~ ., data = cancer_train, family = binomial)## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurredsummary(glm_model)##
## Call:
## glm(formula = diagnosis ~ ., family = binomial, data = cancer_train)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -11.40427 5.10549 -2.234 0.025501 *
## texture_mean 0.43537 0.10727 4.059 4.94e-05 ***
## smoothness_mean 117.85202 40.95343 2.878 0.004006 **
## concavity_mean 42.36850 12.08800 3.505 0.000457 ***
## symmetry_mean 23.52253 19.65488 1.197 0.231393
## fractal_dimension_mean -318.16610 88.23909 -3.606 0.000311 ***
## texture_se -0.88536 0.88585 -0.999 0.317577
## perimeter_se -1.36216 0.73491 -1.854 0.063810 .
## area_se 0.24501 0.06166 3.973 7.09e-05 ***
## smoothness_se 110.53026 174.59289 0.633 0.526685
## concave.points_se -233.80006 107.72999 -2.170 0.029989 *
## symmetry_se -111.31879 57.53932 -1.935 0.053033 .
## compactness_worst 14.44933 4.95394 2.917 0.003537 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 602.315 on 455 degrees of freedom
## Residual deviance: 88.727 on 443 degrees of freedom
## AIC: 114.73
##
## Number of Fisher Scoring iterations: 9library(car)
vif(glm_model)## texture_mean smoothness_mean concavity_mean
## 2.694404 3.163111 3.334797
## symmetry_mean fractal_dimension_mean texture_se
## 2.775519 3.695366 3.053795
## perimeter_se area_se smoothness_se
## 8.670477 9.899194 2.129733
## concave.points_se symmetry_se compactness_worst
## 4.064652 2.951036 4.302383The above logistic model, is to just show what was taken out/ what was left as well as show casing the VIF values, letting us know that all the values are below 10
Removing the values that inflated analysis via correlation, while
also removing id because it is irrelevant and would skew
the data while providing no significant value, will be done further
down
Will be running through multiple models to find the best one
# Load necessary libraries
library(caret)
library(randomForest)## randomForest 4.7-1.2## Type rfNews() to see new features/changes/bug fixes.##
## Attaching package: 'randomForest'## The following object is masked from 'package:ggplot2':
##
## margin## The following object is masked from 'package:dplyr':
##
## combinelibrary(e1071) # For SVM
library(xgboost)##
## Attaching package: 'xgboost'## The following object is masked from 'package:dplyr':
##
## slicelibrary(pROC)## Type 'citation("pROC")' for a citation.##
## Attaching package: 'pROC'## The following objects are masked from 'package:stats':
##
## cov, smooth, varlibrary(dplyr)
library(car)
cancer_data = read.csv("CancerData.csv")
# Remove 'id' column
cancer_data <- cancer_data[, !(names(cancer_data) %in% c("id"))]
# Encode 'diagnosis' as factor (B = 0, M = 1)
cancer_data$diagnosis <- as.numeric(factor(cancer_data$diagnosis, levels = c("B", "M"))) - 1
# Keep a copy of the full dataset before feature selection
cancer_data_full <- cancer_data
# Remove multicollinear variables for logistic regression
cancer_data <- dplyr::select(cancer_data, -radius_mean, -perimeter_mean, -area_mean, -compactness_mean,
-concave.points_mean, -area_worst, -smoothness_worst, -concavity_worst,
-fractal_dimension_se, -concave.points_worst, -perimeter_worst, -radius_worst,
-compactness_se, -texture_worst, -symmetry_worst, -radius_se, -concavity_se,
-fractal_dimension_worst)
# Split into training (80%) and testing (20%) sets for both datasets
set.seed(2025)
trainIndex <- createDataPartition(cancer_data$diagnosis, p = 0.8, list = FALSE)
train_data <- cancer_data[trainIndex, ]
test_data <- cancer_data[-trainIndex, ]
train_data_full <- cancer_data_full[trainIndex, ] # Full dataset (all features)
test_data_full <- cancer_data_full[-trainIndex, ]
print("trainig set number of Benign and Malignant observations")## [1] "trainig set number of Benign and Malignant observations"table(train_data$diagnosis)##
## 0 1
## 279 177print("testing set number of Benign and Malignant observations")## [1] "testing set number of Benign and Malignant observations"table(test_data$diagnosis)##
## 0 1
## 78 35# Standardize numeric features (excluding 'diagnosis')
preprocess_params <- preProcess(train_data[, -1], method = c("center", "scale"))
train_data[, -1] <- predict(preprocess_params, train_data[, -1])
test_data[, -1] <- predict(preprocess_params, test_data[, -1])
preprocess_params_full <- preProcess(train_data_full[, -1], method = c("center", "scale"))
train_data_full[, -1] <- predict(preprocess_params_full, train_data_full[, -1])
test_data_full[, -1] <- predict(preprocess_params_full, test_data_full[, -1])
# Convert diagnosis to factor
train_data$diagnosis <- factor(train_data$diagnosis, levels = c(0, 1), labels = c("Benign", "Malignant"))
test_data$diagnosis <- factor(test_data$diagnosis, levels = c(0, 1), labels = c("Benign", "Malignant"))
train_data_full$diagnosis <- factor(train_data_full$diagnosis, levels = c(0, 1), labels = c("Benign", "Malignant"))
test_data_full$diagnosis <- factor(test_data_full$diagnosis, levels = c(0, 1), labels = c("Benign", "Malignant"))
# Define training control for cross-validation
train_control <- trainControl(method = "cv", number = 5, classProbs = TRUE, summaryFunction = twoClassSummary)
# Train Logistic Regression (using reduced dataset)
logistic_model <- train(diagnosis ~ ., data = train_data, method = "glm",
family = binomial, trControl = train_control, metric = "ROC")
# Train Random Forest (using full dataset)
rf_model <- train(diagnosis ~ ., data = train_data_full, method = "rf",
trControl = train_control, metric = "ROC", ntree = 100)
# Train SVM (using full dataset)
svm_model <- train(diagnosis ~ ., data = train_data_full, method = "svmRadial",
trControl = train_control, metric = "ROC")
# Train XGBoost (using full dataset)
xgb_grid <- expand.grid(
nrounds = 100, # Number of boosting iterations
max_depth = 3,
eta = 0.1,
gamma = 0,
colsample_bytree = 0.8,
min_child_weight = 1,
subsample = 0.8
)
xgb_model <- train(
diagnosis ~ .,
data = train_data_full,
method = "xgbTree",
trControl = train_control,
metric = "ROC",
tuneGrid = xgb_grid
)
# Function to evaluate models
evaluate_model <- function(model, test_data) {
predictions <- predict(model, test_data)
prob_predictions <- predict(model, test_data, type = "prob")[, 2]
accuracy <- mean(predictions == test_data$diagnosis)
auc <- roc(test_data$diagnosis, prob_predictions)$auc
cat("\nModel:", model$method)
cat("\nAccuracy:", round(accuracy, 4))
cat("\nAUC-ROC:", round(auc, 4))
cat("\nConfusion Matrix:\n")
print(confusionMatrix(predictions, test_data$diagnosis))
}
# Evaluate models
evaluate_model(logistic_model, test_data) # Using reduced dataset## Setting levels: control = Benign, case = Malignant## Setting direction: controls < cases##
## Model: glm
## Accuracy: 0.9469
## AUC-ROC: 0.9901
## Confusion Matrix:
## Confusion Matrix and Statistics
##
## Reference
## Prediction Benign Malignant
## Benign 75 3
## Malignant 3 32
##
## Accuracy : 0.9469
## 95% CI : (0.888, 0.9803)
## No Information Rate : 0.6903
## P-Value [Acc > NIR] : 1.511e-11
##
## Kappa : 0.8758
##
## Mcnemar's Test P-Value : 1
##
## Sensitivity : 0.9615
## Specificity : 0.9143
## Pos Pred Value : 0.9615
## Neg Pred Value : 0.9143
## Prevalence : 0.6903
## Detection Rate : 0.6637
## Detection Prevalence : 0.6903
## Balanced Accuracy : 0.9379
##
## 'Positive' Class : Benign
## evaluate_model(rf_model, test_data_full) # Using full dataset## Setting levels: control = Benign, case = Malignant
## Setting direction: controls < cases##
## Model: rf
## Accuracy: 0.9823
## AUC-ROC: 0.9828
## Confusion Matrix:
## Confusion Matrix and Statistics
##
## Reference
## Prediction Benign Malignant
## Benign 77 1
## Malignant 1 34
##
## Accuracy : 0.9823
## 95% CI : (0.9375, 0.9978)
## No Information Rate : 0.6903
## P-Value [Acc > NIR] : 8.537e-16
##
## Kappa : 0.9586
##
## Mcnemar's Test P-Value : 1
##
## Sensitivity : 0.9872
## Specificity : 0.9714
## Pos Pred Value : 0.9872
## Neg Pred Value : 0.9714
## Prevalence : 0.6903
## Detection Rate : 0.6814
## Detection Prevalence : 0.6903
## Balanced Accuracy : 0.9793
##
## 'Positive' Class : Benign
## evaluate_model(svm_model, test_data_full) # Using full dataset## Setting levels: control = Benign, case = Malignant
## Setting direction: controls < cases##
## Model: svmRadial
## Accuracy: 0.9646
## AUC-ROC: 0.9938
## Confusion Matrix:
## Confusion Matrix and Statistics
##
## Reference
## Prediction Benign Malignant
## Benign 75 1
## Malignant 3 34
##
## Accuracy : 0.9646
## 95% CI : (0.9118, 0.9903)
## No Information Rate : 0.6903
## P-Value [Acc > NIR] : 1.826e-13
##
## Kappa : 0.9185
##
## Mcnemar's Test P-Value : 0.6171
##
## Sensitivity : 0.9615
## Specificity : 0.9714
## Pos Pred Value : 0.9868
## Neg Pred Value : 0.9189
## Prevalence : 0.6903
## Detection Rate : 0.6637
## Detection Prevalence : 0.6726
## Balanced Accuracy : 0.9665
##
## 'Positive' Class : Benign
## evaluate_model(xgb_model, test_data_full) # Using full dataset## Setting levels: control = Benign, case = Malignant
## Setting direction: controls < cases##
## Model: xgbTree
## Accuracy: 0.9823
## AUC-ROC: 0.9912
## Confusion Matrix:
## Confusion Matrix and Statistics
##
## Reference
## Prediction Benign Malignant
## Benign 77 1
## Malignant 1 34
##
## Accuracy : 0.9823
## 95% CI : (0.9375, 0.9978)
## No Information Rate : 0.6903
## P-Value [Acc > NIR] : 8.537e-16
##
## Kappa : 0.9586
##
## Mcnemar's Test P-Value : 1
##
## Sensitivity : 0.9872
## Specificity : 0.9714
## Pos Pred Value : 0.9872
## Neg Pred Value : 0.9714
## Prevalence : 0.6903
## Detection Rate : 0.6814
## Detection Prevalence : 0.6903
## Balanced Accuracy : 0.9793
##
## 'Positive' Class : Benign
## # Load required libraries
library(caTools)
library(rpart)## Warning: package 'rpart' was built under R version 4.3.3library(rpart.plot) # For better tree visualization## Warning: package 'rpart.plot' was built under R version 4.3.3# Ensure 'diagnosis' is a factor
cancer_data$diagnosis <- factor(cancer_data$diagnosis, levels = c(0, 1), labels = c("Benign", "Malignant"))
# Set seed for reproducibility
set.seed(2025)
# Perform stratified split
split_2 <- sample.split(cancer_data$diagnosis, SplitRatio = 0.8)
# Create training and test sets
cancer_train_2 <- subset(cancer_data, split_2 == TRUE)
cancer_test_2 <- subset(cancer_data, split_2 == FALSE)
# Train Decision Tree Model
tree_model <- rpart(diagnosis ~ ., data = cancer_train_2, method = "class")
# Plot the tree using an improved visualization
rpart.plot(tree_model, type = 2, extra = 104, tweak = 1.2, box.palette = "RdYlGn", shadow.col = "gray", nn = TRUE)
# Get variable importance
rf_importance <- varImp(rf_model)
# Print importance
print(rf_importance)## rf variable importance
##
## only 20 most important variables shown (out of 30)
##
## Overall
## concave.points_worst 100.000
## area_worst 80.975
## area_mean 71.959
## radius_worst 62.302
## concave.points_mean 59.854
## perimeter_mean 55.627
## concavity_worst 42.759
## area_se 41.396
## radius_mean 38.970
## perimeter_worst 33.813
## concavity_mean 27.732
## compactness_worst 27.351
## radius_se 25.590
## perimeter_se 22.055
## compactness_mean 16.623
## texture_mean 15.874
## fractal_dimension_worst 9.994
## texture_worst 8.734
## concave.points_se 8.183
## smoothness_worst 7.095# Plot importance
plot(rf_importance, main = "Variable Importance - Random Forest")