#Importing Data
sharks <- read.csv("~/Penguin/sharks.csv")Investigating Blotching as a Stress Indicator in Caribbean Reef Sharks (Carcharhinus perezi): Implications for Conservation and Capture Practices
1. Importing Data
1.1 Importing Libraries
#Importing Libraries
library(ggplot2)
library(arm)
library(tidyverse)
library(car)
library(HH)
library(lattice)
library(outliers)
library(scales)
library(lawstat)
library(ggbeeswarm)
library(dplyr)
library(VIM)1.2 Exploring the Data
#Understanding of the Dataset
#Calling data
sharks ID sex blotch BPM weight length air water meta
1 SH001 Female 37.17081 148 74.69050 186.6703 37.73957 23.37377 64.11183
2 SH002 Female 34.54973 158 73.41627 189.3189 35.68413 21.42088 73.68676
3 SH003 Female 36.32861 125 71.80837 283.6332 34.79854 20.05114 54.43466
4 SH004 Male 35.33881 161 104.62985 171.0986 36.15973 21.64319 86.32615
5 SH005 Female 37.39799 138 67.13098 264.3160 33.61477 21.76143 107.97796
6 SH006 Male 33.54668 126 110.49396 269.9829 36.38343 20.85200 108.86475
7 SH007 Male 36.68291 166 100.85795 194.2929 33.14734 21.80969 99.74645
8 SH008 Female 36.29497 135 101.20073 128.4664 36.77278 21.30411 96.33309
9 SH009 Male 35.40344 132 94.96854 268.6220 35.27123 22.21935 78.97403
10 SH010 Female 36.02478 127 71.25366 163.4187 35.68505 24.55002 72.28744
11 SH011 Female 31.77830 126 67.48792 179.0241 35.69932 24.49316 109.47375
12 SH012 Female 36.23767 131 70.03673 235.0309 33.66390 20.18835 62.02516
13 SH013 Male 35.68104 133 109.20626 244.0018 37.50058 23.63367 110.15313
14 SH014 Male 39.83638 121 90.88816 193.3701 34.44364 23.39661 99.84946
15 SH015 Female 37.04890 166 67.66870 253.2767 33.97566 23.21299 102.88892
16 SH016 Male 34.75400 128 87.65517 243.8493 33.91872 24.77314 85.70257
17 SH017 Female 34.17118 145 100.18700 180.6655 33.77393 23.95949 101.74559
18 SH018 Female 36.36105 155 104.51024 150.0938 35.71842 22.43661 94.89843
19 SH019 Male 33.49141 154 97.43775 168.4244 35.06666 21.11872 104.33486
20 SH020 Male 35.09741 125 93.30120 290.8302 36.07481 20.56476 95.31837
21 SH021 Male 35.75184 136 67.20550 269.3138 35.09389 22.55188 78.00404
22 SH022 Female 34.41702 122 106.51215 233.0735 36.28748 22.81342 69.08480
23 SH023 Female 36.33441 165 72.31583 211.3676 34.20907 25.46146 75.80276
24 SH024 Male 34.98489 150 108.56342 246.7264 33.46063 24.21346 52.73695
25 SH025 Female 35.11890 122 109.26327 206.5210 34.82810 22.92370 83.34694
26 SH026 Female 34.25971 165 102.63724 171.3584 37.34757 20.26606 76.20320
27 SH027 Male 39.13972 164 101.01174 252.1332 35.67246 21.82772 103.00903
28 SH028 Male 35.79007 140 97.12517 245.5119 33.67580 23.48505 68.32779
29 SH029 Male 35.17775 122 68.97648 218.6683 37.60242 23.31552 105.39974
30 SH030 Male 34.34153 144 80.31640 225.5624 34.79981 21.17395 90.90345
31 SH031 Female 35.25938 123 104.11146 281.7872 33.41046 21.96719 70.04117
32 SH032 Male 33.60036 159 87.55489 145.9111 35.26918 21.83619 73.42190
33 SH033 Male 35.64141 151 98.28177 218.3989 37.65183 22.81566 98.43076
34 SH034 Male 33.19158 145 109.07543 132.1652 36.90255 24.39488 95.38902
35 SH035 Male 38.27560 165 101.83150 193.5621 33.19902 21.68819 62.85867
36 SH036 Male 33.38074 133 81.03245 191.9316 33.84517 23.79306 93.62915
37 SH037 Female 36.70323 155 85.92942 131.7407 34.23563 25.44754 56.77674
38 SH038 Male 37.18545 128 93.33004 223.3584 34.86881 21.49496 75.69368
39 SH039 Female 33.86559 151 91.51238 141.6090 36.28981 23.90051 55.69342
40 SH040 Male 35.68198 131 78.43668 270.7260 36.62203 20.42393 103.43309
41 SH041 Male 34.11847 124 103.81184 150.0035 34.09605 25.11045 75.68498
42 SH042 Female 36.23841 126 84.34877 239.1682 37.87300 22.08561 93.31726
43 SH043 Male 37.70230 120 65.64434 218.6684 34.30250 20.81708 97.72654
44 SH044 Male 32.09225 145 95.88958 193.0045 36.08625 25.45430 53.69290
45 SH045 Female 35.01777 131 78.20756 245.9147 34.49825 25.55001 53.96627
46 SH046 Male 35.30483 136 101.89161 148.9993 36.65791 21.38283 65.71702
47 SH047 Female 35.73423 122 77.17206 245.9975 35.84840 24.58774 94.06933
48 SH048 Female 34.50264 157 102.84529 282.6606 35.42263 22.85964 112.25187
49 SH049 Female 35.54855 166 66.42762 250.3885 36.53131 25.36878 83.54757
50 SH050 Male 34.12747 149 102.92790 176.4550 37.63191 22.99183 108.13009
51 SH051 Female 35.51145 155 73.49472 260.5813 33.76855 23.30255 69.69122
52 SH052 Male 34.20984 145 66.71214 255.2545 35.12223 24.52193 71.57597
53 SH053 Male 35.76808 130 103.61025 277.7319 36.90622 24.75636 101.66732
54 SH054 Female 33.81010 147 66.69425 285.6476 35.72520 24.68691 99.01820
55 SH055 Male 32.37115 165 95.55005 163.4528 35.38565 22.54444 50.50741
56 SH056 Female 34.12868 122 108.46339 266.3492 35.73114 22.35189 54.77869
57 SH057 Female 34.38152 157 66.01216 288.7894 36.36709 25.52974 86.13684
58 SH058 Female 32.78833 121 104.75922 152.0740 34.04335 20.47321 75.20951
59 SH059 Male 36.50001 119 106.96948 217.8249 34.65448 24.72011 76.39855
60 SH060 Male 37.29134 135 67.77458 289.2569 33.56370 21.24816 64.03911
61 SH061 Female 33.14264 129 105.94553 210.0712 37.53218 23.40290 112.31804
62 SH062 Male 36.43598 166 104.12000 167.7886 35.38408 22.82472 67.21918
63 SH063 Female 34.35993 166 86.65600 228.3451 35.93839 25.38981 100.02049
64 SH064 Female 34.31053 155 65.46517 285.3384 34.28830 20.83338 75.19538
65 SH065 Male 34.73515 122 81.99963 155.4796 34.94378 24.62508 105.35837
66 SH066 Male 35.46505 148 89.87555 249.3298 37.46285 22.19886 109.55623
67 SH067 Male 36.56332 128 65.89645 181.7185 37.81910 20.39562 81.73635
68 SH068 Female 33.72053 142 103.80795 128.6539 35.22908 22.58208 89.75130
69 SH069 Female 35.39024 142 98.68314 221.7492 37.65225 25.58017 82.48984
70 SH070 Male 32.85958 158 83.81398 261.6298 33.45248 25.94927 56.49589
71 SH071 Female 36.87037 157 87.79575 270.3762 34.23995 20.71237 57.96726
72 SH072 Female 34.58863 163 89.61748 168.2099 35.77540 24.82431 68.69199
73 SH073 Female 36.24140 151 109.25117 198.0185 35.02442 24.88054 81.38041
74 SH074 Female 34.94177 163 78.20613 156.6616 37.63906 22.23139 96.09884
75 SH075 Female 33.80528 143 87.89158 196.1898 34.60457 22.76125 111.12821
76 SH076 Male 34.47937 159 94.70072 195.8206 37.05234 20.09560 63.29272
77 SH077 Female 36.27716 148 102.47105 227.0403 35.81215 25.37362 66.88572
78 SH078 Male 34.20434 119 66.22930 182.4831 37.98965 21.11023 90.55868
79 SH079 Male 35.13952 143 87.16104 273.9157 33.60145 21.26372 85.02801
80 SH080 Female 36.52400 152 92.37577 147.7080 37.12488 24.10008 100.13287
81 SH081 Male 35.35378 151 90.51166 238.2917 37.92181 21.09180 51.95288
82 SH082 Female 35.86922 132 102.96644 273.4815 34.63531 22.36627 91.45744
83 SH083 Female 33.76378 164 98.49024 143.2425 36.98502 21.76132 89.98110
84 SH084 Female 34.99762 130 104.98846 177.7733 36.35152 20.93068 88.04446
85 SH085 Male 34.42745 135 72.35138 241.8481 33.36558 21.44692 81.05827
86 SH086 Male 37.16959 122 79.30636 261.9043 34.57330 20.98942 50.68187
87 SH087 Female 33.98649 129 87.20821 241.8463 35.29138 24.02701 72.45724
88 SH088 Male 34.05025 146 83.32350 272.6493 35.59623 22.80616 58.48252
89 SH089 Female 34.83144 123 110.87828 277.1108 36.98113 20.53800 76.64611
90 SH090 Female 34.93018 158 81.86116 216.0979 33.28689 25.58217 93.57089
91 SH091 Male 35.60692 165 65.77708 172.4047 37.81372 23.40148 62.52203
92 SH092 Male 34.16414 121 82.91272 164.4089 36.06992 20.55318 101.12146
93 SH093 Male 36.90737 138 75.41480 135.7683 35.64557 20.11706 81.36636
94 SH094 Female 34.65726 140 71.08682 221.7926 37.03156 24.30985 107.17402
95 SH095 Female 32.60900 161 103.51608 175.0983 33.09616 25.34174 71.91561
96 SH096 Male 35.90758 152 98.27774 197.7596 37.03040 22.57737 80.77199
97 SH097 Female 35.27513 127 80.53280 153.9831 36.19002 24.70726 109.09920
98 SH098 Female 33.07815 154 101.94281 158.8229 34.09929 21.45744 52.44972
99 SH099 Male 33.96733 157 82.00881 155.1547 35.86211 20.88343 76.29960
100 SH100 Male 34.44525 120 109.42289 177.5218 35.60108 25.33677 90.88504
101 SH101 Male 36.42572 134 69.26562 196.4749 37.99978 23.93187 68.47177
102 SH102 Male 34.26732 154 85.74503 153.5896 34.73182 21.51349 96.27170
103 SH103 Female 32.27762 142 80.08924 243.8365 36.56592 20.98350 58.53386
104 SH104 Male 37.22830 165 78.34911 128.8481 37.39113 25.74924 101.57178
105 SH105 Male 32.53531 122 98.52265 212.9415 36.16896 22.86719 82.82166
106 SH106 Male 35.90348 151 92.37943 213.6005 33.80076 21.16600 61.64709
107 SH107 Male 36.39784 125 75.20744 265.7713 33.08772 21.75165 95.93255
108 SH108 Male 36.68703 135 73.29044 179.1079 35.37759 24.89065 91.28896
109 SH109 Female 35.72632 136 84.70922 184.3002 33.93537 22.97058 96.15302
110 SH110 Male 34.65632 134 78.89234 191.1178 36.70432 21.09131 54.94158
111 SH111 Female 33.76447 143 83.05695 264.8931 36.01802 25.34560 68.95380
112 SH112 Male 37.17692 151 96.54306 224.6350 37.27791 25.50143 62.35721
113 SH113 Male 36.76577 122 89.71193 280.3756 35.26790 21.92786 111.93940
114 SH114 Female 35.54950 155 87.56020 177.9312 37.44562 25.59447 94.39156
115 SH115 Male 34.93594 127 73.88824 199.1637 33.51968 21.84163 91.43666
116 SH116 Male 35.44028 166 66.00525 256.1074 36.13855 20.30288 88.35029
117 SH117 Female 36.48768 132 93.63509 269.5792 33.90883 25.98160 88.91327
118 SH118 Male 35.37963 136 68.55041 208.2467 36.87915 22.91738 51.89270
119 SH119 Male 37.59267 153 89.61978 238.0066 34.58231 21.10297 53.07295
120 SH120 Male 35.73577 128 67.95431 216.0158 37.38775 21.46644 63.92133
121 SH121 Male 33.72274 159 92.38551 188.3666 33.37237 25.20610 75.50738
122 SH122 Male 35.95868 123 99.47556 205.8371 37.14915 25.30833 110.96871
123 SH123 Female 35.56566 121 100.69014 211.7997 34.63772 25.03145 76.68962
124 SH124 Male 35.92057 145 92.32507 160.4630 36.10210 21.00988 64.82984
125 SH125 Female 34.04251 162 109.40178 179.0106 36.09293 21.75793 77.26870
126 SH126 Female 33.77159 145 101.47440 208.8009 35.02722 20.10380 94.90592
127 SH127 Female 33.86392 142 75.86195 177.6679 37.51978 21.73670 83.56013
128 SH128 Male 35.46943 164 104.23528 262.4866 35.30450 20.71000 82.62410
129 SH129 Female 33.80302 151 84.40131 224.5868 37.09203 25.58499 86.67182
130 SH130 Male 35.07222 130 105.06924 204.9788 34.49577 24.00500 65.43414
131 SH131 Male 34.74639 143 72.94091 285.3108 35.82829 25.74827 81.97022
132 SH132 Female 33.86019 129 84.31666 225.4904 34.55580 23.21792 67.17507
133 SH133 Male 38.65662 146 72.42396 189.7878 35.64647 22.31245 77.64661
134 SH134 Female 32.31056 129 91.77134 232.3262 37.70202 20.94913 69.41677
135 SH135 Female 37.23568 131 68.26047 246.2894 34.78965 25.59980 70.72911
136 SH136 Female 36.85702 120 72.24852 290.7134 35.27348 21.49555 80.62858
137 SH137 Male 32.88800 140 102.23423 176.4455 36.35886 23.66294 80.96468
138 SH138 Male 38.06194 134 83.55583 221.6356 34.58011 22.09738 78.78784
139 SH139 Female 33.59581 141 85.35059 128.6751 34.01522 23.30305 75.29192
140 SH140 Male 35.99556 131 107.88970 251.8000 37.79018 24.50147 89.86581
141 SH141 Female 33.79549 137 103.46005 277.5909 34.80523 21.56376 107.51920
142 SH142 Female 33.10335 124 103.88024 290.9374 35.48487 20.12939 61.95953
143 SH143 Male 33.82318 155 105.12856 249.9972 34.13104 23.11390 60.06371
144 SH144 Male 37.22728 123 107.52144 178.5039 35.05795 24.21061 109.47619
145 SH145 Male 35.39418 134 84.55558 128.2796 36.58785 20.76213 56.86031
146 SH146 Female 36.39183 127 87.02997 132.1405 34.31642 24.09147 74.47677
147 SH147 Female 36.84328 124 99.16543 282.8593 33.03791 21.06602 81.42454
148 SH148 Male 35.85999 166 105.09013 147.4057 33.81071 22.20610 80.74154
149 SH149 Female 33.56897 146 79.24966 135.5375 37.10377 21.48847 111.92199
150 SH150 Female 33.11113 131 65.47062 145.7330 37.10396 24.76164 105.00771
151 SH151 Male 35.36557 120 69.17696 148.1670 35.63953 24.16385 91.02469
152 SH152 Male 36.48702 146 73.59540 254.4253 36.94934 21.49606 84.87480
153 SH153 Male 35.92896 134 97.62558 213.5802 35.98778 25.79449 88.05992
154 SH154 Female 36.35739 120 81.89987 238.1954 37.27579 20.26600 55.55064
155 SH155 Female 33.88382 123 75.54827 176.1646 34.85995 23.27576 70.28917
156 SH156 Female 34.56139 143 82.59498 133.0148 37.48426 23.11390 61.33650
157 SH157 Male 36.56256 137 86.05231 181.6873 33.48171 25.74904 70.69646
158 SH158 Female 36.92970 160 75.05355 159.2658 34.40128 24.24493 79.65915
159 SH159 Male 36.30869 138 107.18462 185.0738 36.88023 24.33483 69.18763
160 SH160 Male 33.75869 138 88.21856 290.9527 36.19064 21.50509 107.84346
161 SH161 Female 30.77585 149 109.05626 253.9729 34.46067 24.02721 64.15829
162 SH162 Male 34.02139 145 82.21740 256.9053 36.21332 24.20691 109.02966
163 SH163 Female 33.38396 148 96.73251 189.9405 33.91255 25.18574 69.99987
164 SH164 Female 35.98082 146 70.03150 188.8569 34.57147 20.15593 50.93368
165 SH165 Female 34.49482 137 81.66194 137.8904 34.78508 20.84970 55.98825
166 SH166 Male 36.07216 150 72.48854 204.7737 36.03342 22.96511 79.55119
167 SH167 Male 38.51132 165 105.38634 169.0132 33.38560 22.00389 92.26167
168 SH168 Female 35.24772 148 103.33159 252.9665 37.08024 20.62234 66.38338
169 SH169 Male 36.53646 137 73.95419 136.7197 36.12408 20.15134 89.47353
170 SH170 Female 32.67439 143 103.26350 146.5351 36.57913 21.37123 89.22346
171 SH171 Female 34.89859 140 93.91948 132.1698 37.78333 25.60188 84.97639
172 SH172 Male 35.12783 160 80.67021 289.8701 34.08678 25.77848 95.72839
173 SH173 Male 34.48057 159 96.64833 269.9207 33.43879 21.62152 102.98517
174 SH174 Male 37.43851 136 75.32586 185.4717 37.92650 23.44797 72.83689
175 SH175 Female 34.54851 142 77.77787 160.3368 36.32860 23.53152 97.07738
176 SH176 Female 35.54189 136 66.49372 242.2694 36.52021 22.70112 112.43894
177 SH177 Male 35.50834 162 91.68781 128.2534 33.46132 24.25271 80.11243
178 SH178 Female 34.45879 155 76.42407 267.4729 34.28698 22.10824 90.42851
179 SH179 Female 36.07762 166 106.26913 240.2251 35.16094 23.83241 64.97782
180 SH180 Male 36.36155 152 93.07487 185.9836 34.67379 23.28713 50.39657
181 SH181 Male 36.02138 149 107.72480 142.8448 35.87439 21.25294 68.93254
182 SH182 Male 35.53009 142 101.05765 224.9920 36.93111 25.83883 64.06787
183 SH183 Male 36.13323 165 87.62539 178.8709 33.49332 22.86968 59.46141
184 SH184 Female 33.09675 125 78.53654 246.3244 34.11874 23.34812 105.64879
185 SH185 Male 33.49157 125 93.54783 184.6255 35.13868 23.41397 81.25652
186 SH186 Male 37.21730 159 72.31295 280.6037 33.72278 23.40415 91.68645
187 SH187 Male 36.26017 135 91.89506 199.8991 34.57746 20.19062 66.21984
188 SH188 Male 32.75580 151 87.42107 143.7484 36.86885 22.90739 89.00652
189 SH189 Male 35.31524 159 78.23924 157.1800 35.16408 21.41785 93.69293
190 SH190 Female 38.66238 141 90.15724 165.2321 33.37159 21.55313 112.31862
191 SH191 Male 33.85064 151 91.44474 208.1706 33.34797 25.78562 72.25575
192 SH192 Female 36.27604 128 68.69878 190.9609 36.32506 21.02351 72.66432
193 SH193 Male 34.86074 146 81.34990 156.7090 35.32475 22.28507 62.59773
194 SH194 Male 36.58108 134 97.75359 133.1614 36.96306 25.58874 73.08765
195 SH195 Female 34.41919 160 101.72666 277.7658 33.13397 25.04594 102.55151
196 SH196 Male 36.67552 127 76.70792 149.8624 36.29244 23.81301 102.54686
197 SH197 Male 37.62275 123 90.17847 257.5127 34.94288 20.67057 79.98693
198 SH198 Female 35.69544 131 86.91432 255.7991 35.58446 21.48523 106.58384
199 SH199 Male 37.07165 159 74.37317 185.9547 33.68490 20.50748 55.51194
200 SH200 Male 34.60328 159 95.56294 237.9323 36.51688 21.06436 98.17417
201 SH201 Male 36.04940 119 72.62179 162.4149 36.84475 20.62519 108.89156
202 SH202 Male 35.86671 164 107.75189 151.2548 33.34401 22.46135 86.05692
203 SH203 Male 38.64013 122 81.62802 194.8412 34.93538 22.43826 93.26034
204 SH204 Female 34.78846 123 66.33142 170.7840 37.58242 22.33434 72.36955
205 SH205 Male 37.04875 122 110.66800 237.5887 37.74290 21.05642 86.71372
206 SH206 Female 32.20917 164 99.78551 227.9193 36.43191 20.26350 99.58747
207 SH207 Female 34.56033 129 71.91227 290.1311 35.36025 23.28969 61.05480
208 SH208 Male 35.03548 129 66.83643 263.1934 37.48646 20.63547 92.57415
209 SH209 Female 34.14408 155 65.15314 250.2264 33.40181 20.82104 106.95097
210 SH210 Male 35.48251 128 110.49392 205.9378 37.21552 21.40080 61.45664
211 SH211 Female 33.26947 164 81.88777 215.2635 33.81956 20.12551 96.40223
212 SH212 Male 32.27892 163 98.90980 211.1515 33.94479 21.89620 106.00333
213 SH213 Male 36.87935 150 95.52091 277.9631 36.95092 21.67558 108.71009
214 SH214 Male 37.67336 155 77.04085 225.9307 37.05104 21.99929 92.88962
215 SH215 Male 34.66563 119 72.06605 194.7612 37.72538 24.89097 52.07729
216 SH216 Male 33.56095 130 69.20206 211.4640 33.20529 24.76176 57.40244
217 SH217 Male 34.96694 137 72.55576 257.6338 35.69012 23.36290 86.12398
218 SH218 Male 33.82718 128 83.81067 133.9490 37.71951 24.45560 94.08808
219 SH219 Male 33.50852 129 97.61688 223.0908 33.94239 23.84800 98.60744
220 SH220 Female 34.47858 131 94.67604 273.5521 34.11300 23.57607 51.02802
221 SH221 Female 35.99021 129 108.59903 195.2602 33.51585 24.20466 68.93962
222 SH222 Male 33.33818 128 74.72527 222.2863 36.79951 24.46908 108.98971
223 SH223 Male 37.00103 163 80.62482 163.0760 34.85521 24.82031 59.71121
224 SH224 Female 35.28434 152 94.81944 210.5426 33.82469 21.96495 79.23714
225 SH225 Female 34.77076 147 97.03831 284.7500 35.47918 24.13970 59.38391
226 SH226 Male 35.02983 143 91.89068 176.1361 34.92279 25.98523 78.28148
227 SH227 Male 33.70580 123 108.58425 249.7813 37.95582 24.82551 69.87094
228 SH228 Male 34.99563 148 72.13075 144.3198 33.32429 23.45195 109.06037
229 SH229 Female 35.81950 125 74.82072 265.5075 37.44526 21.34394 51.62363
230 SH230 Female 34.84883 120 100.16557 232.3737 37.56621 23.13661 109.16231
231 SH231 Male 33.14350 128 100.71676 226.6396 37.06714 23.92129 99.28393
232 SH232 Female 36.92090 132 91.61429 192.9478 35.55935 21.29054 57.57463
233 SH233 Female 35.48229 131 75.03100 224.2624 34.23656 21.14766 104.02512
234 SH234 Female 33.89644 140 81.08696 238.7075 34.58767 25.88602 88.11245
235 SH235 Male 34.10182 156 70.11244 130.7063 37.91824 24.07606 107.05396
236 SH236 Female 36.06121 125 71.30789 147.0164 36.18505 23.46830 78.94451
237 SH237 Female 34.07307 148 93.66121 199.3706 36.31361 21.73450 72.40215
238 SH238 Female 34.79541 138 91.53824 241.4079 34.10377 24.09668 84.26550
239 SH239 Female 34.98931 141 89.64871 231.7945 37.84878 22.19589 89.19871
240 SH240 Female 34.12705 149 73.11996 275.8609 36.59425 25.64541 106.71781
241 SH241 Male 35.66434 156 93.95195 172.2191 36.57991 23.89903 97.44425
242 SH242 Female 34.64274 165 70.45932 207.7734 36.48022 20.30784 54.09448
243 SH243 Male 34.07018 137 96.40814 148.7859 35.43456 23.34639 72.37134
244 SH244 Female 32.74815 151 82.12538 262.7706 33.18654 22.14781 88.15269
245 SH245 Female 34.88511 137 85.28268 279.2720 34.57891 21.22774 91.39811
246 SH246 Female 35.69862 120 110.94466 201.4641 36.69199 24.22643 110.98538
247 SH247 Female 34.10099 143 65.39909 196.7610 34.30429 23.75784 79.49685
248 SH248 Female 33.56870 158 87.15990 157.8510 34.13062 23.40831 73.50700
249 SH249 Female 37.29475 145 96.88163 282.5016 35.85920 21.09733 71.78561
250 SH250 Female 37.90292 126 107.19693 151.7995 33.04494 22.78920 71.86493
251 SH251 Male 35.66700 155 102.51636 163.5317 35.57957 25.01420 86.75932
252 SH252 Female 38.27531 151 74.69447 153.0456 37.18947 20.71505 91.35984
253 SH253 Male 33.86044 122 93.17921 230.0938 35.99259 24.70831 92.99403
254 SH254 Male 34.73333 143 93.27573 259.4982 37.73990 20.80868 97.52831
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54 51.69939
55 47.64576
56 51.30177
57 45.82523
58 48.09742
59 53.78593
60 51.78464
61 48.31524
62 52.41902
63 49.99928
64 49.61324
65 51.68339
66 51.04494
67 49.55312
68 45.90688
69 50.61433
70 47.48592
71 53.94849
72 50.99606
73 49.48395
74 49.36566
75 47.37765
76 49.16147
77 50.21770
78 49.78298
79 53.21268
80 53.78310
81 50.25283
82 51.12423
83 48.30569
84 49.85196
85 48.95057
86 53.06348
87 51.84685
88 48.15301
89 53.07349
90 49.75234
91 50.39840
92 51.20819
93 52.50975
94 50.04201
95 47.25511
96 53.78970
97 49.12667
98 49.92469
99 50.30870
100 50.51845
101 51.31445
102 48.67303
103 47.07040
104 51.98709
105 44.64474
106 50.59440
107 50.76879
108 49.80048
109 52.36699
110 49.89161
111 48.73722
112 54.79425
113 51.18954
114 48.91308
115 51.96076
116 50.43764
117 50.73841
118 52.14371
119 53.66833
120 50.89749
121 49.37737
122 52.11932
123 50.64543
124 51.01759
125 49.13213
126 47.92219
127 50.55757
128 49.80526
129 50.19277
130 50.13911
131 50.19285
132 46.78373
133 54.47089
134 47.78017
135 52.77678
136 51.54685
137 47.09099
138 52.47047
139 50.87541
140 47.65424
141 48.25289
142 47.55423
143 48.05781
144 50.60404
145 51.12350
146 52.49579
147 52.02509
148 51.94036
149 50.94988
150 50.64477
151 50.41775
152 50.48023
153 51.13113
154 52.02550
155 49.55520
156 52.10174
157 49.60139
158 53.81307
159 51.00424
160 48.82545
161 45.31157
162 47.88384
163 48.43633
164 50.89634
165 51.92694
166 50.57666
167 54.69200
168 50.23635
169 49.02411
170 47.11011
171 48.88285
172 49.14147
173 49.64868
174 52.63916
175 48.21670
176 51.34882
177 50.47331
178 49.16008
179 51.19454
180 50.04455
181 51.64892
182 50.53234
183 50.22172
184 48.52451
185 49.50023
186 53.81606
187 51.36398
188 49.74816
189 51.12401
190 55.12170
191 47.71242
192 51.68166
193 49.30371
194 50.79232
195 49.24551
196 51.03116
197 51.34402
198 49.44762
199 50.46984
200 49.29360
201 48.89701
202 50.25519
203 53.45442
204 47.12126
205 51.22780
206 46.46783
207 48.59292
208 49.23616
209 47.46398
210 47.86542
211 46.08500
212 50.08355
213 53.05863
214 52.41913
215 49.84933
216 47.13358
217 51.53943
218 46.33580
219 48.96726
220 50.53704
221 49.06487
222 48.03981
223 51.79526
224 49.99628
225 49.69935
226 50.49601
227 47.30531
228 49.76418
229 49.25833
230 49.24973
231 48.45078
232 55.02983
233 50.03516
234 47.90852
235 49.28132
236 52.88504
237 48.80291
238 50.13841
239 51.13299
240 50.12264
241 49.15964
242 50.39268
243 49.55292
244 45.52213
245 46.95435
246 50.25569
247 49.54298
248 46.76742
249 53.95736
250 52.85021
251 50.95442
252 54.25875
253 48.02634
254 50.45905
255 51.66043
256 51.36171
257 52.83560
258 48.11986
259 50.84090
260 49.40703
261 51.06647
262 47.27213
263 50.67571
264 53.53304
265 51.01849
266 53.43177
267 50.93599
268 51.31898
269 52.43260
270 47.04606
271 48.04941
272 49.72568
273 52.41726
274 48.96359
275 48.71256
276 48.87889
277 49.58868
278 50.87993
279 49.64042
280 47.94792
281 54.06261
282 47.97999
283 51.30813
284 51.23310
285 48.65615
286 49.64635
287 46.76780
288 50.13744
289 51.73770
290 50.36233
291 52.19427
292 52.19196
293 52.02757
294 47.94131
295 49.12175
296 49.53097
297 52.57367
298 47.52810
299 49.44280
300 48.41129
301 50.29773
302 52.79886
303 46.26686
304 46.05108
305 46.23747
306 53.10939
307 49.02755
308 51.20894
309 52.06400
310 49.95799
311 52.14297
312 51.57061
313 47.05292
314 49.00989
315 47.94731
316 48.24758
317 49.57484
318 50.74025
319 47.96024
320 52.55598
321 51.49505
322 50.01362
323 51.27924
324 49.49710
325 45.22390
326 49.28035
327 49.70779
328 51.20013
329 49.83698
330 54.33117
331 51.07560
332 51.79984
333 51.29194
334 45.76090
335 53.02412
336 50.16812
337 51.61258
338 51.30954
339 51.45210
340 50.45979
341 50.78879
342 52.37263
343 48.07822
344 54.05790
345 48.91885
346 45.87899
347 49.56443
348 49.15212
349 53.96122
350 51.95405
351 49.84155
352 51.25291
353 52.90357
354 46.95454
355 49.88291
356 51.72062
357 48.78801
358 47.76394
359 48.72243
360 50.15889
361 49.79721
362 48.42723
363 49.04939
364 49.70568
365 50.46341
366 49.55837
367 52.14514
368 48.39105
369 46.17011
370 48.63788
371 49.61791
372 47.75904
373 46.29181
374 49.21944
375 49.10393
376 51.48731
377 51.44714
378 46.10707
379 48.36763
380 49.82041
381 49.96346
382 47.53576
383 50.95838
384 56.82916
385 51.22813
386 47.21805
387 52.91236
388 50.12798
389 49.56710
390 50.69337
391 50.50971
392 54.47356
393 50.95881
394 48.77546
395 49.56845
396 54.54979
397 46.28239
398 54.16516
399 49.54275
400 50.21908
401 46.32807
402 54.27737
403 47.16676
404 52.92352
405 50.37530
406 50.83634
407 51.15836
408 48.19870
409 49.21340
410 49.88061
411 51.09545
412 51.77534
413 50.23290
414 49.86163
415 49.52463
416 47.24256
417 50.25876
418 50.62649
419 48.70445
420 48.52425
421 47.94873
422 47.15586
423 49.80686
424 52.22695
425 47.14508
426 46.65459
427 48.87254
428 50.78153
429 49.84879
430 52.85327
431 50.86464
432 50.88588
433 47.50464
434 48.11393
435 49.99973
436 48.04591
437 49.28590
438 50.66410
439 49.19377
440 47.02258
441 50.10694
442 49.76410
443 49.95988
444 49.07783
445 52.34601
446 51.62836
447 52.21376
448 49.20962
449 54.44601
450 52.37204
451 50.60091
452 50.51313
453 52.69699
454 48.91824
455 52.87533
456 49.45900
457 52.32235
458 50.12494
459 51.96627
460 50.75388
461 47.55695
462 52.77333
463 51.38182
464 50.28497
465 50.04182
466 52.47648
467 49.52439
468 51.63451
469 46.97514
470 53.09173
471 50.94501
472 49.02867
473 51.47058
474 47.31781
475 50.15977
476 50.00950
477 49.97932
478 50.82219
479 48.43085
480 52.17651
481 52.71425
482 52.24325
483 49.56941
484 51.97333
485 50.10833
486 47.80744
487 48.89706
488 48.57565
489 49.87668
490 49.75043
491 51.86649
492 49.83649
493 44.87603
494 47.83517
495 47.33958
496 48.46034
497 45.42679
498 53.05511
499 52.05860
500 49.28923#View the First Few Rows of the Dataset
head(sharks) ID sex blotch BPM weight length air water meta
1 SH001 Female 37.17081 148 74.69050 186.6703 37.73957 23.37377 64.11183
2 SH002 Female 34.54973 158 73.41627 189.3189 35.68413 21.42088 73.68676
3 SH003 Female 36.32861 125 71.80837 283.6332 34.79854 20.05114 54.43466
4 SH004 Male 35.33881 161 104.62985 171.0986 36.15973 21.64319 86.32615
5 SH005 Female 37.39799 138 67.13098 264.3160 33.61477 21.76143 107.97796
6 SH006 Male 33.54668 126 110.49396 269.9829 36.38343 20.85200 108.86475
depth
1 53.22635
2 49.63903
3 49.44057
4 50.29711
5 49.03183
6 46.84148#Structure of the Dataset
str(sharks)'data.frame': 500 obs. of 10 variables:
$ ID : chr "SH001" "SH002" "SH003" "SH004" ...
$ sex : chr "Female" "Female" "Female" "Male" ...
$ blotch: num 37.2 34.5 36.3 35.3 37.4 ...
$ BPM : int 148 158 125 161 138 126 166 135 132 127 ...
$ weight: num 74.7 73.4 71.8 104.6 67.1 ...
$ length: num 187 189 284 171 264 ...
$ air : num 37.7 35.7 34.8 36.2 33.6 ...
$ water : num 23.4 21.4 20.1 21.6 21.8 ...
$ meta : num 64.1 73.7 54.4 86.3 108 ...
$ depth : num 53.2 49.6 49.4 50.3 49 ...#Summary Statistics
summary(sharks) ID sex blotch BPM
Length:500 Length:500 Min. :30.78 Min. :119.0
Class :character Class :character 1st Qu.:34.16 1st Qu.:129.0
Mode :character Mode :character Median :35.05 Median :142.0
Mean :35.13 Mean :141.8
3rd Qu.:36.05 3rd Qu.:153.2
Max. :40.08 Max. :166.0
weight length air water
Min. : 65.10 Min. :128.3 Min. :33.00 Min. :20.01
1st Qu.: 75.68 1st Qu.:172.0 1st Qu.:34.42 1st Qu.:21.55
Median : 87.82 Median :211.1 Median :35.43 Median :23.11
Mean : 87.94 Mean :211.0 Mean :35.54 Mean :23.02
3rd Qu.:100.40 3rd Qu.:251.8 3rd Qu.:36.71 3rd Qu.:24.37
Max. :110.94 Max. :291.0 Max. :38.00 Max. :25.99
meta depth
Min. : 50.03 Min. :44.64
1st Qu.: 67.39 1st Qu.:48.90
Median : 82.45 Median :50.14
Mean : 82.04 Mean :50.14
3rd Qu.: 95.97 3rd Qu.:51.35
Max. :112.45 Max. :56.83 #Check for Missing Values
colSums(is.na(sharks)) ID sex blotch BPM weight length air water meta depth
0 0 0 0 0 0 0 0 0 0 #No missing Values
# Visualize missing data
aggr(sharks, col = c("navyblue", "red"), numbers = TRUE,
sortVars = TRUE, labels = names(sharks),
cex.axis = 0.7, gap = 3, ylab = c("Missing Data", "Pattern"))
Variables sorted by number of missings:
Variable Count
ID 0
sex 0
blotch 0
BPM 0
weight 0
length 0
air 0
water 0
meta 0
depth 0#Get the Dimensions of the Dataset
dim(sharks)[1] 500 10#Unique Values for Categorical Variables/ designate sex as a factor
sharks$fSex <- factor(sharks$sex)1.2.1 Checking Outliers
#OUTLIERS
#Outliers are visually represented as individual points outside the whiskers of the box.
boxplot.stats(sharks$blotch)$out[1] 39.83638 39.13972 30.77585 40.08356#Highlight outliers in the blotching time boxplot
boxplot(sharks$blotch, main = "Blotching Time with Outliers", col = "lightblue")
#use Z-scores to detect outliers
sharks <- sharks %>%
mutate(blotch_zscore = scale(blotch))
# Outliers: Z-scores > 3 or < -3
outliers <- sharks %>% filter(abs(blotch_zscore) > 3)
print(outliers) ID sex blotch BPM weight length air water meta
1 SH014 Male 39.83638 121 90.88816 193.3701 34.44364 23.39661 99.84946
2 SH161 Female 30.77585 149 109.05626 253.9729 34.46067 24.02721 64.15829
3 SH392 Male 40.08356 141 110.88848 203.7803 34.34650 24.45843 60.16624
depth fSex blotch_zscore
1 55.30608 Male 3.300184
2 45.31157 Female -3.047004
3 54.47356 Male 3.473342#A common threshold for identifying outliers is a Z-score greater than 3 or less than -3
#The outliers data frame displays the rows that have blotch values with Z-scores exceeding the threshold.1.2.2 Visualize the distribution of data
#vector of variables
Names <- c("blotch","BPM","weight","length","air","water","meta","depth")
# plot
dotplot(as.matrix(as.matrix(sharks[,Names])),
groups=FALSE,
strip = strip.custom(bg = 'white',
par.strip.text = list(cex = 1.2)),
scales = list(x = list(relation = "free", draw = TRUE),
y = list(relation = "free", draw = FALSE)),
col = 1, cex = 1, pch = 16,
xlab = list(label = "Value of the variable", cex = 1.2),
ylab = list(label = "Order of the data",
cex = 1.2))
#Dots that are far away from the main cluster of dots might indicate potential outliers.1.2.3 Outilers Analysis Continued
#For "depth" there appears to be one shark that is set unusually high.
#"blotch" there is one shark that is unusually low and another unusually high.
#Using, Grubb's test to test whether the values are farthest the mean in an outlier.#Using, Grubb's test to test whether the values are farthest the mean in an outlier.
grubbs.test(sharks$depth,type = 10)
Grubbs test for one outlier
data: sharks$depth
G = 3.31179, U = 0.97798, p-value = 0.2182
alternative hypothesis: highest value 56.82916 is an outlier#Grubbs test for one outlier
#data: sharks$depth G = 3.31179, U = 0.97798, p-value = 0.2182 alternative hypothesis: highest value 56.82916 is an outlier.
#The test indicates that the highest value 56.82916 is not an outlier since the p-value exceeds 0.05.grubbs.test(sharks$blotch,type = 11)
Grubbs test for two opposite outliers
data: sharks$blotch
G = 6.52035, U = 0.95722, p-value = 0.4064
alternative hypothesis: 30.77585 and 40.08356 are outliers#The test indicates that the values 30.77585 and 40.08356 are not outliers since the
#p-values exceeds 0.05.1.2.4 Testing Normality and Homogeneity of the data-set.
#NORMALITY AND HOMOGENEITY OF VARIABLES
par(mfrow = c(2,2), mar = c(5,5,2,2), cex.lab = 1)
hist(sharks$blotch, main = "Histogram of Variable blotch", xlab = "Time taken for blotching to cover 30% of ventral surface", col = "blue", border = "black")
hist(sharks$BPM, main = "Histogram of Variable BPM", xlab = "Heart rate", col = "blue", border = "black")
hist(sharks$weight, main = "Histogram of Variable Weight", xlab = "Total body weight - measured by hoisting the animal into a specialised sling", col = "blue", border = "black")
hist(sharks$length, main = "Histogram of Variable length", xlab = "Total body length, measured from tip if the snout to the tip of the upper lode of the tail fin.", col = "blue", border = "black")
hist(sharks$air, main = "Histogram of Variable air", xlab = "Ambient air temperature", col = "blue", border = "black")
hist(sharks$water, main = "Histogram of Variable water", xlab = "Water temperature at surface at time of processing", col = "blue", border = "black")
hist(sharks$meta, main = "Histogram of Variable meta", xlab = "Measurement of stress hormone cortisol via blood sample", col = "blue", border = "black")
hist(sharks$depth, xlab = "depth at which the animal was hooked",
col = "lightblue", border = "black", main = "Histogram of variable depth")
1.2.5 Shapiro Test for each variable.
#Test for normality for each variable.
shapiro.test(sharks$blotch)
Shapiro-Wilk normality test
data: sharks$blotch
W = 0.99695, p-value = 0.4769#The p-value is 0.4769, which is greater than 0.05. Normally distributed.
shapiro.test(sharks$BPM)
Shapiro-Wilk normality test
data: sharks$BPM
W = 0.947, p-value = 2.178e-12#p-value = 2.178e-12. Not normally distributed
shapiro.test(sharks$weight)
Shapiro-Wilk normality test
data: sharks$weight
W = 0.94662, p-value = 1.929e-12#p-value = 1.929e-12.Not normally distributed
shapiro.test(sharks$length)
Shapiro-Wilk normality test
data: sharks$length
W = 0.95668, p-value = 5.963e-11#p-value = 5.963e-11. Not normally distributed
shapiro.test(sharks$air)
Shapiro-Wilk normality test
data: sharks$air
W = 0.95885, p-value = 1.338e-10#p-value = 1.338e-10. Not normally distributed
shapiro.test(sharks$meta)
Shapiro-Wilk normality test
data: sharks$meta
W = 0.96374, p-value = 9.141e-10#p-value = 9.141e-10. Not normally distributed
shapiro.test(sharks$depth)
Shapiro-Wilk normality test
data: sharks$depth
W = 0.99746, p-value = 0.6485#p-value = 0.6485. Normally distributed2. Define Hypothesis for the study
#Define Hypothesis
#Is there a significant correlation between air temperature and water temperature?
#Does the time to blotch increase, decrease, or stay consistent after a second capture?
#Can variables like heart rate, weight, and cortisol levels predict blotching time3. Testing Hypothesis 1
#Testing Hypothesis
#Is there a significant correlation between air temperature and water temperature?
#Null Hypothesis (H₀): There is no significant linear correlation between air and water temperature (correlation = 0).
#Alternative Hypothesis (H₁): There is a significant linear correlation between air and water temperature (correlation ≠ 0).#Advanced Visualization of correlation between air temp and water temp
ggplot(sharks, aes(x = air, y = water)) +
geom_point(color = "blue") +
geom_smooth(method = "lm", color = "red", se = FALSE) +
labs(title = "Scatterplot with Trendline: Air vs Water",
x = "Air Temperature",
y = "Water Temperature")
#Perform the correlation test using the cor.test() function.
#Statistical Correlation
#Calculate the correlation coefficient to quantify the strength and direction of the relationship.
#As variables "air" and "water" are two continuous non-normal variables, used Spearman's rank correlation
# Calculate Spearman correlation
correlation_spearman <- cor(sharks$air, sharks$water, method = "spearman", use = "complete.obs")
# Print the result
print(paste("Spearman Correlation:", correlation_spearman))[1] "Spearman Correlation: -0.056373441493766"#Interpretation of the Spearman Correlation
#The value is -0.056, the correlation is very close to 0, indicates a weak or no linear relationship between air temp and water temp.
#The negative sign suggests a slight negative trend, air temperature increases, the water temperature decreases slightly.3.1 Testing Hypothesis 2
#Importing Sharksub Data Set
#Importing Data
sharksub <- read.csv("~/Penguin/sharksub.csv")
#Exploring Data
str(sharksub)'data.frame': 50 obs. of 4 variables:
$ ID : chr "SH269" "SH163" "SH008" "SH239" ...
$ sex : chr "Female" "Female" "Female" "Female" ...
$ blotch1: num 36.1 33.4 36.3 35 35.7 ...
$ blotch2: num 37.2 34.4 36.5 36 36.8 ...summary(sharksub) ID sex blotch1 blotch2
Length:50 Length:50 Min. :32.49 Min. :33.47
Class :character Class :character 1st Qu.:34.38 1st Qu.:35.31
Mode :character Mode :character Median :34.94 Median :35.94
Mean :35.03 Mean :35.96
3rd Qu.:35.90 3rd Qu.:36.78
Max. :37.07 Max. :38.18 head(sharksub) ID sex blotch1 blotch2
1 SH269 Female 36.07201 37.15417
2 SH163 Female 33.38396 34.38548
3 SH008 Female 36.29497 36.46102
4 SH239 Female 34.98931 36.03899
5 SH332 Female 35.70572 36.77689
6 SH328 Female 34.90283 35.94991#Checking for zero values
sum(sharksub$blotchdiff == 0) * 100 / nrow(sharksub)[1] 0#No zero3.1.1 NORMALITY AND HOMOGENEITY Test for sharksub data
#NORMALITY AND HOMOGENEITY OF DEPENDENT VARIABLES
par(mfrow = c(2,2), mar = c(5,5,2,2), cex.lab = 1)
hist(sharksub$blotch1, xlab = "", col = "lightblue",
border = "black", main = "blotch1 (seconds)")
hist(sharksub$blotch2, xlab = "", col = "lightblue",
border = "black", main = "blotch2 (seconds)")
# blotching data approximately normal
#Shapiro-Wilk test for deviation from normality for blothch1
shapiro.test(sharksub$blotch1)
Shapiro-Wilk normality test
data: sharksub$blotch1
W = 0.97958, p-value = 0.5345#normal distribution because p value higher than 0.05
#Shapiro test for blotch2
shapiro.test(sharksub$blotch2)
Shapiro-Wilk normality test
data: sharksub$blotch2
W = 0.97936, p-value = 0.5255#Normal distribution.
# Homogeneity of variance
# Bartlett Test (for normal data)
# For blotch1
bartlett.test(blotch1 ~ sex, data = sharksub)
Bartlett test of homogeneity of variances
data: blotch1 by sex
Bartlett's K-squared = 0.0015243, df = 1, p-value = 0.9689#The variances of blotch1 for males and females can be considered equal
#For blotch2
bartlett.test(blotch2 ~ sex, data = sharksub)
Bartlett test of homogeneity of variances
data: blotch2 by sex
Bartlett's K-squared = 0.14723, df = 1, p-value = 0.7012#blotch not deviate significantly from homogeneity3.1.2 Differences between blotch 1 and blotch 2
#Visualize the differences between blotch1 and blotch2
# Boxplot to compare blotching times
boxplot(sharksub$blotch1, sharksub$blotch2,
names = c("Blotch1", "Blotch2"),
main = "Blotching Time for First vs Second Capture",
ylab = "Blotching Time",
col = c("lightblue", "lightgreen"))
# Scatterplot with a line connecting paired values
plot(sharksub$blotch1, sharksub$blotch2,
xlab = "Blotch1",
ylab = "Blotch2",
main = "Paired Blotch Time Comparison")
#Hypothesis Testing
#Null Hypothesis (H₀): There is no significant difference between blotch1 and blotch2.
#Alternative Hypothesis (H₁): There is a significant difference between blotch1 and blotch2.#The blotch times are measured on the same individuals,Soa paired t-test was used.
# Paired t-test
t_test_result <- t.test(sharksub$blotch1, sharksub$blotch2, paired = TRUE)
# View the test results
print(t_test_result)
Paired t-test
data: sharksub$blotch1 and sharksub$blotch2
t = -17.39, df = 49, p-value < 2.2e-16
alternative hypothesis: true mean difference is not equal to 0
95 percent confidence interval:
-1.037176 -0.822301
sample estimates:
mean difference
-0.9297384 3.1.3 Does the sex affect to the blotch? further analysis…
#Boxplots of blotch1 and blotch2 with sex.
par(mfrow = c(2,2), mar = c(5,5,2,2), cex.lab = 1)
boxplot(blotch1 ~ sex,
ylab = "blotch1 (seconds)",
xlab = "sex",
col = "lightblue",
data = sharksub,
las=1)
boxplot(blotch2 ~ sex,
ylab = "blotch2 (seconds)",
xlab = "sex",
col = "lightblue",
data = sharksub,
las=1)
#There is not significant effect on blotching whether the shark was a male or a female. The mean values were not showing a significant difference. 
#Create new variable for blotch differencces
sharksub$blotchngdiff <- sharksub$blotch2 - sharksub$blotch1
# Use a Shapiro-Wilk test to check for normality
shapiro.test(sharksub$blotchngdiff)
Shapiro-Wilk normality test
data: sharksub$blotchngdiff
W = 0.43157, p-value = 1.212e-12# Visualize the differences with a histogram
hist(sharksub$blotchngdiff, main = "Histogram of Differences", xlab = "Difference in Blotching Times")
# The differences in blotching times (sharksub$blotchngdiff) are not normally distributepar(mfrow = c(1,2), mar = c(5,5,2,2), cex.lab = 1)
boxplot(blotchngdiff ~ sex,
ylab = "change in blotching time(blotchdiff) when sharks were caught for second time",
xlab = "sex",
col = "lightblue",
data = sharksub,
las = 1)
#Gender-Based Comparison of Blotching Time Differences
t.test(blotchngdiff ~ sex, data = sharksub,var.equal = TRUE)
Two Sample t-test
data: blotchngdiff by sex
t = 0.40707, df = 48, p-value = 0.6858
alternative hypothesis: true difference in means between group Female and group Male is not equal to 0
95 percent confidence interval:
-0.1729411 0.2607433
sample estimates:
mean in group Female mean in group Male
0.9516890 0.9077879 #There is not significant effect on blotching whether the shark was a male or a female. The mean values were not showing a significant difference.3.2 Testing Hypothesis 3
Checking all correlation with blotch.
#Investigating relationship between BPM and blotch
ggplot(sharks, aes(x = BPM, y = blotch)) +
geom_point(color = "blue") +
geom_smooth(method = "lm", color = "red") +
labs(title = "BPM vs Blotch", x = "BPM (Beats per minute)", y = "Blotch (Seconds)")
#the relationship between BPM and blotch is non-linear#Investigating relationship between weight and blotch
ggplot(sharks, aes(x = weight, y = blotch)) +
geom_point(color = "blue") +
geom_smooth(method = "lm", color = "red") +
labs(title = "Weight vs Blotch", x = "Weight (Kg)", y = "Blotch (Seconds)")
#the relationship between weight and blotch is non-linear#Investigating relationship between length and blotch
ggplot(sharks, aes(x = length, y = blotch)) +
geom_point(color = "blue") +
geom_smooth(method = "lm", color = "red") +
labs(title = "Length vs Blotch", x = "Length (cm)", y = "Blotch (seconds)")
#the relationship between length and blotch is non-linear#Investigating relationship between air and blotch
ggplot(sharks, aes(x = air, y = blotch)) +
geom_point(color = "blue") +
geom_smooth(method = "lm", color = "red") +
labs(title = "air vs Blotch", x = "air temperature (Celsius) ", y = "Blotch (seconds)")
#the relationship between ambient air temperature and blotch is non-linear#Investigating relationship between water and blotch
ggplot(sharks, aes(x = water, y = (blotch))) +
xlim(19,27) + ylim(30,42) +
geom_point(shape = 16, size = 3, alpha = 0.7) +
geom_smooth(method = 'lm', colour = 'red', se = FALSE, size = 1.5) +
theme(panel.background = element_blank()) +
theme(panel.border = element_rect(fill = NA, size = 1)) +
theme(strip.background = element_rect(fill = "white",
color = "white", size = 1)) +
theme(text = element_text(size=13)) +
xlab("surface water temperature (celcius)") + ylab("blotch (seconds)")
##the relationship between surface temperature and blotch is non-linear#Investigating relationship between meta and blotch
ggplot(sharks, aes(x = meta, y = blotch)) +
geom_point(color = "blue") +
geom_smooth(method = "lm", color = "red") +
labs(title = "meta vs Blotch", x = "Measurement of stress hormone cortisol via blood sample (mcg/dl)", y = "Blotch (seconds)")
#the relationship between surface meta and blotch is non-linear#Investigating relationship between depth and blotch
ggplot(sharks, aes(x = depth, y = blotch)) +
geom_point(color = "blue") +
geom_smooth(method = "lm", color = "red") +
labs(title = "depth vs Blotch", x = "depth at which the animal was hooked (Metres)", y = "Blotch (seconds)")
#the relationship between depth at animal hooked and blotch is linear significant positive relationship#Check Correlations
#the relationship between depth at animal hooked and blotch is linear significant positive relationship3.2.1 Simple Linear Regression model
# Fit a simple linear regression model
depth_model <- lm(blotch ~ depth, data = sharks)
# Summary of the model
summary(depth_model)
Call:
lm(formula = blotch ~ depth, data = sharks)
Residuals:
Min 1Q Median 3Q Max
-2.81869 -0.65427 -0.01035 0.58825 2.83116
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 9.82178 1.11207 8.832 <2e-16 ***
depth 0.50467 0.02216 22.772 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 1 on 498 degrees of freedom
Multiple R-squared: 0.5101, Adjusted R-squared: 0.5091
F-statistic: 518.6 on 1 and 498 DF, p-value: < 2.2e-16# Check residuals for normality
plot(depth_model, which = 2)
shapiro.test(residuals(depth_model))
Shapiro-Wilk normality test
data: residuals(depth_model)
W = 0.99748, p-value = 0.653library(lmtest)
dwtest(depth_model)
Durbin-Watson test
data: depth_model
DW = 2.0966, p-value = 0.8604
alternative hypothesis: true autocorrelation is greater than 03.2.2 Multiple linear Regression model
# Fit a multiple linear regression model
multi_model <- lm(blotch ~ depth + BPM + weight + length + sex, data = sharks)
# View model summary
summary(multi_model)
Call:
lm(formula = blotch ~ depth + BPM + weight + length + sex, data = sharks)
Residuals:
Min 1Q Median 3Q Max
-2.9429 -0.6297 -0.0332 0.6141 2.9488
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 9.5084653 1.2703316 7.485 3.31e-13 ***
depth 0.5042274 0.0220283 22.890 < 2e-16 ***
BPM -0.0018814 0.0031412 -0.599 0.549489
weight 0.0017185 0.0032929 0.522 0.601995
length 0.0013689 0.0009565 1.431 0.153023
sexMale 0.3074703 0.0887632 3.464 0.000579 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.9898 on 494 degrees of freedom
Multiple R-squared: 0.5241, Adjusted R-squared: 0.5193
F-statistic: 108.8 on 5 and 494 DF, p-value: < 2.2e-16# Compare models using Akaike Information Criterion (AIC)
AIC(depth_model, multi_model) df AIC
depth_model 3 1423.059
multi_model 7 1416.602# Compute Adjusted R-squared
summary(depth_model)$adj.r.squared[1] 0.5091332summary(multi_model)$adj.r.squared[1] 0.51926153.2.3 Model Validation
#Validate the Model
# Split data into training and testing
set.seed(123)
train_indices <- sample(1:nrow(sharks), 0.7 * nrow(sharks))
train_data <- sharks[train_indices, ]
test_data <- sharks[-train_indices, ]
# Fit model on training data
train_model <- lm(blotch ~ depth, data = train_data)
# Predict on test data
test_data$predicted_blotch <- predict(train_model, test_data)
# Evaluate performance
library(Metrics)
# Mean Absolute Error
mae(test_data$blotch, test_data$predicted_blotch) [1] 0.8333955# Root Mean Squared Error
rmse(test_data$blotch, test_data$predicted_blotch) [1] 1.0319293.2.4 Model Validation
#Predict Using the Model
# Predict blotch for new depth values
new_data <- data.frame(depth = c(50, 100, 150))
new_data$predicted_blotch <- predict(depth_model, new_data)
print(new_data) depth predicted_blotch
1 50 35.05544
2 100 60.28911
3 150 85.52277#Visualize Predictions
ggplot(sharks, aes(x = depth, y = blotch)) +
geom_point(color = "blue") +
geom_smooth(method = "lm", color = "red") +
labs(title = "Depth vs Blotch Prediction",
x = "Depth (metres)",
y = "Blotch (seconds)") +
geom_point(data = new_data, aes(x = depth, y = predicted_blotch),
color = "green", size = 3, shape = 18)