Project1
Sathisswaran Yanasagaran (480013046), Jackie Tan (470062874), Jonathan Chee (480436496), Anastasia Adinda (480041887)
4/7/2018
R PROJECT 1 (ENVX1002/DATA1001)
Tutorial Time: Thursday, 4 p.m. - 6 p.m.
Data collected from a group of students from the same school taking the same math course.
data = read.csv("/Users/Jonathan/Desktop/ENVX1002/ENVX1002/Data/student-mat.csv")
data## school sex age address famsize Pstatus Medu Fedu Mjob Fjob
## 1 GP F 18 U GT3 A 4 4 at_home teacher
## 2 GP F 17 U GT3 T 1 1 at_home other
## 3 GP F 15 U LE3 T 1 1 at_home other
## 4 GP F 15 U GT3 T 4 2 health services
## 5 GP F 16 U GT3 T 3 3 other other
## 6 GP M 16 U LE3 T 4 3 services other
## 7 GP M 16 U LE3 T 2 2 other other
## 8 GP F 17 U GT3 A 4 4 other teacher
## 9 GP M 15 U LE3 A 3 2 services other
## 10 GP M 15 U GT3 T 3 4 other other
## 11 GP F 15 U GT3 T 4 4 teacher health
## 12 GP F 15 U GT3 T 2 1 services other
## 13 GP M 15 U LE3 T 4 4 health services
## 14 GP M 15 U GT3 T 4 3 teacher other
## 15 GP M 15 U GT3 A 2 2 other other
## 16 GP F 16 U GT3 T 4 4 health other
## 17 GP F 16 U GT3 T 4 4 services services
## 18 GP F 16 U GT3 T 3 3 other other
## 19 GP M 17 U GT3 T 3 2 services services
## 20 GP M 16 U LE3 T 4 3 health other
## 21 GP M 15 U GT3 T 4 3 teacher other
## 22 GP M 15 U GT3 T 4 4 health health
## 23 GP M 16 U LE3 T 4 2 teacher other
## 24 GP M 16 U LE3 T 2 2 other other
## 25 GP F 15 R GT3 T 2 4 services health
## 26 GP F 16 U GT3 T 2 2 services services
## 27 GP M 15 U GT3 T 2 2 other other
## 28 GP M 15 U GT3 T 4 2 health services
## 29 GP M 16 U LE3 A 3 4 services other
## 30 GP M 16 U GT3 T 4 4 teacher teacher
## 31 GP M 15 U GT3 T 4 4 health services
## 32 GP M 15 U GT3 T 4 4 services services
## 33 GP M 15 R GT3 T 4 3 teacher at_home
## 34 GP M 15 U LE3 T 3 3 other other
## 35 GP M 16 U GT3 T 3 2 other other
## 36 GP F 15 U GT3 T 2 3 other other
## 37 GP M 15 U LE3 T 4 3 teacher services
## 38 GP M 16 R GT3 A 4 4 other teacher
## 39 GP F 15 R GT3 T 3 4 services health
## 40 GP F 15 R GT3 T 2 2 at_home other
## 41 GP F 16 U LE3 T 2 2 other other
## 42 GP M 15 U LE3 T 4 4 teacher other
## 43 GP M 15 U GT3 T 4 4 services teacher
## 44 GP M 15 U GT3 T 2 2 services services
## 45 GP F 16 U LE3 T 2 2 other at_home
## 46 GP F 15 U LE3 A 4 3 other other
## 47 GP F 16 U LE3 A 3 3 other services
## 48 GP M 16 U GT3 T 4 3 health services
## 49 GP M 15 U GT3 T 4 2 teacher other
## 50 GP F 15 U GT3 T 4 4 services teacher
## 51 GP F 16 U LE3 T 2 2 services services
## 52 GP F 15 U LE3 T 4 2 health other
## 53 GP M 15 U LE3 A 4 2 health health
## 54 GP F 15 U GT3 T 4 4 services services
## 55 GP F 15 U LE3 A 3 3 other other
## 56 GP F 16 U GT3 A 2 1 other other
## 57 GP F 15 U GT3 A 4 3 services services
## 58 GP M 15 U GT3 T 4 4 teacher health
## 59 GP M 15 U LE3 T 1 2 other at_home
## 60 GP F 16 U GT3 T 4 2 services other
## 61 GP F 16 R GT3 T 4 4 health teacher
## 62 GP F 16 U GT3 T 1 1 services services
## 63 GP F 16 U LE3 T 1 2 other services
## 64 GP F 16 U GT3 T 4 3 teacher health
## 65 GP F 15 U LE3 T 4 3 services services
## 66 GP F 16 U LE3 T 4 3 teacher services
## 67 GP M 15 U GT3 A 4 4 other services
## 68 GP F 16 U GT3 T 3 1 services other
## 69 GP F 15 R LE3 T 2 2 health services
## 70 GP F 15 R LE3 T 3 1 other other
## 71 GP M 16 U GT3 T 3 1 other other
## 72 GP M 15 U GT3 T 4 2 other other
## 73 GP F 15 R GT3 T 1 1 other other
## 74 GP M 16 U GT3 T 3 1 other other
## 75 GP F 16 U GT3 T 3 3 other services
## 76 GP M 15 U GT3 T 4 3 teacher other
## 77 GP M 15 U GT3 T 4 0 teacher other
## 78 GP F 16 U GT3 T 2 2 other other
## 79 GP M 17 U GT3 T 2 1 other other
## 80 GP F 16 U GT3 T 3 4 at_home other
## 81 GP M 15 U GT3 T 2 3 other services
## 82 GP M 15 U GT3 T 2 3 other other
## 83 GP F 15 U LE3 T 3 2 services other
## 84 GP M 15 U LE3 T 2 2 services services
## 85 GP F 15 U GT3 T 1 1 other other
## 86 GP F 15 U GT3 T 4 4 services services
## 87 GP F 16 U LE3 T 2 2 at_home other
## 88 GP F 15 U GT3 T 4 2 other other
## 89 GP M 16 U GT3 T 2 2 services other
## 90 GP M 16 U LE3 A 4 4 teacher health
## 91 GP F 16 U GT3 T 3 3 other other
## 92 GP F 15 U GT3 T 4 3 services other
## 93 GP F 16 U LE3 T 3 1 other other
## 94 GP F 16 U GT3 T 4 2 teacher services
## 95 GP M 15 U LE3 T 2 2 services health
## 96 GP F 15 R GT3 T 1 1 at_home other
## 97 GP M 16 R GT3 T 4 3 services other
## 98 GP F 16 U GT3 T 2 1 other other
## 99 GP F 16 U GT3 T 4 4 other other
## 100 GP F 16 U GT3 T 4 3 other at_home
## 101 GP M 16 U GT3 T 4 4 services services
## 102 GP M 16 U GT3 T 4 4 services teacher
## 103 GP M 15 U GT3 T 4 4 services other
## 104 GP F 15 U GT3 T 3 2 services other
## 105 GP M 15 U GT3 A 3 4 services other
## 106 GP F 15 U GT3 A 3 3 other health
## 107 GP F 15 U GT3 T 2 2 other other
## 108 GP M 16 U GT3 T 3 3 services other
## 109 GP M 15 R GT3 T 4 4 other other
## 110 GP F 16 U LE3 T 4 4 health health
## 111 GP M 15 U LE3 A 4 4 teacher teacher
## 112 GP F 16 R GT3 T 3 3 services other
## 113 GP F 16 U GT3 T 2 2 at_home other
## 114 GP M 15 U LE3 T 4 2 teacher other
## 115 GP M 15 R GT3 T 2 1 health services
## 116 GP M 16 U GT3 T 4 4 teacher teacher
## 117 GP M 15 U GT3 T 4 4 other teacher
## 118 GP M 16 U GT3 T 3 3 other services
## 119 GP M 17 R GT3 T 1 3 other other
## 120 GP M 15 U GT3 T 3 4 other other
## 121 GP F 15 U GT3 T 1 2 at_home services
## 122 GP M 15 U GT3 T 2 2 services services
## 123 GP F 16 U LE3 T 2 4 other health
## 124 GP M 16 U GT3 T 4 4 health other
## 125 GP F 16 U GT3 T 2 2 other other
## 126 GP M 15 U GT3 T 3 4 services services
## 127 GP F 15 U LE3 A 3 4 other other
## 128 GP F 19 U GT3 T 0 1 at_home other
## 129 GP M 18 R GT3 T 2 2 services other
## 130 GP M 16 R GT3 T 4 4 teacher teacher
## 131 GP F 15 R GT3 T 3 4 services teacher
## 132 GP F 15 U GT3 T 1 1 at_home other
## 133 GP F 17 U LE3 T 2 2 other other
## 134 GP F 16 U GT3 A 3 4 services other
## 135 GP M 15 R GT3 T 3 4 at_home teacher
## 136 GP F 15 U GT3 T 4 4 services at_home
## 137 GP M 17 R GT3 T 3 4 at_home other
## 138 GP F 16 U GT3 A 3 3 other other
## 139 GP M 16 U LE3 T 1 1 services other
## 140 GP F 15 U GT3 T 4 4 teacher teacher
## 141 GP M 15 U GT3 T 4 3 teacher services
## 142 GP M 16 U LE3 T 2 2 services services
## 143 GP F 15 U GT3 T 4 4 teacher services
## 144 GP F 16 U LE3 T 1 1 at_home at_home
## 145 GP M 17 U GT3 T 2 1 other other
## 146 GP F 15 U GT3 T 1 1 other services
## 147 GP F 15 U GT3 T 3 2 health services
## 148 GP F 15 U GT3 T 1 2 at_home other
## 149 GP M 16 U GT3 T 4 4 teacher teacher
## 150 GP M 15 U LE3 A 2 1 services other
## 151 GP M 18 U LE3 T 1 1 other other
## 152 GP M 16 U LE3 T 2 1 at_home other
## 153 GP F 15 R GT3 T 3 3 services services
## 154 GP M 19 U GT3 T 3 2 services at_home
## 155 GP F 17 U GT3 T 4 4 other teacher
## 156 GP M 15 R GT3 T 2 3 at_home services
## 157 GP M 17 R LE3 T 1 2 other other
## 158 GP F 18 R GT3 T 1 1 at_home other
## 159 GP M 16 R GT3 T 2 2 at_home other
## 160 GP M 16 U GT3 T 3 3 other services
## 161 GP M 17 R LE3 T 2 1 at_home other
## 162 GP M 15 R GT3 T 3 2 other other
## 163 GP M 16 U LE3 T 1 2 other other
## 164 GP M 17 U GT3 T 1 3 at_home services
## 165 GP M 17 R LE3 T 1 1 other services
## 166 GP M 16 U GT3 T 3 2 services services
## 167 GP M 16 U GT3 T 2 2 other other
## 168 GP F 16 U GT3 T 4 2 health services
## 169 GP F 16 U GT3 T 2 2 other other
## 170 GP F 16 U GT3 T 4 4 health health
## 171 GP M 16 U GT3 T 3 4 other other
## 172 GP M 16 U GT3 T 1 0 other other
## 173 GP M 17 U LE3 T 4 4 teacher other
## 174 GP F 16 U GT3 T 1 3 at_home services
## 175 GP F 16 U LE3 T 3 3 other other
## 176 GP M 17 U LE3 T 4 3 teacher other
## 177 GP F 16 U GT3 T 2 2 services other
## 178 GP M 17 U GT3 T 3 3 other other
## 179 GP M 16 R GT3 T 4 2 teacher services
## 180 GP M 17 U GT3 T 4 3 other other
## 181 GP M 16 U GT3 T 4 3 teacher other
## 182 GP M 16 U GT3 T 3 3 services other
## 183 GP F 17 U GT3 T 2 4 services services
## 184 GP F 17 U LE3 T 3 3 other other
## 185 GP F 16 U GT3 T 3 2 other other
## 186 GP M 17 U GT3 T 3 3 services services
## 187 GP M 16 U GT3 T 1 2 services services
## 188 GP M 16 U LE3 T 2 1 other other
## 189 GP F 17 U GT3 A 3 3 health other
## 190 GP M 17 R GT3 T 1 2 at_home other
## 191 GP F 16 U GT3 T 2 3 services services
## 192 GP F 17 U GT3 T 1 1 at_home services
## 193 GP M 17 U GT3 T 1 2 at_home services
## 194 GP M 16 R GT3 T 3 3 services services
## 195 GP M 16 U GT3 T 2 3 other other
## 196 GP F 17 U LE3 T 2 4 services services
## 197 GP M 17 U GT3 T 4 4 services teacher
## 198 GP M 16 R LE3 T 3 3 teacher other
## 199 GP F 17 U GT3 T 4 4 services teacher
## 200 GP F 16 U LE3 T 4 4 teacher teacher
## 201 GP F 16 U GT3 T 4 3 health other
## 202 GP F 16 U GT3 T 2 3 other other
## 203 GP F 17 U GT3 T 1 1 other other
## 204 GP F 17 R GT3 T 2 2 other other
## 205 GP F 16 R GT3 T 2 2 services services
## 206 GP F 17 U GT3 T 3 4 at_home services
## 207 GP F 16 U GT3 A 3 1 services other
## 208 GP F 16 U GT3 T 4 3 teacher other
## 209 GP F 16 U GT3 T 1 1 at_home other
## 210 GP F 17 R GT3 T 4 3 teacher other
## 211 GP F 19 U GT3 T 3 3 other other
## 212 GP M 17 U LE3 T 4 4 services other
## 213 GP F 16 U GT3 A 2 2 other other
## 214 GP M 18 U GT3 T 2 2 services other
## 215 GP F 17 R LE3 T 4 4 services other
## 216 GP F 17 U LE3 T 3 2 other other
## 217 GP F 17 U GT3 T 4 3 other other
## 218 GP M 18 U LE3 T 3 3 services health
## 219 GP F 17 U GT3 T 2 3 at_home other
## 220 GP F 17 U GT3 T 2 2 at_home at_home
## 221 GP F 17 R GT3 T 2 1 at_home services
## 222 GP F 17 U GT3 T 1 1 at_home other
## 223 GP F 16 U GT3 T 2 3 services teacher
## 224 GP M 18 U GT3 T 2 2 other other
## 225 GP F 16 U GT3 T 4 4 teacher services
## 226 GP F 18 R GT3 T 3 1 other other
## 227 GP F 17 U GT3 T 3 2 other other
## 228 GP M 17 U LE3 T 2 3 services services
## 229 GP M 18 U LE3 T 2 1 at_home other
## 230 GP F 17 U GT3 A 2 1 other other
## 231 GP F 17 U LE3 T 4 3 health other
## 232 GP M 17 R GT3 T 2 2 other other
## 233 GP M 17 U GT3 T 4 4 teacher teacher
## 234 GP M 16 U GT3 T 4 4 health other
## 235 GP M 16 U LE3 T 1 1 other other
## 236 GP M 16 U GT3 T 3 2 at_home other
## 237 GP M 17 U LE3 T 2 2 other other
## 238 GP F 16 U GT3 T 2 1 other other
## 239 GP F 17 R GT3 T 2 1 at_home services
## 240 GP M 18 U GT3 T 2 2 other services
## 241 GP M 17 U LE3 T 4 3 health other
## 242 GP M 17 R LE3 A 4 4 teacher other
## 243 GP M 16 U LE3 T 4 3 teacher other
## 244 GP M 16 U GT3 T 4 4 services services
## 245 GP F 18 U GT3 T 2 1 other other
## 246 GP M 16 U GT3 T 2 1 other other
## 247 GP M 17 U GT3 T 2 3 other other
## 248 GP M 22 U GT3 T 3 1 services services
## 249 GP M 18 R LE3 T 3 3 other services
## 250 GP M 16 U GT3 T 0 2 other other
## 251 GP M 18 U GT3 T 3 2 services other
## 252 GP M 16 U GT3 T 3 3 at_home other
## 253 GP M 18 U GT3 T 2 1 services services
## 254 GP M 16 R GT3 T 2 1 other other
## 255 GP M 17 R GT3 T 2 1 other other
## 256 GP M 17 U LE3 T 1 1 health other
## 257 GP F 17 U LE3 T 4 2 teacher services
## 258 GP M 19 U LE3 A 4 3 services at_home
## 259 GP M 18 U GT3 T 2 1 other other
## 260 GP F 17 U LE3 T 2 2 services services
## 261 GP F 18 U GT3 T 4 3 services other
## 262 GP M 18 U GT3 T 4 3 teacher other
## 263 GP M 18 R GT3 T 3 2 other other
## 264 GP F 17 U GT3 T 3 3 other other
## 265 GP F 18 U GT3 T 2 2 at_home services
## 266 GP M 18 R LE3 A 3 4 other other
## 267 GP M 17 U GT3 T 3 1 services other
## 268 GP F 18 R GT3 T 4 4 teacher other
## 269 GP M 18 U GT3 T 4 2 health other
## 270 GP F 18 R GT3 T 2 1 other other
## 271 GP F 19 U GT3 T 3 3 other services
## 272 GP F 18 U GT3 T 2 3 other services
## 273 GP F 18 U LE3 T 1 1 other other
## 274 GP M 17 R GT3 T 1 2 at_home at_home
## 275 GP F 17 U GT3 T 2 4 at_home health
## 276 GP F 17 U LE3 T 2 2 services other
## 277 GP F 18 R GT3 A 3 2 other services
## 278 GP M 18 U GT3 T 4 4 teacher services
## 279 GP F 18 U GT3 T 4 4 health health
## 280 GP M 18 U LE3 T 4 3 teacher services
## 281 GP M 17 U LE3 A 4 1 services other
## 282 GP M 17 U LE3 A 3 2 teacher services
## 283 GP F 18 R LE3 T 1 1 at_home other
## 284 GP F 18 U GT3 T 1 1 other other
## 285 GP F 17 U GT3 T 2 2 other other
## 286 GP M 17 U GT3 T 1 1 other other
## 287 GP F 18 U GT3 T 2 2 at_home at_home
## 288 GP F 17 U GT3 T 1 1 services teacher
## 289 GP M 18 U GT3 T 2 1 services services
## 290 GP M 18 U LE3 A 4 4 teacher teacher
## 291 GP M 18 U GT3 T 4 2 teacher other
## 292 GP F 17 U GT3 T 4 3 health services
## 293 GP F 18 U LE3 T 2 1 services at_home
## 294 GP F 17 R LE3 T 3 1 services other
## 295 GP M 18 R LE3 T 3 2 services other
## 296 GP M 17 U GT3 T 3 3 health other
## 297 GP F 19 U GT3 T 4 4 health other
## 298 GP F 18 U LE3 T 4 3 other other
## 299 GP F 18 U GT3 T 4 3 other other
## 300 GP M 18 U LE3 T 4 4 teacher teacher
## 301 GP F 18 U LE3 A 4 4 health other
## 302 GP M 17 U LE3 T 4 4 other teacher
## 303 GP F 17 U GT3 T 4 2 other other
## 304 GP F 17 U GT3 T 3 2 health health
## 305 GP M 19 U GT3 T 3 3 other other
## 306 GP F 18 U GT3 T 2 4 services at_home
## 307 GP M 20 U GT3 A 3 2 services other
## 308 GP M 19 U GT3 T 4 4 teacher services
## 309 GP M 19 R GT3 T 3 3 other services
## 310 GP F 19 U LE3 T 1 1 at_home other
## 311 GP F 19 U LE3 T 1 2 services services
## 312 GP F 19 U GT3 T 2 1 at_home other
## 313 GP M 19 U GT3 T 1 2 other services
## 314 GP F 19 U LE3 T 3 2 services other
## 315 GP F 19 U GT3 T 1 1 at_home health
## 316 GP F 19 R GT3 T 2 3 other other
## 317 GP F 18 U GT3 T 2 1 services other
## 318 GP F 18 U GT3 T 4 3 other other
## 319 GP F 17 R GT3 T 3 4 at_home services
## 320 GP F 18 U GT3 T 4 4 teacher other
## 321 GP F 17 U GT3 A 4 3 services services
## 322 GP F 17 U GT3 T 2 2 other other
## 323 GP F 17 R LE3 T 2 2 services services
## 324 GP F 17 U GT3 T 3 1 services services
## 325 GP F 17 U LE3 T 0 2 at_home at_home
## 326 GP M 18 U GT3 T 4 4 other other
## 327 GP M 17 U GT3 T 3 3 other services
## 328 GP M 17 R GT3 T 2 2 services other
## 329 GP F 17 U GT3 T 4 4 teacher services
## 330 GP F 17 U GT3 T 4 4 teacher teacher
## 331 GP M 18 U LE3 T 2 2 other other
## 332 GP F 17 R GT3 T 2 4 at_home other
## 333 GP F 18 U GT3 T 3 3 services services
## 334 GP F 18 U LE3 T 2 2 other other
## 335 GP F 18 R GT3 T 2 2 at_home other
## 336 GP F 17 U GT3 T 3 4 services other
## 337 GP F 19 R GT3 A 3 1 services at_home
## 338 GP F 17 U GT3 T 3 2 other other
## 339 GP F 18 U LE3 T 3 3 services services
## 340 GP F 17 R GT3 A 3 2 other other
## 341 GP F 19 U GT3 T 2 1 services services
## 342 GP M 18 U GT3 T 4 4 teacher services
## 343 GP M 18 U LE3 T 3 4 services other
## 344 GP F 17 U GT3 A 2 2 at_home at_home
## 345 GP F 18 U GT3 T 2 3 at_home other
## 346 GP F 18 U GT3 T 3 2 other services
## 347 GP M 18 R GT3 T 4 3 teacher services
## 348 GP M 18 U GT3 T 4 3 teacher other
## 349 GP F 17 U GT3 T 4 3 health other
## 350 MS M 18 R GT3 T 3 2 other other
## 351 MS M 19 R GT3 T 1 1 other services
## 352 MS M 17 U GT3 T 3 3 health other
## 353 MS M 18 U LE3 T 1 3 at_home services
## 354 MS M 19 R GT3 T 1 1 other other
## 355 MS M 17 R GT3 T 4 3 services other
## 356 MS F 18 U GT3 T 3 3 services services
## 357 MS F 17 R GT3 T 4 4 teacher services
## 358 MS F 17 U LE3 A 3 2 services other
## 359 MS M 18 U LE3 T 1 1 other services
## 360 MS F 18 U LE3 T 1 1 at_home services
## 361 MS F 18 R LE3 A 1 4 at_home other
## 362 MS M 18 R LE3 T 1 1 at_home other
## 363 MS F 18 U GT3 T 3 3 services services
## 364 MS F 17 U LE3 T 4 4 at_home at_home
## 365 MS F 17 R GT3 T 1 2 other services
## 366 MS M 18 R GT3 T 1 3 at_home other
## 367 MS M 18 U LE3 T 4 4 teacher services
## 368 MS F 17 R GT3 T 1 1 other services
## 369 MS F 18 U GT3 T 2 3 at_home services
## 370 MS F 18 R GT3 T 4 4 other teacher
## 371 MS F 19 U LE3 T 3 2 services services
## 372 MS M 18 R LE3 T 1 2 at_home services
## 373 MS F 17 U GT3 T 2 2 other at_home
## 374 MS F 17 R GT3 T 1 2 other other
## 375 MS F 18 R LE3 T 4 4 other other
## 376 MS F 18 R GT3 T 1 1 other other
## 377 MS F 20 U GT3 T 4 2 health other
## 378 MS F 18 R LE3 T 4 4 teacher services
## 379 MS F 18 U GT3 T 3 3 other other
## 380 MS F 17 R GT3 T 3 1 at_home other
## 381 MS M 18 U GT3 T 4 4 teacher teacher
## 382 MS M 18 R GT3 T 2 1 other other
## 383 MS M 17 U GT3 T 2 3 other services
## 384 MS M 19 R GT3 T 1 1 other services
## 385 MS M 18 R GT3 T 4 2 other other
## 386 MS F 18 R GT3 T 2 2 at_home other
## 387 MS F 18 R GT3 T 4 4 teacher at_home
## 388 MS F 19 R GT3 T 2 3 services other
## 389 MS F 18 U LE3 T 3 1 teacher services
## 390 MS F 18 U GT3 T 1 1 other other
## 391 MS M 20 U LE3 A 2 2 services services
## 392 MS M 17 U LE3 T 3 1 services services
## 393 MS M 21 R GT3 T 1 1 other other
## 394 MS M 18 R LE3 T 3 2 services other
## 395 MS M 19 U LE3 T 1 1 other at_home
## reason guardian traveltime studytime failures schoolsup famsup
## 1 course mother 2 2 0 yes no
## 2 course father 1 2 0 no yes
## 3 other mother 1 2 3 yes no
## 4 home mother 1 3 0 no yes
## 5 home father 1 2 0 no yes
## 6 reputation mother 1 2 0 no yes
## 7 home mother 1 2 0 no no
## 8 home mother 2 2 0 yes yes
## 9 home mother 1 2 0 no yes
## 10 home mother 1 2 0 no yes
## 11 reputation mother 1 2 0 no yes
## 12 reputation father 3 3 0 no yes
## 13 course father 1 1 0 no yes
## 14 course mother 2 2 0 no yes
## 15 home other 1 3 0 no yes
## 16 home mother 1 1 0 no yes
## 17 reputation mother 1 3 0 no yes
## 18 reputation mother 3 2 0 yes yes
## 19 course mother 1 1 3 no yes
## 20 home father 1 1 0 no no
## 21 reputation mother 1 2 0 no no
## 22 other father 1 1 0 no yes
## 23 course mother 1 2 0 no no
## 24 reputation mother 2 2 0 no yes
## 25 course mother 1 3 0 yes yes
## 26 home mother 1 1 2 no yes
## 27 home mother 1 1 0 no yes
## 28 other mother 1 1 0 no no
## 29 home mother 1 2 0 yes yes
## 30 home mother 1 2 0 no yes
## 31 home mother 1 2 0 no yes
## 32 reputation mother 2 2 0 no yes
## 33 course mother 1 2 0 no yes
## 34 course mother 1 2 0 no no
## 35 home mother 1 1 0 no yes
## 36 other father 2 1 0 no yes
## 37 home mother 1 3 0 no yes
## 38 reputation mother 2 3 0 no yes
## 39 course mother 1 3 0 yes yes
## 40 reputation mother 1 1 0 yes yes
## 41 home mother 2 2 1 no yes
## 42 home other 1 1 0 no yes
## 43 course father 1 2 0 no yes
## 44 course father 1 1 0 yes yes
## 45 course father 2 2 1 yes no
## 46 course mother 1 2 0 yes yes
## 47 home mother 1 2 0 no yes
## 48 reputation mother 1 4 0 no no
## 49 home mother 1 2 0 no yes
## 50 other father 1 2 1 yes yes
## 51 course mother 3 2 0 no yes
## 52 other mother 1 2 0 no yes
## 53 other father 2 1 1 no no
## 54 course mother 1 1 0 yes yes
## 55 other mother 1 1 0 no no
## 56 other mother 1 2 0 no no
## 57 reputation mother 1 2 0 no yes
## 58 reputation mother 1 2 0 no yes
## 59 home father 1 2 0 yes yes
## 60 course mother 1 2 0 no yes
## 61 other mother 1 2 0 no yes
## 62 course father 4 1 0 yes yes
## 63 reputation father 1 2 0 yes no
## 64 home mother 1 3 0 yes yes
## 65 reputation father 1 2 0 yes no
## 66 course mother 3 2 0 no yes
## 67 reputation mother 1 4 0 no yes
## 68 course mother 1 4 0 yes yes
## 69 reputation mother 2 2 0 yes yes
## 70 reputation father 2 4 0 no yes
## 71 reputation father 2 4 0 no yes
## 72 course mother 1 4 0 no no
## 73 reputation mother 1 2 2 yes yes
## 74 reputation mother 1 1 0 no no
## 75 home mother 1 2 0 yes yes
## 76 home mother 1 2 0 no yes
## 77 course mother 2 4 0 no no
## 78 reputation mother 1 4 0 no no
## 79 home mother 2 1 3 yes yes
## 80 course mother 1 2 0 no yes
## 81 course father 1 1 0 yes yes
## 82 home mother 1 3 0 yes no
## 83 reputation mother 1 2 0 no yes
## 84 home mother 2 2 0 no no
## 85 home father 1 2 0 no yes
## 86 reputation father 2 2 2 no no
## 87 course mother 1 2 0 no yes
## 88 reputation mother 1 3 0 no yes
## 89 reputation father 2 2 1 no no
## 90 reputation mother 1 2 0 no yes
## 91 home mother 1 3 0 no yes
## 92 reputation mother 1 1 0 no no
## 93 home father 1 2 0 yes yes
## 94 home mother 2 2 0 no yes
## 95 reputation mother 1 4 0 no yes
## 96 home mother 2 4 1 yes yes
## 97 reputation mother 2 1 0 yes yes
## 98 course mother 1 2 0 no yes
## 99 reputation mother 1 1 0 no no
## 100 course mother 1 3 0 yes yes
## 101 other mother 1 1 0 yes yes
## 102 other father 1 3 0 no yes
## 103 course mother 1 1 0 no yes
## 104 home mother 2 2 0 yes yes
## 105 course mother 1 2 0 no yes
## 106 reputation father 1 4 0 yes no
## 107 course mother 1 4 0 yes yes
## 108 home father 1 3 0 no yes
## 109 home father 4 4 0 no yes
## 110 other mother 1 3 0 no yes
## 111 course mother 1 1 0 no no
## 112 reputation father 1 3 1 yes yes
## 113 home mother 1 2 1 yes no
## 114 course mother 1 1 0 no no
## 115 reputation mother 1 2 0 no no
## 116 course father 1 2 0 no yes
## 117 reputation father 2 2 0 no yes
## 118 home father 2 1 0 no no
## 119 course father 3 2 1 no yes
## 120 reputation father 1 1 0 no no
## 121 course mother 1 2 0 no no
## 122 home father 1 4 0 no yes
## 123 course father 2 2 0 no yes
## 124 course mother 1 1 0 no yes
## 125 home mother 1 2 0 no no
## 126 home father 1 1 0 yes no
## 127 home mother 1 2 0 yes no
## 128 course other 1 2 3 no yes
## 129 reputation mother 1 1 2 no yes
## 130 course mother 1 1 0 no no
## 131 course father 2 3 2 no yes
## 132 course mother 3 1 0 no yes
## 133 course father 1 1 0 no yes
## 134 course father 1 1 0 no no
## 135 course mother 4 2 0 no yes
## 136 course mother 1 3 0 no yes
## 137 course mother 3 2 0 no no
## 138 course other 2 1 2 no yes
## 139 course mother 1 2 1 no no
## 140 course mother 2 1 0 no no
## 141 course father 2 4 0 yes yes
## 142 reputation father 2 1 2 no yes
## 143 course mother 1 3 0 no yes
## 144 course mother 1 1 0 no no
## 145 home mother 1 1 3 no yes
## 146 course father 1 2 0 no yes
## 147 home father 1 2 3 no yes
## 148 course mother 1 2 0 no yes
## 149 course mother 1 1 0 no yes
## 150 course mother 4 1 3 no no
## 151 course mother 1 1 3 no no
## 152 course mother 1 1 1 no no
## 153 reputation other 2 3 2 no yes
## 154 home mother 1 1 3 no yes
## 155 course mother 1 1 0 yes yes
## 156 course mother 1 2 0 yes no
## 157 reputation mother 1 1 0 no no
## 158 course mother 3 1 3 no yes
## 159 course mother 3 1 0 no no
## 160 course father 1 2 1 no yes
## 161 course mother 2 1 2 no no
## 162 course mother 2 2 2 yes yes
## 163 course mother 2 1 1 no no
## 164 course father 1 1 0 no no
## 165 course mother 4 2 3 no no
## 166 course mother 2 1 1 no yes
## 167 course father 1 2 0 no no
## 168 home father 1 2 0 no no
## 169 home mother 1 2 0 no yes
## 170 reputation mother 1 2 0 no yes
## 171 course father 3 1 2 no yes
## 172 reputation mother 2 2 0 no yes
## 173 reputation mother 1 2 0 no yes
## 174 home mother 1 2 3 no no
## 175 reputation mother 2 2 0 no yes
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## paid activities nursery higher internet romantic famrel freetime goout
## 1 no no yes yes no no 4 3 4
## 2 no no no yes yes no 5 3 3
## 3 yes no yes yes yes no 4 3 2
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## 363 no no yes yes yes yes 4 3 2
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## 394 no no no yes yes no 4 4 1
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## Dalc Walc health absences G1 G2 G3
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## 3 2 3 3 10 7 8 10
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## 394 3 4 5 0 11 12 10
## 395 3 3 5 5 8 9 9dim(data)## [1] 395 33Data selected for project has a total of 395 students with a total of 33 investigative variables.
str(data)## 'data.frame': 395 obs. of 33 variables:
## $ school : Factor w/ 2 levels "GP","MS": 1 1 1 1 1 1 1 1 1 1 ...
## $ sex : Factor w/ 2 levels "F","M": 1 1 1 1 1 2 2 1 2 2 ...
## $ age : int 18 17 15 15 16 16 16 17 15 15 ...
## $ address : Factor w/ 2 levels "R","U": 2 2 2 2 2 2 2 2 2 2 ...
## $ famsize : Factor w/ 2 levels "GT3","LE3": 1 1 2 1 1 2 2 1 2 1 ...
## $ Pstatus : Factor w/ 2 levels "A","T": 1 2 2 2 2 2 2 1 1 2 ...
## $ Medu : int 4 1 1 4 3 4 2 4 3 3 ...
## $ Fedu : int 4 1 1 2 3 3 2 4 2 4 ...
## $ Mjob : Factor w/ 5 levels "at_home","health",..: 1 1 1 2 3 4 3 3 4 3 ...
## $ Fjob : Factor w/ 5 levels "at_home","health",..: 5 3 3 4 3 3 3 5 3 3 ...
## $ reason : Factor w/ 4 levels "course","home",..: 1 1 3 2 2 4 2 2 2 2 ...
## $ guardian : Factor w/ 3 levels "father","mother",..: 2 1 2 2 1 2 2 2 2 2 ...
## $ traveltime: int 2 1 1 1 1 1 1 2 1 1 ...
## $ studytime : int 2 2 2 3 2 2 2 2 2 2 ...
## $ failures : int 0 0 3 0 0 0 0 0 0 0 ...
## $ schoolsup : Factor w/ 2 levels "no","yes": 2 1 2 1 1 1 1 2 1 1 ...
## $ famsup : Factor w/ 2 levels "no","yes": 1 2 1 2 2 2 1 2 2 2 ...
## $ paid : Factor w/ 2 levels "no","yes": 1 1 2 2 2 2 1 1 2 2 ...
## $ activities: Factor w/ 2 levels "no","yes": 1 1 1 2 1 2 1 1 1 2 ...
## $ nursery : Factor w/ 2 levels "no","yes": 2 1 2 2 2 2 2 2 2 2 ...
## $ higher : Factor w/ 2 levels "no","yes": 2 2 2 2 2 2 2 2 2 2 ...
## $ internet : Factor w/ 2 levels "no","yes": 1 2 2 2 1 2 2 1 2 2 ...
## $ romantic : Factor w/ 2 levels "no","yes": 1 1 1 2 1 1 1 1 1 1 ...
## $ famrel : int 4 5 4 3 4 5 4 4 4 5 ...
## $ freetime : int 3 3 3 2 3 4 4 1 2 5 ...
## $ goout : int 4 3 2 2 2 2 4 4 2 1 ...
## $ Dalc : int 1 1 2 1 1 1 1 1 1 1 ...
## $ Walc : int 1 1 3 1 2 2 1 1 1 1 ...
## $ health : int 3 3 3 5 5 5 3 1 1 5 ...
## $ absences : int 6 4 10 2 4 10 0 6 0 0 ...
## $ G1 : int 5 5 7 15 6 15 12 6 16 14 ...
## $ G2 : int 6 5 8 14 10 15 12 5 18 15 ...
## $ G3 : int 6 6 10 15 10 15 11 6 19 15 ...Data selected for project is a good all-rounder data with multiple types of quantitative and qualitative variables.
Source of Data
P. Cortez and A. Silva. Using Data Mining to Predict Secondary School Student Performance. In A. Brito and J. Teixeira Eds., Proceedings of 5th FUture BUsiness TEChnology Conference (FUBUTEC 2008) pp. 5-12, Porto, Portugal, April, 2008, EUROSIS, ISBN 978-9077381-39-7.
Fabio Pagnotta, Hossain Mohammad Amran. Email:fabio.pagnotta@studenti.unicam.it, mohammadamra.hossain ‘@’ studenti.unicam.it University Of Camerino
Assessment of Source
The source is from a research paper that Professor Paulo Cortez and Alice Silva had put together. It was presented in the Future Business Technology Conference (FUBUTEC) 2008. FUBUTEC hosts colaboration between business organisations with an intention to bring business technology research to a new level. As such Professor Cortez and Ms Silva’s work can be considered to be of a creditable origin for it to be included in the proceeding of FUBUTEC 2008.
Stakeholders
- Cortez, Paulo (Main stakeholder)
Paulo Cortez is an Associate Professor at the Department of Information Systems and Coordinator of the Information Systems and Technologies (IST) research group of ALGORITMI Research Centre, University of Minho.
Current research interests:
Business Intelligence: Decision Support Systems, Data Mining and Forecasting;
Artificial Intelligence (AI): Neural Networks, Evolutionary Computation and AI Applications.
Paulo Cortez has also co-author of more than 110 indexed (e.g., ISI, Scopus) publications in international scientific journals and conferences.
- Silva, Alice
Alice Silva was an informatics teacher at Arcozola Secondary School in Portugal in 2008. She is a holder of a masters degree in Informations Systems from the University of Minho.
Domain Knowledge
Portugal is one of the poorest countries in Western Europe as well as one of the least educated with highest rates of failures along with annual cuts to education budgets. Portugal is also known for a country with the highet rates of students dropping out amoung the Organisation for Economic Co-operation and Development countries with 37.1% of students dropping out in the year of 2011 and with just 28% of the popoulation between the ages of 25 and 64 completing high shcool.
Professor Cortez and Ms Silva realised that the students in Portugal generally perform badly in Mathematics and Portuguese. They wanted to find out the reason for this and conducted this research to study the reason behind the poor performance in the subjects of Mathematics and Portuguese language amongst the students in Portugal. The data was collected from the Gabriel Pereira school and Mousinho da Silveira school. The attributes collected are stated in the data dictionary below. We seek to examine this data and draw relationships between the various attributes to understand the students and the families of Portugal better.
Data Dictionary
school - student’s school (‘GP’ - Gabriel Pereira / ‘MS’ - Mousinho da Silveira)
sex - student’s sex (‘F’ - female or ‘M’ - male)
age - student’s age
address - student’s home address type (‘U’ - urban or ‘R’ - rural)
famsize - family size (‘LE3’ - less or equal to 3 or ‘GT3’ - greater than 3)
Pstatus - parent’s cohabitation status (‘T’ - living together or ‘A’ - apart)
Medu - mother’s education (0 - none, 1 - primary education (4th grade), 2 - 5th to 8 9th grade, 3 - secondary education or 4 - higher education)
Fedu - father’s education (0 - none, 1 - primary education (4th grade), 2 - 5th to 9th grade, 3 - secondary education or 4 - higher education)
Mjob - mother’s job (‘teacher’, ‘health’ care related, civil ‘services’ (e.g. administrative or police), ‘at_home’ or ‘other’)
Fjob - father’s job (‘teacher’, ‘health’ care related, civil ‘services’ (e.g. administrative or police), ‘at_home’ or ‘other’)
reason - reason to choose this school (close to ‘home’, school ‘reputation’,‘course’ preference or ‘other’)
guardian - student’s guardian (‘mother’, ‘father’ or ‘other’)
traveltime - home to school travel time (1 - <15 min., 2 - 15 to 30 min., 3 - 30 min. to 1 hour, or 4 - >1 hour)
studytime - weekly study time (1 - <2 hours, 2 - 2 to 5 hours, 3 - 5 to 10 hours, or 4 - >10 hours)
failures - number of past class failures (1<=n<3, else 4)
schoolsup - extra educational support (yes or no)
famsup - family educational support (yes or no)
paid - extra paid classes within the course subject (yes or no)
activities - extra-curricular activities (yes or no)
nursery - attended nursery school (yes or no)
higher - wants to take higher education (yes or no)
internet - Internet access at home (yes or no)
romantic - with a romantic relationship (yes or no)
famrel - quality of family relationships (from 1 - very bad to 5 - excellent)
freetime - free time after school (from 1 - very low to 5 - very high)
goout - going out with friends (from 1 - very low to 5 - very high)
Dalc - workday alcohol consumption (from 1 - very low to 5 - very high)
Walc - weekend alcohol consumption (from 1 - very low to 5 - very high)
health - current health status (from 1 - very bad to 5 - very good)
absences - number of school absences (from 0 to 93)
These grades are related with the course subject, Math or Portuguese:
GRADE (out of 20)
G1 - first period grade (numeric: from 0 to 20) G2 - second period grade (numeric: from 0 to 20) G3 - final grade (numeric: from 0 to 20, output target)
RESEARCH QUESTION 1
Does having accessible internet at home prove to be more of a leanring aid or a distraction for students?
With the current fast and increasingly advanced technology, technology, especially the internet, becomes more accessible for every household. Some experts in the field of eduation view the internet as a tool that would be beneficial when featured and implemented in education systems all around the world. However, others have argued against the capability of the internet in supporting teenagers and children in their education by putting forward the argument of the internet as a form of distraction.
Using data gathered from schools in Portugal, we set out to investigate if having accessible internet at home prove to be more of a learning aid or a distraction for students. This is done by using qualitative data on whether individual students have the internet at home and their personal final grade at the end of the year, which is represented using comparative boxplot as a grpahical method of analysis, the results are shown below:
boxplot(data$G3 ~ data$internet, col="skyblue", main="Internet vs Grades", ylab="Internet", xlab="Grades", horizontal=TRUE, outlier = FALSE)
Median scores of students with and without the internet respectively
median(data$G3 [data$internet == "yes"])## [1] 11median(data$G3 [data$internet == "no"])## [1] 10Inter-Quartile Range of students with and without the internet respectively
IQR(data$G3 [data$internet == "yes"])## [1] 5IQR(data$G3 [data$internet == "no"])## [1] 4.75Maximum values of scores of students with and without the internet respectively
max(data$G3 [data$internet == "yes"])## [1] 20max(data$G3 [data$internet == "no"])## [1] 18Quantile of students with the internet
quantile(data$G3 [data$internet == "yes"])## 0% 25% 50% 75% 100%
## 0 9 11 14 20Quantile of students without the internet
quantile(data$G3 [data$internet == "no"])## 0% 25% 50% 75% 100%
## 0.00 7.25 10.00 12.00 18.00By analysing and comparing the median final grade scores of students (out of 20) who have internet access at home to students without internet access at home, which are visualised by the comparative boxplot, it can be seen that the average final score of students with internet access at home are higher than students’ who have no internet access at home. Furthemore, other details within the graphical summary further supports interent as learning tool. For instance, the maximum value of grades (excluding the outlier) of students with accessible internet at home is 20 with the minimum value of 4. On the other hand, both the maximum and minimum value of grades of students without internet access at home is 18 and 0 respectively, which is considerably lower than those of students with internet access. The interquartile range of students with the internet also lies higher on the scale than that of students without internet (both upper and lower quartile is higher for students with interent).
From the boxplot:
- Higher Median score of students with interent access at home
- IQR lies higher on the scale of grades for students with internet
- Top 25% of students with internet is scoring 14 and above comparative to 12 for students without interent
- Maximum score of student with internet is 20, comparatively higher than the maximum score of 18 from students without the interent at home.
- Minimum score (excluding outlier) of students without internet is lower at 0, which is considerably lower than the minimum score of 4 scored by students with the internet.
After analysis of both graphical and numerical summary, it can be concluded that having internet at home proves to be more of a learning aid than a distraction from the students’ studies. Hence, the internet proves to improve grades in students and implementing it into the education system is definitely something to consider.
RESEARCH QUESTION 2
Does weekday consumption of alcohol affect acedemic studies?
The consumption of alcohol by teenagers who are still in school is often looked down upon by both society and many experts in the healthcare industry. It is often the common notion that alcohol consumption in teenagers has a negative impact on the mental and physical development of the brain and impedes learning ability, decreasing the concentration span. Using the data, the effects of alcohol on learning ability and performance of teenagers could be validated or disproved.
par(mfrow = c(1,2))
boxplot(data$G3~ data$Walc, col="cyan", main="Does alcohol consumption on weekdays affect acedemics?", ylab="Level of consumption of Alcohol", xlab="Grades", horizontal=TRUE) 
Maximum score of students who consume very low amounts, moderately low, moderate, high and extremely high levels of alcohol during the weekday respectively
max(data$G3 [data$Walc == 1])## [1] 20max(data$G3 [data$Walc == 2])## [1] 19max(data$G3 [data$Walc == 3])## [1] 18max(data$G3 [data$Walc == 4])## [1] 17max(data$G3 [data$Walc == 5])## [1] 18Average score of students who drink moderately low amounts of alcohol during the weekday
mean(data$G3 [data$Walc == 1])## [1] 10.7351mean(data$G3 [data$Walc == 2])## [1] 10.08235mean(data$G3 [data$Walc == 3])## [1] 10.725mean(data$G3 [data$Walc == 4])## [1] 9.686275mean(data$G3 [data$Walc == 5])## [1] 10.14286From the results shown above, it could be seen that there is no clear trend on whether weekday alcohol consumption would affect students performance in school. One evidence can be seen in the marks of students who have a tendency to consume heavy amounts of alcohol during weekdays score on average very much the same as those students who drink very little to moderate amounts of alcohol, achieving on average 10 out of 20 in their final grade. Even by looking at the maximum values, there is no clear trend. By comparing the maximum scores of students between their respective groups (grouped by level of consumption of alc), the maximum values stays constantly at around 18 out of 20. This tells us that even students who drink excessively on weekends can achieve as high as those students who drink very little alcohol on the weekends. Therefore, the conclusive results show that the level of alcohol consumption does not affect the academic results of students to a great extent.
RESEARCH QUESTION 3
Is it possible that location is a deciding factor for parents when choosing educational institutions for their children?
With children and teenagers growing up comes many stressful decisions, such as choosing a secondary level institution. Many factors come into play for parents when choosing the best educational institution for their children and teenagers. Some of which include reputation, distance away from home and fees. In this case, the data that would be examined is the travel time, which can be considered as the distance away from home, as it could then be used to determine whether or not it is a major factor for parents in deciding the educational institutions they want their children to be admitted into.
Travel_Time = data$traveltime
hist(Travel_Time, prob = T)
m = mean(data$traveltime)
sd = sd(data$traveltime)
curve(dnorm(x, mean = m, sd = sd),col = "darkgreen", lwd = 4, add = TRUE)
abline(v=1.448101, col = "Red")
abline(v= 1, col = "blue")
mean(data$traveltime)## [1] 1.448101median(data$traveltime)## [1] 1sd(data$traveltime)## [1] 0.6975048By looking at the histogram and curve above, it is clear that this data set is skewed heavily to the right (positive skewedness) with many statistical indicators. One of the indicators is the peak of the curve that is near to the left end of the graph, while most of the bars of the histogram exists on the left hand side of the graph. Secondly, the mean is higher than the median. Lastly, by constructing a boxplot,it can be seen that the right tail is much longer. All these statistical features indicates that the histogram and curve is very skewed to the right (positive skewedness) with majority of students living less than 30 mins away from the institution.
boxplot(data$traveltime, xlab = "Travel Time" , main = "Boxplot distribution of travel time of students",horizontal = TRUE)
When an histogram and boxplot is skewed in such a manner, there is a very likely chance that it is due to the introduction of a heavy bias. Since the trait/factor being investigated was time travelled, it could be safely concluded that majority of students did indeed live close to the school. Hence, it can be determined that the distance of the school can be a playing factor in choosing a secondary institutions for many parents. On the other hand, it could also be caused by government regulation that makes it compulsory for parents to admit their children to school closer to their homes.
RESEARCH QUESTION 4
How difficult are assessments in Gabriel Pereira school and are there any exceptionally good or exceptionally bad students in the cohort, if so what is the proportion of those students?
The level of difficulty of assessments and examination can be determined by a histogram paired with a normal curve. If the school’s assessments are too easy, the majority of students would do well and there will be a skew to the left as rhe majority of student’s scores will be concentrated to the right where the marks are represented to be higher on the x-axis. If the school’s assessments are too hard, the majority of students would probably do poorly with lower marks than usual, hence there will be a very distinct right skew pattern where the majority of the students are concentrated towards the left. However, if the level of difficulty is suitable for the students, the final marks of students should follow a normal curve. with the mean approximately equal to the median and majority of the students doing averagely well with some extremities.
Summary:
Relatively easy assessments: Left Skewed (Median > Mean)
Relatively suitable assessments: Normal Curve (Median = Mean)
Relatively difficult assessments: Right Skewed (Median < Mean)
Distribution_of_Final_Grade_of_Students = data$G3
hist(Distribution_of_Final_Grade_of_Students, prob = T)
m = mean(data$G3)
sd = sd(data$G3)
curve(dnorm(x, mean = m, sd = sd), main = "Distribution of Final Grade of Students",col = "darkgreen", lwd = 2, add = TRUE)
abline(v=10.41519, col="red")
abline(v=11, col="yellow")
mean(data$G3)## [1] 10.41519median(data$G3)## [1] 11sd(data$G3)## [1] 4.581443From plotting the final grade of students, it can be seen that the shape of the curve is very close to a normal curve. This indicates that majority of students are doing only averagely well with majority of them scoring between 6 out of 20 to 14 out of 20. Since the mean and median are relatively close to one another, it goes to show that there is minimal skewedness hence it was a fair assessment/examination where the difficulty was neither too easy nor too hard.
However, since the final grade marks can vary depending on the difficulty of the examination and assessments, such as in the easy assessments/examination, the majority of the curve will be left skewed and for harder assesments/examinations, the majority will be right skewed, it is not posible to have a final set marks to measure grades as the mean, median and most importantly the spread changes all the time. Instead, to measure the level of standard of a student, it is recommended that the data is compared against the whole cohort. The best way to do so is with a normal curve. The result would most probably be with exceptional students lie above the higher 2SD point and extremely poorly achieving sutdents lie outside the lower 2SD point.
Distribution_of_Final_Grade_of_Students = data$G3
hist(Distribution_of_Final_Grade_of_Students, prob = T)
m = mean(data$G3)
sd = sd(data$G3)
curve(dnorm(x, mean = m, sd = sd), col = "darkgreen", lwd = 2, add = TRUE)
abline(v=10.41519, col="red")
abline(v=5.833747, col="blue")
abline(v=14.996633, col="blue")
abline(v=19.578, col="blue")
abline(v=1.252304, col="blue")
Note: The blue line represents 1 standard deviation unit
Are there any exceptionally good students?
Exceptional students lie above the 2SD point.
2SD above the mean –> 10.4159 + 2(4.581443) = 19.57
Therefore, the criteria of exceptionally good students would score above 19.57 out of 20.
length(data$G3[data$G3 > 19.57])## [1] 1Hence it could be concluded that there is only ONE student that has an exceptionally good result.
length(data$G3[data$G3 > 19.57])/length(data$G3) * 100## [1] 0.2531646This means that only 0.25% of the students in this cohort fall outside the 2SD point, and thus fall under the category of “exceptionally good students”.
Hence, only 0.25% of the students in this cohort is an exceptional student.
Are there any exceptionally academically poor students?
Exceptionally academically poor students lie below the negative 2SD point.
2SD below the mean –> 10.4159 - 2(4.581443) = 1.252304
Therefore, the criteria of an exceptionally academically poor students score below 1.252304 out of 20.
length(data$G3[data$G3 < 1.252304])## [1] 38Hence, it could be concluded that there are 38 exceptionally acedemically poor students.
length(data$G3[data$G3 < 1.252304])/length(data$G3) * 100## [1] 9.620253This means that 9.62% of students from the cohort fell below the negative 2SD point and fall under the category of “exceptionally poor students”.
Hence, 9.62% of the students in this cohort did exceptionally poor acedemically in their studies.
RESEARCH QUESTION 5
Which gender is more likely to seek school support? And is the acedemic school support effective?
data1 = table(data$schoolsup , data$sex)
data1##
## F M
## no 172 172
## yes 36 15barplot(data1, main="Which gender is most likely to seek school support", xlab="gender", legend = rownames(data1), beside=TRUE, col = c("palevioletred1","paleturquoise"))
From the barplot above it can be seen that female students in general tend to seek acedemic support from the school over male students as the green portion of female students is clearly larger than the green portion depicted on the males.
Does the school’s acedemic support program prove to be of any help?
A boxplot graphing the median scores of female student who did not seek school support is compared to female student who did, as well as a pair of boxplots that compare their male counterparts, wass created to investigate the question.
par(mfrow = c(2, 1))
boxplot(data$G3 [data$sex == "F"] [data$schoolsup == "yes"], main = "Final Grade Results of Female students with School Support",xlab = "Results" , ylab= "With Support", col = "pink", horizontal = TRUE)
boxplot(data$G3 [data$sex == "F"] [data$schoolsup == "no"], main = "Final Grade Results of Female students without School Support",xlab = "Results", ylab= "Without Sup", col= "salmon", horizontal = TRUE)
From the results, it can be seen that female students who sought school support generally do acedemically better than those who did not seek school support as the median final grade of female students who took school support lie at 11 out of 20 whereas the median final score of female students who did not seek school support lies at only 10 out of 20. Hence, it can be determined that male students who sought school support generally do acedemically better than those who did not seek any school support.
par(mfrow = c(2, 1))
boxplot(data$G3 [data$sex == "M"] [data$schoolsup == "yes"], main = "Final Grade Results of male students with School Support",xlab = "Results" , ylab= "With Support", col="green", horizontal = TRUE)
boxplot(data$G3 [data$sex == "M"] [data$schoolsup == "no"], main = "Final Grade Results of male students without School Support",xlab = "Results" , ylab= "Without Support", col="lightgreen" , horizontal = TRUE)
From the results, it can be seen that male students who sought school support generally do acedemically better than those who did not seek school support as the median final grade of male students who took school support lie at 12 out of 20 whereas the median final score of students who did not seek school support lies at only 11 out of 20. Hence, it can be determined that male students who sought school support generally do acedemically better than those who did not seek any school support.
Despite these results, the data is susceptible to Simpson’s paradox, and thus, to investigate this, the 2 gender groups are combined in a pair of boxplot that calculate and compare the median G3 scores of those who sought school support and those who did not.
par(mfrow = c(2,1))
boxplot(data$G3 [data$schoolsup == "yes"], main = "Students with School Support",xlab = "Results" , ylab= "With Support", horizontal = TRUE)
boxplot(data$G3 [data$schoolsup == "no"], main = "Students without School Support",xlab = "Results" , ylab= "Without Support", horizontal = TRUE )
mean(data$G3 [data$schoolsup == "yes"])## [1] 9.431373mean(data$G3 [data$schoolsup == "no"])## [1] 10.56105From the data, it can be concluded that there is a Simpson’s paradox in data. The evidence is that, although the support system seemed to help students’ result when it is seen as only boy or girl, when we see the overall data, the student without the support system scored better. One possible reason for this result is because students who are already capable in their studies are less likely to seek any academic support.