Lab 1: Intro to R
Author Name
2025-04-09
Explore data
download.file("http://www.openintro.org/stat/data/evals.RData", destfile = "evals.RData")
load("evals.RData")
evals## score rank ethnicity gender language age cls_perc_eval
## 1 4.7 tenure track minority female english 36 55.81395
## 2 4.1 tenure track minority female english 36 68.80000
## 3 3.9 tenure track minority female english 36 60.80000
## 4 4.8 tenure track minority female english 36 62.60163
## 5 4.6 tenured not minority male english 59 85.00000
## 6 4.3 tenured not minority male english 59 87.50000
## 7 2.8 tenured not minority male english 59 88.63636
## 8 4.1 tenured not minority male english 51 100.00000
## 9 3.4 tenured not minority male english 51 56.92308
## 10 4.5 tenured not minority female english 40 86.95652
## 11 3.8 tenured not minority female english 40 88.88889
## 12 4.5 tenured not minority female english 40 96.00000
## 13 4.6 tenured not minority female english 40 85.00000
## 14 3.9 tenured not minority female english 40 56.00000
## 15 3.9 tenured not minority female english 40 88.09524
## 16 4.3 tenured not minority female english 40 90.00000
## 17 4.5 tenured not minority female english 40 83.33334
## 18 4.8 tenure track not minority female english 31 87.50000
## 19 4.6 tenure track not minority female english 31 90.90909
## 20 4.6 tenure track not minority female english 31 79.16666
## 21 4.9 tenure track not minority female english 31 88.88889
## 22 4.6 tenure track not minority female english 31 88.13559
## 23 4.5 tenure track not minority female english 31 56.32184
## 24 4.4 tenured not minority male english 62 64.53901
## 25 4.6 tenured not minority male english 62 54.79452
## 26 4.7 tenured not minority male english 62 60.76923
## 27 4.5 tenured not minority male english 62 61.75439
## 28 4.8 tenured not minority male english 62 56.98529
## 29 4.9 tenured not minority male english 62 58.04196
## 30 4.5 tenured not minority male english 62 61.58941
## 31 4.4 tenure track not minority female english 33 80.48781
## 32 4.3 tenure track not minority female english 33 85.29412
## 33 4.1 tenure track not minority female english 33 90.24390
## 34 4.2 tenure track not minority female english 33 70.73170
## 35 3.5 tenure track not minority female english 33 82.35294
## 36 3.4 tenured not minority female english 51 60.97561
## 37 4.5 tenured not minority female english 51 95.45454
## 38 4.4 tenured not minority female english 51 61.90476
## 39 4.4 tenured not minority female english 51 94.11765
## 40 2.5 tenured not minority female english 51 80.00000
## 41 4.3 tenured not minority female english 51 100.00000
## 42 4.5 tenured not minority female english 51 100.00000
## 43 4.8 tenure track not minority female english 33 80.00000
## 44 4.8 tenure track not minority female english 33 87.87878
## 45 4.4 tenure track not minority female english 33 25.00000
## 46 4.7 tenure track not minority female english 33 59.18367
## 47 4.4 tenure track not minority female english 33 86.20689
## 48 4.7 tenure track not minority female english 33 87.50000
## 49 4.5 tenure track not minority female english 33 85.00000
## 50 4.0 teaching not minority male english 47 84.21053
## 51 4.3 teaching not minority male english 47 75.00000
## 52 4.4 teaching not minority male english 47 93.33334
## 53 4.5 teaching not minority male english 47 95.65218
## 54 5.0 teaching not minority male english 47 90.90909
## 55 4.9 teaching not minority male english 47 58.62069
## 56 4.6 teaching not minority male english 47 76.19048
## 57 5.0 teaching not minority male english 47 83.33334
## 58 4.7 teaching not minority male english 47 84.21053
## 59 5.0 teaching not minority male english 47 80.00000
## 60 3.6 tenure track minority male non-english 35 72.00000
## 61 3.7 tenure track minority male non-english 35 90.90909
## 62 4.3 tenure track minority male non-english 35 95.83334
## 63 4.1 teaching not minority male english 37 88.23529
## 64 4.2 teaching not minority male english 37 61.90476
## 65 4.7 teaching not minority male english 37 80.00000
## 66 4.7 teaching not minority male english 37 96.00000
## 67 3.5 teaching not minority male english 37 71.42857
## 68 4.1 tenured not minority male english 42 70.00000
## 69 4.2 tenured not minority male english 42 60.00000
## 70 4.0 tenured not minority male english 42 66.66666
## 71 4.0 tenured not minority male english 42 43.85965
## 72 3.9 tenured not minority male english 42 70.17544
## 73 4.4 tenured not minority male english 42 78.43137
## 74 3.8 tenured not minority male english 42 60.00000
## 75 3.5 tenured not minority male non-english 49 83.33334
## 76 4.2 tenured not minority male non-english 49 83.78378
## 77 3.5 tenured not minority male non-english 49 51.72414
## 78 3.6 tenured not minority male non-english 49 85.18519
## 79 2.9 tenure track not minority female english 37 82.14286
## 80 3.3 tenure track not minority female english 37 65.38461
## 81 3.3 tenure track not minority female english 37 80.76923
## 82 3.2 tenure track not minority female english 37 96.66666
## 83 4.6 tenured not minority male english 45 69.69697
## 84 4.2 tenured not minority male english 45 25.42373
## 85 4.3 tenured not minority male english 45 45.22613
## 86 4.4 tenured not minority male english 45 84.37500
## 87 4.1 tenured not minority male english 45 94.59460
## 88 4.6 tenured not minority male english 45 74.53416
## 89 4.4 teaching not minority female english 56 65.85366
## 90 4.8 teaching not minority female english 56 88.63636
## 91 4.3 teaching not minority female english 56 66.03773
## 92 3.6 teaching not minority female english 56 69.38776
## 93 4.3 teaching not minority female english 56 84.37500
## 94 4.0 teaching not minority male english 48 74.07407
## 95 4.2 teaching not minority male english 48 60.60606
## 96 4.1 teaching not minority male english 48 73.68421
## 97 4.1 teaching not minority male english 48 58.55856
## 98 4.4 teaching not minority male english 48 63.75839
## 99 4.3 teaching not minority male english 48 66.66666
## 100 4.4 teaching not minority male english 48 62.50000
## 101 4.4 teaching not minority male english 48 80.71429
## 102 4.9 tenured not minority female english 46 80.64516
## 103 5.0 tenured not minority female english 46 93.33334
## 104 4.4 tenured not minority female english 46 79.31035
## 105 4.8 tenured not minority female english 46 92.00000
## 106 4.9 tenured not minority female english 46 50.00000
## 107 4.3 tenured not minority female english 46 66.66666
## 108 5.0 tenured not minority female english 46 100.00000
## 109 4.7 tenured not minority female english 46 81.57895
## 110 4.5 tenured not minority female english 46 80.00000
## 111 3.5 teaching not minority female english 57 60.71429
## 112 3.9 teaching not minority female english 57 43.47826
## 113 4.0 teaching not minority female english 57 78.94736
## 114 4.0 teaching not minority female english 57 30.43478
## 115 3.7 teaching not minority female english 57 31.81818
## 116 3.4 teaching not minority female english 57 70.00000
## 117 3.3 teaching not minority female english 57 42.10526
## 118 3.8 teaching not minority female english 57 73.91304
## 119 3.9 teaching not minority female english 57 45.45454
## 120 3.4 teaching not minority female english 57 80.00000
## 121 3.7 teaching not minority female english 52 86.36364
## 122 4.1 teaching not minority female english 52 87.09677
## 123 3.7 teaching not minority female english 52 95.23810
## 124 3.5 teaching not minority female english 52 86.11111
## 125 3.5 teaching not minority female english 52 89.47369
## 126 4.4 teaching not minority female english 52 62.16216
## 127 3.4 tenure track minority female non-english 29 73.07692
## 128 4.3 tenured not minority male english 62 76.92308
## 129 3.7 tenured not minority male english 62 51.08696
## 130 4.7 tenured not minority male english 62 92.00000
## 131 3.9 tenured not minority male english 62 50.95541
## 132 3.6 tenured not minority male english 62 37.19512
## 133 4.5 tenured not minority male english 64 62.50000
## 134 4.5 tenured not minority male english 64 75.00000
## 135 4.8 tenured not minority male english 64 46.80851
## 136 4.8 tenured not minority male english 64 71.42857
## 137 4.7 tenured not minority male english 64 73.33334
## 138 4.5 tenured not minority male english 64 62.50000
## 139 4.3 tenured not minority male english 64 53.84615
## 140 4.8 tenure track not minority female english 34 76.92308
## 141 4.1 tenure track not minority female english 34 82.50000
## 142 4.4 tenured not minority male english 58 52.83019
## 143 4.3 tenured not minority male english 58 47.01987
## 144 3.6 tenured not minority male english 58 76.59574
## 145 4.5 tenured not minority male english 58 59.83607
## 146 4.3 tenured not minority male english 58 68.88889
## 147 4.4 tenured minority male non-english 52 81.25000
## 148 4.7 tenured minority male non-english 52 100.00000
## 149 4.8 tenured minority male non-english 52 75.00000
## 150 3.5 tenured minority male non-english 52 83.33334
## 151 3.8 tenured minority male non-english 52 68.75000
## 152 3.6 tenured minority male non-english 52 80.00000
## 153 4.2 tenured minority male non-english 52 64.28571
## 154 3.6 tenured not minority male english 73 70.58823
## 155 4.4 tenured not minority male english 73 76.92308
## 156 3.7 tenured not minority male english 73 76.19048
## 157 4.3 tenured not minority male english 73 76.47059
## 158 4.6 tenured not minority male english 70 35.07463
## 159 4.6 tenured not minority male english 70 10.41667
## 160 4.1 tenured not minority male english 70 53.12500
## 161 3.6 tenured not minority male english 70 34.78261
## 162 2.3 tenure track not minority female english 41 83.33334
## 163 4.3 teaching not minority male english 63 65.11628
## 164 4.4 teaching not minority male english 63 78.57143
## 165 3.6 teaching not minority male english 63 66.66666
## 166 4.4 teaching not minority male english 63 77.77778
## 167 3.9 teaching not minority male english 63 75.00000
## 168 3.8 teaching not minority male english 63 80.00000
## 169 3.4 teaching not minority male english 63 48.93617
## 170 4.9 tenured not minority male english 47 66.66666
## 171 4.1 tenured not minority male english 47 71.42857
## 172 3.2 tenured not minority male english 47 83.33334
## 173 4.2 tenured not minority male english 39 34.95935
## 174 3.9 tenured not minority male english 39 48.73418
## 175 4.9 tenured not minority male english 39 80.00000
## 176 4.7 tenured not minority male english 39 93.33334
## 177 4.4 tenured not minority male english 39 93.10345
## 178 4.2 tenure track minority female english 47 100.00000
## 179 4.0 tenure track minority female english 47 100.00000
## 180 4.4 tenure track minority female english 47 100.00000
## 181 3.9 tenure track minority female english 47 92.30769
## 182 4.4 tenure track minority female english 47 70.00000
## 183 3.0 tenure track minority female english 47 96.15385
## 184 3.5 tenure track minority female english 47 92.30769
## 185 2.8 tenure track minority female english 47 92.30769
## 186 4.6 tenure track minority female english 47 95.23810
## 187 4.3 tenure track minority female english 47 100.00000
## 188 3.4 tenure track minority female english 47 92.59259
## 189 3.0 tenure track minority female english 47 96.29630
## 190 4.2 tenure track minority female english 47 96.00000
## 191 4.3 tenured not minority male english 54 100.00000
## 192 4.1 tenured not minority male english 54 66.66666
## 193 4.6 tenured not minority male english 54 94.11765
## 194 3.9 tenured minority female english 44 54.54546
## 195 3.5 tenured minority female english 44 72.91666
## 196 4.0 tenured minority female english 44 100.00000
## 197 4.0 tenured minority female english 44 89.74359
## 198 3.9 tenured minority male english 47 74.07407
## 199 3.3 tenured minority male english 47 64.28571
## 200 4.0 tenured minority male english 47 80.76923
## 201 3.8 tenured minority male english 47 81.25000
## 202 4.2 tenured minority male english 47 81.25000
## 203 4.0 tenured minority male english 47 92.30769
## 204 3.8 tenured minority male english 47 100.00000
## 205 3.3 tenured minority male english 47 88.23529
## 206 4.1 tenured not minority male english 62 92.30769
## 207 4.7 tenured not minority male english 62 86.66666
## 208 4.4 tenured not minority male english 62 70.00000
## 209 4.8 tenured not minority male english 60 73.52941
## 210 4.8 tenured not minority male english 60 75.00000
## 211 4.6 tenured not minority male english 60 78.57143
## 212 4.6 tenured not minority male english 60 66.66666
## 213 4.8 tenured not minority male english 60 61.53846
## 214 4.4 tenured not minority male english 60 42.85714
## 215 4.7 tenured not minority male english 60 68.88889
## 216 4.7 tenured not minority male english 60 80.00000
## 217 3.3 tenure track not minority male english 37 88.23529
## 218 4.4 tenure track not minority male english 42 92.85714
## 219 4.3 tenure track not minority male english 42 100.00000
## 220 4.9 tenure track not minority male english 42 92.85714
## 221 4.4 tenure track not minority male english 42 100.00000
## 222 4.7 tenure track not minority male english 42 86.66666
## 223 4.3 tenured not minority male english 35 82.35294
## 224 4.8 tenured not minority male english 35 91.30434
## 225 4.5 tenured not minority male english 35 85.96491
## 226 4.7 tenured not minority male english 35 88.00000
## 227 3.3 teaching not minority female english 39 91.66666
## 228 4.7 teaching not minority female english 39 78.26087
## 229 4.6 teaching not minority female english 39 86.95652
## 230 3.6 teaching not minority female english 39 96.42857
## 231 4.0 tenured not minority male english 49 62.22222
## 232 4.1 tenured not minority male english 49 64.28571
## 233 4.0 tenured not minority male english 49 85.96491
## 234 4.5 tenured not minority male english 61 81.48148
## 235 4.6 tenured not minority male english 61 81.57895
## 236 4.8 tenured not minority male english 61 86.36364
## 237 4.6 tenured not minority male english 61 62.79070
## 238 4.9 tenure track not minority male english 33 96.77419
## 239 3.1 tenure track not minority male english 33 92.30769
## 240 3.7 tenure track not minority male english 33 86.66666
## 241 3.7 tenured not minority female english 58 76.47059
## 242 3.9 tenured not minority female english 56 63.15789
## 243 3.9 tenured not minority female english 56 80.00000
## 244 3.2 tenured not minority female english 56 73.91304
## 245 4.4 teaching not minority female english 50 81.48148
## 246 4.2 teaching not minority female english 50 75.00000
## 247 4.7 teaching not minority female english 50 66.66666
## 248 3.9 teaching not minority female english 50 95.83334
## 249 3.6 teaching not minority female english 50 90.47619
## 250 3.4 teaching not minority female english 50 64.28571
## 251 4.4 teaching not minority female english 50 79.31035
## 252 4.4 tenured not minority male english 52 85.07462
## 253 4.1 tenured not minority male english 52 91.01124
## 254 3.6 tenured not minority male english 52 90.24390
## 255 3.5 tenured not minority male english 52 83.60656
## 256 4.1 tenured not minority male english 52 71.75572
## 257 3.8 tenured not minority male english 52 78.07018
## 258 4.0 tenured not minority male english 52 89.26174
## 259 4.8 tenured not minority male english 52 95.65218
## 260 4.2 tenured not minority male english 52 79.59184
## 261 4.6 tenured not minority male english 52 81.48148
## 262 4.3 tenured not minority male english 52 90.00000
## 263 4.8 tenured not minority male english 52 90.00000
## 264 3.8 tenured not minority male english 52 86.95652
## 265 4.5 tenure track not minority female english 33 66.66666
## 266 4.9 tenure track not minority female english 33 100.00000
## 267 4.9 tenure track not minority female english 33 90.90909
## 268 4.8 tenure track not minority female english 33 71.42857
## 269 4.7 tenure track not minority female english 33 63.63636
## 270 4.6 tenure track not minority female english 33 100.00000
## 271 4.3 tenured not minority male english 57 89.61039
## 272 4.4 tenured not minority male english 57 87.80488
## 273 4.5 tenured not minority male english 57 81.81818
## 274 4.2 tenured not minority male english 57 80.76923
## 275 4.8 tenured not minority female english 38 70.76923
## 276 4.6 tenured not minority female english 38 69.42675
## 277 4.9 tenured not minority female english 38 79.41177
## 278 4.8 tenured not minority female english 38 76.11940
## 279 4.8 tenured not minority female english 38 76.25000
## 280 4.6 tenured not minority female english 38 74.45255
## 281 4.7 tenured not minority female english 38 84.05797
## 282 4.1 tenure track not minority female english 34 59.34066
## 283 3.8 tenure track not minority female english 34 57.50000
## 284 4.0 tenure track not minority female english 34 58.88889
## 285 4.1 tenure track not minority female english 34 55.88235
## 286 4.0 tenure track not minority female english 34 56.16438
## 287 4.1 tenure track not minority female english 34 56.81818
## 288 3.5 tenure track not minority male english 34 66.66666
## 289 4.1 tenure track not minority male english 34 80.00000
## 290 3.6 tenure track not minority male english 34 57.14286
## 291 4.0 tenure track not minority male english 32 34.27419
## 292 3.9 tenure track not minority male english 32 41.07143
## 293 3.8 tenure track not minority male english 32 39.67611
## 294 4.4 tenure track not minority male english 32 90.90909
## 295 4.7 tenure track not minority male english 32 69.90292
## 296 3.8 tenured not minority female english 42 70.96774
## 297 4.1 tenured not minority female english 42 62.19512
## 298 4.1 tenured not minority female english 43 68.62745
## 299 4.7 tenured not minority female english 43 51.42857
## 300 4.3 tenured not minority female english 43 76.47059
## 301 4.4 tenured not minority female english 43 75.67567
## 302 4.5 tenured not minority female english 43 92.85714
## 303 3.1 tenured not minority female english 43 65.41354
## 304 3.7 tenured not minority female english 43 67.32284
## 305 4.5 tenured not minority female english 43 76.92308
## 306 3.0 tenured not minority female english 43 58.86525
## 307 4.6 tenured not minority female english 43 100.00000
## 308 3.7 tenure track not minority male non-english 35 57.89474
## 309 3.6 tenure track not minority male non-english 35 52.38095
## 310 3.2 tenured not minority female english 62 81.48148
## 311 3.3 tenured not minority female english 62 56.25000
## 312 2.9 tenured not minority female english 62 73.68421
## 313 4.2 tenured not minority male english 42 52.32558
## 314 4.5 tenured not minority male english 39 75.86207
## 315 3.8 tenured not minority female english 52 72.72727
## 316 3.7 tenured not minority female english 52 71.42857
## 317 3.7 tenured not minority female english 52 70.45454
## 318 4.0 tenured not minority female english 52 75.38461
## 319 3.7 tenured not minority female english 52 50.79365
## 320 4.5 teaching not minority female english 52 78.66666
## 321 3.8 teaching not minority female english 52 81.39535
## 322 3.9 teaching not minority female english 52 73.75000
## 323 4.6 teaching not minority female english 52 86.53846
## 324 4.5 teaching not minority female english 52 70.83334
## 325 4.2 teaching not minority female english 52 75.75758
## 326 4.0 teaching not minority female english 52 67.00000
## 327 3.8 tenured not minority male english 64 81.81818
## 328 3.5 tenured not minority male english 64 50.00000
## 329 2.7 tenured not minority male english 64 81.81818
## 330 4.0 tenured not minority male english 64 45.45454
## 331 4.6 tenured not minority male english 64 50.00000
## 332 3.9 tenured not minority male english 64 100.00000
## 333 4.5 tenured not minority male english 50 93.75000
## 334 3.7 tenured not minority male english 50 90.00000
## 335 2.4 tenured not minority male english 60 71.87500
## 336 3.1 tenured not minority male english 60 70.00000
## 337 2.5 tenured not minority male english 60 62.50000
## 338 3.0 tenured not minority female english 51 70.14925
## 339 4.5 tenure track not minority male english 43 86.36364
## 340 4.8 tenure track not minority male english 43 53.57143
## 341 4.9 tenure track not minority male english 43 60.00000
## 342 4.5 tenure track not minority male english 43 73.33334
## 343 4.6 tenure track not minority male english 43 76.92308
## 344 4.5 tenure track not minority male english 43 94.44444
## 345 4.9 tenure track not minority male english 43 84.61539
## 346 4.4 tenure track not minority male english 43 60.00000
## 347 4.6 tenure track not minority male english 43 100.00000
## 348 4.6 teaching minority male english 50 70.83334
## 349 5.0 teaching minority male english 50 90.90909
## 350 4.9 teaching minority male english 50 84.00000
## 351 4.6 teaching minority male english 50 88.46154
## 352 4.8 teaching minority male english 50 86.36364
## 353 4.9 teaching minority male english 50 76.92308
## 354 4.9 teaching minority male english 50 85.00000
## 355 4.9 teaching minority male english 50 81.81818
## 356 5.0 teaching minority male english 50 95.23810
## 357 4.5 teaching minority male english 50 90.47619
## 358 3.5 tenured not minority male english 52 66.66666
## 359 3.8 tenured not minority male english 52 70.76923
## 360 3.9 tenured not minority male english 52 62.90322
## 361 3.9 tenured not minority male english 52 50.74627
## 362 4.2 tenured not minority male english 52 72.50000
## 363 4.1 tenured not minority male english 52 60.00000
## 364 4.8 tenured not minority male english 51 60.62718
## 365 4.8 tenured not minority male english 51 64.24870
## 366 4.8 tenured not minority male english 51 63.87337
## 367 4.8 tenured not minority male english 51 65.40447
## 368 4.9 tenured not minority male english 51 61.10057
## 369 4.2 tenured not minority male english 38 50.57471
## 370 4.5 tenured not minority male english 38 78.57143
## 371 3.9 tenured not minority male english 38 50.63291
## 372 4.4 tenured not minority male english 38 65.21739
## 373 4.0 tenured not minority female english 47 79.16666
## 374 3.6 tenured not minority female english 47 56.71642
## 375 3.7 tenured minority female english 43 45.63107
## 376 2.7 tenured minority female english 43 48.94737
## 377 4.5 teaching not minority female english 38 48.52941
## 378 4.4 teaching not minority female english 38 60.00000
## 379 3.9 teaching not minority female english 38 45.31250
## 380 3.6 teaching not minority female english 38 74.19355
## 381 4.4 teaching not minority female english 38 58.06452
## 382 4.4 teaching not minority female english 38 81.08108
## 383 4.7 tenured not minority male english 43 76.92308
## 384 4.5 tenured not minority male english 43 61.53846
## 385 4.1 tenured not minority male english 43 80.00000
## 386 3.7 tenured not minority male english 43 82.27848
## 387 4.3 tenured not minority male english 57 53.84615
## 388 3.5 tenured not minority male english 57 54.08163
## 389 3.7 tenured not minority male english 57 59.79382
## 390 4.0 tenured not minority female english 51 81.81818
## 391 4.0 tenured not minority female english 51 85.89744
## 392 3.1 tenured not minority female english 51 64.28571
## 393 4.5 tenured not minority female english 51 85.00000
## 394 4.8 teaching not minority male english 45 70.58823
## 395 4.2 teaching not minority male english 45 85.00000
## 396 4.9 teaching not minority male english 45 68.42105
## 397 4.8 teaching not minority male english 45 73.07692
## 398 3.5 tenured not minority male english 57 92.85714
## 399 3.6 tenured not minority male english 57 66.66666
## 400 4.4 tenured not minority male english 57 100.00000
## 401 3.4 tenured not minority male english 57 84.21053
## 402 3.9 tenured not minority male english 57 75.00000
## 403 3.8 tenured not minority male english 57 87.50000
## 404 4.8 tenured not minority male english 57 91.66666
## 405 4.6 tenured not minority male english 57 88.23529
## 406 5.0 tenured not minority male english 57 40.00000
## 407 3.8 tenured not minority male english 57 93.75000
## 408 4.2 tenured not minority male english 57 70.58823
## 409 3.3 teaching not minority female english 47 76.19048
## 410 4.7 teaching not minority female english 47 88.23529
## 411 4.6 teaching not minority female english 47 100.00000
## 412 4.6 teaching not minority female english 47 94.11765
## 413 4.0 teaching not minority female english 47 88.23529
## 414 4.2 tenured minority female english 54 100.00000
## 415 4.9 tenured minority female english 54 93.75000
## 416 4.5 tenured minority female english 54 80.76923
## 417 4.8 tenured minority female english 54 77.77778
## 418 3.8 tenured minority female english 54 80.00000
## 419 4.8 teaching not minority male english 58 94.11765
## 420 5.0 teaching not minority male english 58 100.00000
## 421 5.0 teaching not minority male english 58 85.71429
## 422 4.9 teaching not minority male english 58 85.00000
## 423 4.6 teaching not minority male english 58 95.00000
## 424 5.0 teaching not minority male english 58 84.61539
## 425 4.8 teaching not minority male english 58 87.50000
## 426 4.9 teaching not minority male english 58 94.11765
## 427 4.9 tenured not minority male english 42 83.33334
## 428 3.9 tenured not minority male english 42 91.66666
## 429 3.9 tenured not minority male english 42 85.00000
## 430 4.5 tenure track not minority male english 33 70.83334
## 431 4.5 tenure track not minority male english 33 43.22581
## 432 3.3 tenured not minority male english 62 28.94737
## 433 3.1 tenured not minority male english 62 40.00000
## 434 2.8 tenured not minority male english 62 40.93960
## 435 3.1 tenured not minority male english 62 35.76642
## 436 4.2 tenured not minority male english 62 44.82759
## 437 3.4 tenured not minority male english 62 50.90909
## 438 3.0 tenured not minority male english 62 49.26471
## 439 3.3 tenure track minority female english 35 62.50000
## 440 3.6 tenure track minority female english 35 33.33333
## 441 3.7 tenure track minority female english 35 39.81482
## 442 3.6 tenured not minority male english 61 69.23077
## 443 4.3 tenured not minority male english 61 86.66666
## 444 4.1 tenured not minority female english 52 54.95496
## 445 4.9 tenured not minority female english 52 82.35294
## 446 4.8 tenured not minority female english 52 100.00000
## 447 3.7 tenure track not minority female non-english 60 85.18519
## 448 3.9 tenure track not minority female non-english 60 94.73684
## 449 4.5 tenure track not minority female non-english 60 84.61539
## 450 3.6 tenure track not minority female non-english 60 94.73684
## 451 4.4 tenure track not minority female non-english 60 50.00000
## 452 3.4 tenure track not minority female non-english 60 35.00000
## 453 4.4 tenure track not minority female non-english 60 88.88889
## 454 4.5 tenure track not minority male english 32 74.24242
## 455 4.5 tenure track not minority male english 32 87.40157
## 456 4.5 tenure track not minority male english 32 72.94118
## 457 4.6 tenure track not minority male english 32 75.24753
## 458 4.1 tenure track not minority male english 32 42.85714
## 459 4.5 tenure track not minority male english 32 60.46511
## 460 3.5 tenure track minority female non-english 42 57.14286
## 461 4.4 tenure track minority female non-english 42 77.61194
## 462 4.4 tenure track minority female non-english 42 81.81818
## 463 4.1 tenure track minority female non-english 42 80.00000
## cls_did_eval cls_students cls_level cls_profs cls_credits bty_f1lower
## 1 24 43 upper single multi credit 5
## 2 86 125 upper single multi credit 5
## 3 76 125 upper single multi credit 5
## 4 77 123 upper single multi credit 5
## 5 17 20 upper multiple multi credit 4
## 6 35 40 upper multiple multi credit 4
## 7 39 44 upper multiple multi credit 4
## 8 55 55 upper single multi credit 5
## 9 111 195 upper single multi credit 5
## 10 40 46 upper single multi credit 2
## 11 24 27 upper single multi credit 2
## 12 24 25 upper multiple multi credit 2
## 13 17 20 upper single multi credit 2
## 14 14 25 upper single multi credit 2
## 15 37 42 upper single multi credit 2
## 16 18 20 upper multiple multi credit 2
## 17 15 18 upper multiple multi credit 2
## 18 42 48 upper multiple multi credit 7
## 19 40 44 upper multiple multi credit 7
## 20 38 48 upper multiple multi credit 7
## 21 40 45 upper multiple multi credit 7
## 22 52 59 upper multiple multi credit 7
## 23 49 87 upper single multi credit 7
## 24 182 282 upper multiple multi credit 6
## 25 160 292 upper multiple multi credit 6
## 26 79 130 upper multiple multi credit 6
## 27 176 285 upper single multi credit 6
## 28 155 272 upper multiple multi credit 6
## 29 166 286 upper multiple multi credit 6
## 30 186 302 upper single multi credit 6
## 31 33 41 upper single multi credit 4
## 32 29 34 upper single multi credit 4
## 33 37 41 upper single multi credit 4
## 34 29 41 upper single multi credit 4
## 35 28 34 upper single multi credit 4
## 36 25 41 upper multiple multi credit 4
## 37 21 22 upper multiple multi credit 4
## 38 13 21 upper multiple multi credit 4
## 39 16 17 upper multiple multi credit 4
## 40 24 30 lower multiple multi credit 4
## 41 23 23 upper multiple multi credit 4
## 42 20 20 upper multiple multi credit 4
## 43 48 60 upper multiple multi credit 3
## 44 29 33 upper single multi credit 3
## 45 11 44 upper multiple multi credit 3
## 46 29 49 upper single multi credit 3
## 47 25 29 upper single multi credit 3
## 48 42 48 upper multiple multi credit 3
## 49 34 40 upper multiple multi credit 3
## 50 16 19 upper single multi credit 5
## 51 12 16 upper multiple multi credit 5
## 52 14 15 upper single multi credit 5
## 53 22 23 upper single multi credit 5
## 54 10 11 lower multiple multi credit 5
## 55 17 29 lower multiple multi credit 5
## 56 16 21 upper multiple multi credit 5
## 57 15 18 lower multiple multi credit 5
## 58 16 19 upper single multi credit 5
## 59 16 20 lower multiple multi credit 5
## 60 18 25 upper single multi credit 5
## 61 30 33 upper single multi credit 5
## 62 23 24 upper single multi credit 5
## 63 30 34 upper multiple multi credit 4
## 64 13 21 upper single multi credit 4
## 65 24 30 upper multiple multi credit 4
## 66 24 25 upper multiple multi credit 4
## 67 25 35 upper multiple multi credit 4
## 68 28 40 upper multiple multi credit 4
## 69 18 30 upper multiple multi credit 4
## 70 28 42 upper multiple multi credit 4
## 71 25 57 upper single multi credit 4
## 72 40 57 upper single multi credit 4
## 73 40 51 upper single multi credit 4
## 74 18 30 upper multiple multi credit 4
## 75 30 36 upper multiple multi credit 3
## 76 31 37 upper single multi credit 3
## 77 15 29 upper multiple multi credit 3
## 78 23 27 upper single multi credit 3
## 79 23 28 upper single multi credit 6
## 80 34 52 upper multiple multi credit 6
## 81 21 26 upper single multi credit 6
## 82 29 30 upper single multi credit 6
## 83 23 33 upper single multi credit 2
## 84 45 177 lower single multi credit 2
## 85 90 199 lower single multi credit 2
## 86 27 32 upper single multi credit 2
## 87 35 37 upper single multi credit 2
## 88 120 161 lower single multi credit 2
## 89 27 41 upper single multi credit 3
## 90 39 44 upper single multi credit 3
## 91 35 53 upper multiple multi credit 3
## 92 34 49 upper multiple multi credit 3
## 93 27 32 upper single multi credit 3
## 94 100 135 lower multiple multi credit 3
## 95 20 33 upper multiple multi credit 3
## 96 14 19 upper multiple multi credit 3
## 97 65 111 lower multiple multi credit 3
## 98 95 149 lower multiple multi credit 3
## 99 18 27 upper multiple multi credit 3
## 100 85 136 lower multiple multi credit 3
## 101 113 140 lower multiple multi credit 3
## 102 25 31 upper multiple multi credit 4
## 103 14 15 lower multiple multi credit 4
## 104 23 29 upper multiple multi credit 4
## 105 23 25 upper multiple multi credit 4
## 106 9 18 upper multiple multi credit 4
## 107 30 45 upper multiple multi credit 4
## 108 15 15 lower multiple multi credit 4
## 109 31 38 upper multiple multi credit 4
## 110 12 15 lower multiple multi credit 4
## 111 17 28 upper multiple multi credit 5
## 112 10 23 upper multiple multi credit 5
## 113 15 19 upper multiple multi credit 5
## 114 7 23 upper multiple multi credit 5
## 115 7 22 upper multiple multi credit 5
## 116 14 20 upper multiple multi credit 5
## 117 8 19 upper multiple multi credit 5
## 118 17 23 upper multiple multi credit 5
## 119 10 22 upper multiple multi credit 5
## 120 12 15 upper multiple multi credit 5
## 121 19 22 upper single multi credit 6
## 122 27 31 upper multiple multi credit 6
## 123 20 21 upper multiple multi credit 6
## 124 31 36 upper multiple multi credit 6
## 125 17 19 upper multiple one credit 6
## 126 23 37 upper single multi credit 6
## 127 19 26 upper single multi credit 3
## 128 30 39 upper single multi credit 4
## 129 94 184 lower single multi credit 4
## 130 46 50 upper single multi credit 4
## 131 80 157 lower single multi credit 4
## 132 61 164 lower single multi credit 4
## 133 15 24 upper multiple multi credit 5
## 134 51 68 upper multiple multi credit 5
## 135 22 47 upper multiple multi credit 5
## 136 10 14 upper multiple multi credit 5
## 137 11 15 upper multiple multi credit 5
## 138 15 24 upper multiple multi credit 5
## 139 21 39 upper multiple multi credit 5
## 140 20 26 upper multiple multi credit 8
## 141 33 40 upper multiple multi credit 8
## 142 84 159 upper single multi credit 4
## 143 71 151 upper single multi credit 4
## 144 36 47 lower single multi credit 4
## 145 73 122 upper single multi credit 4
## 146 31 45 lower single multi credit 4
## 147 13 16 upper single multi credit 4
## 148 23 23 upper single multi credit 4
## 149 12 16 upper single multi credit 4
## 150 15 18 upper single multi credit 4
## 151 11 16 upper single multi credit 4
## 152 12 15 upper single multi credit 4
## 153 18 28 upper multiple multi credit 4
## 154 12 17 upper single multi credit 1
## 155 10 13 upper single multi credit 1
## 156 16 21 upper multiple multi credit 1
## 157 13 17 upper single multi credit 1
## 158 47 134 upper single multi credit 5
## 159 5 48 upper single multi credit 5
## 160 34 64 upper single multi credit 5
## 161 24 69 upper single multi credit 5
## 162 10 12 upper single multi credit 3
## 163 28 43 upper single multi credit 5
## 164 11 14 upper multiple multi credit 5
## 165 10 15 upper single multi credit 5
## 166 14 18 upper multiple multi credit 5
## 167 12 16 upper multiple multi credit 5
## 168 8 10 upper multiple multi credit 5
## 169 23 47 upper multiple multi credit 5
## 170 10 15 upper multiple multi credit 1
## 171 10 14 upper multiple multi credit 1
## 172 10 12 upper single multi credit 1
## 173 86 246 lower multiple multi credit 5
## 174 154 316 lower multiple multi credit 5
## 175 12 15 upper multiple multi credit 5
## 176 14 15 upper multiple multi credit 5
## 177 27 29 upper single multi credit 5
## 178 21 21 lower single multi credit 2
## 179 8 8 upper multiple multi credit 2
## 180 16 16 lower single one credit 2
## 181 24 26 lower single multi credit 2
## 182 7 10 upper multiple multi credit 2
## 183 25 26 lower single multi credit 2
## 184 24 26 lower single multi credit 2
## 185 24 26 lower single multi credit 2
## 186 20 21 lower single one credit 2
## 187 12 12 lower single multi credit 2
## 188 25 27 lower single multi credit 2
## 189 26 27 lower single multi credit 2
## 190 24 25 lower single multi credit 2
## 191 15 15 upper single multi credit 1
## 192 10 15 upper single multi credit 1
## 193 16 17 upper single multi credit 1
## 194 30 55 upper multiple multi credit 6
## 195 35 48 upper single multi credit 6
## 196 21 21 upper multiple multi credit 6
## 197 35 39 upper multiple multi credit 6
## 198 20 27 upper single multi credit 2
## 199 9 14 upper single multi credit 2
## 200 21 26 upper single multi credit 2
## 201 13 16 upper multiple multi credit 2
## 202 13 16 upper multiple multi credit 2
## 203 12 13 upper multiple multi credit 2
## 204 14 14 upper single multi credit 2
## 205 15 17 upper multiple multi credit 2
## 206 12 13 upper multiple multi credit 3
## 207 13 15 upper single multi credit 3
## 208 7 10 upper multiple multi credit 3
## 209 25 34 upper multiple multi credit 4
## 210 12 16 upper single multi credit 4
## 211 11 14 upper single multi credit 4
## 212 8 12 upper single multi credit 4
## 213 24 39 upper single multi credit 4
## 214 15 35 upper single multi credit 4
## 215 31 45 upper multiple multi credit 4
## 216 36 45 lower multiple multi credit 4
## 217 15 17 upper single multi credit 4
## 218 13 14 upper multiple multi credit 3
## 219 14 14 upper multiple multi credit 3
## 220 13 14 upper multiple multi credit 3
## 221 12 12 upper multiple multi credit 3
## 222 13 15 upper multiple multi credit 3
## 223 42 51 upper single multi credit 4
## 224 21 23 lower multiple multi credit 4
## 225 49 57 upper single multi credit 4
## 226 44 50 lower multiple multi credit 4
## 227 22 24 lower single multi credit 8
## 228 18 23 upper multiple multi credit 8
## 229 20 23 upper multiple multi credit 8
## 230 27 28 lower single multi credit 8
## 231 28 45 upper single multi credit 6
## 232 27 42 upper single multi credit 6
## 233 49 57 upper single multi credit 6
## 234 22 27 lower single multi credit 5
## 235 31 38 upper multiple multi credit 5
## 236 19 22 lower single multi credit 5
## 237 27 43 upper multiple multi credit 5
## 238 30 31 upper single multi credit 7
## 239 12 13 upper single multi credit 7
## 240 13 15 upper single multi credit 7
## 241 26 34 upper single multi credit 3
## 242 12 19 upper single multi credit 2
## 243 16 20 upper single multi credit 2
## 244 17 23 upper single multi credit 2
## 245 22 27 lower single multi credit 2
## 246 24 32 lower single one credit 2
## 247 14 21 lower single one credit 2
## 248 23 24 upper multiple multi credit 2
## 249 19 21 upper multiple multi credit 2
## 250 18 28 upper multiple multi credit 2
## 251 23 29 upper multiple multi credit 2
## 252 57 67 upper multiple multi credit 4
## 253 81 89 upper multiple multi credit 4
## 254 74 82 upper multiple multi credit 4
## 255 102 122 upper multiple multi credit 4
## 256 94 131 upper multiple multi credit 4
## 257 89 114 upper multiple multi credit 4
## 258 133 149 upper multiple multi credit 4
## 259 22 23 upper single multi credit 4
## 260 78 98 upper multiple multi credit 4
## 261 22 27 upper single multi credit 4
## 262 27 30 upper single multi credit 4
## 263 27 30 upper single multi credit 4
## 264 60 69 upper multiple multi credit 4
## 265 10 15 upper multiple multi credit 3
## 266 10 10 upper multiple multi credit 3
## 267 10 11 upper multiple multi credit 3
## 268 10 14 upper multiple multi credit 3
## 269 7 11 upper multiple multi credit 3
## 270 14 14 upper multiple multi credit 3
## 271 69 77 upper multiple multi credit 5
## 272 36 41 upper single multi credit 5
## 273 72 88 upper multiple multi credit 5
## 274 63 78 upper multiple multi credit 5
## 275 46 65 upper single multi credit 6
## 276 109 157 lower multiple multi credit 6
## 277 54 68 upper single multi credit 6
## 278 51 67 upper single multi credit 6
## 279 61 80 upper single multi credit 6
## 280 102 137 lower multiple multi credit 6
## 281 58 69 upper multiple multi credit 6
## 282 54 91 lower multiple multi credit 2
## 283 46 80 lower multiple multi credit 2
## 284 53 90 lower multiple multi credit 2
## 285 19 34 upper multiple multi credit 2
## 286 41 73 upper multiple multi credit 2
## 287 25 44 upper multiple multi credit 2
## 288 24 36 upper multiple multi credit 6
## 289 16 20 upper single multi credit 6
## 290 20 35 lower multiple multi credit 6
## 291 85 248 lower multiple multi credit 3
## 292 69 168 lower multiple multi credit 3
## 293 98 247 lower multiple multi credit 3
## 294 20 22 upper single multi credit 3
## 295 72 103 upper multiple multi credit 3
## 296 44 62 lower multiple multi credit 5
## 297 51 82 upper multiple multi credit 5
## 298 35 51 lower multiple multi credit 2
## 299 18 35 upper multiple multi credit 2
## 300 26 34 lower multiple multi credit 2
## 301 28 37 lower multiple multi credit 2
## 302 13 14 lower multiple multi credit 2
## 303 174 266 lower multiple multi credit 2
## 304 171 254 lower multiple multi credit 2
## 305 10 13 upper multiple multi credit 2
## 306 166 282 lower multiple multi credit 2
## 307 17 17 upper multiple multi credit 2
## 308 11 19 upper single multi credit 4
## 309 22 42 lower multiple multi credit 4
## 310 22 27 upper multiple multi credit 1
## 311 9 16 upper multiple multi credit 1
## 312 14 19 upper multiple multi credit 1
## 313 45 86 upper multiple multi credit 3
## 314 22 29 upper multiple multi credit 5
## 315 64 88 upper multiple multi credit 5
## 316 70 98 upper multiple multi credit 5
## 317 31 44 upper multiple multi credit 6
## 318 49 65 upper multiple multi credit 6
## 319 32 63 upper multiple multi credit 6
## 320 59 75 upper multiple multi credit 2
## 321 35 43 upper multiple multi credit 2
## 322 59 80 upper multiple multi credit 2
## 323 45 52 upper multiple multi credit 2
## 324 34 48 upper multiple multi credit 2
## 325 50 66 upper multiple multi credit 2
## 326 67 100 upper multiple multi credit 2
## 327 9 11 upper multiple multi credit 2
## 328 8 16 upper multiple multi credit 2
## 329 18 22 upper multiple multi credit 2
## 330 5 11 upper multiple multi credit 2
## 331 5 10 upper multiple multi credit 2
## 332 16 16 upper multiple multi credit 2
## 333 15 16 upper multiple multi credit 6
## 334 9 10 upper multiple multi credit 6
## 335 23 32 upper multiple multi credit 1
## 336 7 10 upper multiple multi credit 1
## 337 10 16 upper multiple multi credit 1
## 338 47 67 upper multiple multi credit 4
## 339 19 22 lower multiple multi credit 3
## 340 15 28 lower multiple one credit 3
## 341 18 30 lower multiple one credit 3
## 342 11 15 lower multiple multi credit 3
## 343 10 13 lower multiple multi credit 3
## 344 17 18 lower multiple one credit 3
## 345 22 26 lower multiple one credit 3
## 346 18 30 lower multiple one credit 3
## 347 14 14 lower multiple multi credit 3
## 348 17 24 lower multiple one credit 1
## 349 20 22 lower multiple one credit 1
## 350 21 25 lower multiple one credit 1
## 351 23 26 lower multiple one credit 1
## 352 19 22 lower multiple one credit 1
## 353 20 26 lower multiple one credit 1
## 354 17 20 lower multiple one credit 1
## 355 18 22 lower multiple one credit 1
## 356 20 21 lower multiple one credit 1
## 357 19 21 lower multiple one credit 1
## 358 46 69 upper multiple multi credit 7
## 359 46 65 upper multiple multi credit 7
## 360 39 62 upper multiple multi credit 7
## 361 34 67 upper multiple multi credit 7
## 362 29 40 upper multiple multi credit 7
## 363 27 45 upper multiple multi credit 7
## 364 348 574 lower multiple multi credit 6
## 365 372 579 lower multiple multi credit 6
## 366 343 537 lower multiple multi credit 6
## 367 380 581 lower multiple multi credit 6
## 368 322 527 lower multiple multi credit 6
## 369 44 87 lower multiple multi credit 3
## 370 66 84 lower multiple multi credit 3
## 371 40 79 lower multiple multi credit 3
## 372 60 92 lower multiple multi credit 3
## 373 19 24 lower single multi credit 5
## 374 38 67 lower single multi credit 5
## 375 47 103 lower multiple multi credit 5
## 376 93 190 lower multiple multi credit 5
## 377 33 68 lower multiple multi credit 3
## 378 36 60 lower single multi credit 3
## 379 29 64 lower single multi credit 3
## 380 23 31 lower single multi credit 3
## 381 36 62 lower multiple multi credit 3
## 382 30 37 lower multiple multi credit 3
## 383 10 13 lower multiple multi credit 4
## 384 8 13 lower multiple multi credit 4
## 385 12 15 upper single multi credit 4
## 386 65 79 upper single multi credit 4
## 387 7 13 upper multiple multi credit 3
## 388 53 98 upper multiple multi credit 3
## 389 58 97 upper multiple multi credit 3
## 390 9 11 upper multiple multi credit 5
## 391 67 78 upper multiple multi credit 5
## 392 36 56 upper multiple multi credit 5
## 393 17 20 upper multiple multi credit 5
## 394 12 17 lower single one credit 1
## 395 17 20 lower multiple one credit 1
## 396 13 19 lower multiple multi credit 1
## 397 19 26 lower multiple one credit 1
## 398 13 14 lower multiple multi credit 2
## 399 12 18 lower single multi credit 2
## 400 12 12 lower single multi credit 2
## 401 16 19 lower multiple multi credit 2
## 402 12 16 lower multiple multi credit 2
## 403 14 16 lower multiple multi credit 2
## 404 11 12 lower multiple multi credit 2
## 405 15 17 lower multiple multi credit 2
## 406 6 15 upper multiple multi credit 2
## 407 15 16 lower multiple multi credit 2
## 408 12 17 lower multiple multi credit 2
## 409 16 21 lower multiple multi credit 8
## 410 15 17 lower multiple one credit 8
## 411 10 10 lower multiple one credit 8
## 412 16 17 lower multiple one credit 8
## 413 15 17 lower multiple multi credit 8
## 414 18 18 lower single multi credit 8
## 415 15 16 lower single multi credit 8
## 416 21 26 lower single multi credit 8
## 417 14 18 lower single multi credit 8
## 418 16 20 lower single multi credit 8
## 419 16 17 lower single multi credit 8
## 420 21 21 lower single multi credit 8
## 421 18 21 lower single multi credit 8
## 422 17 20 lower single multi credit 8
## 423 19 20 lower single multi credit 8
## 424 11 13 lower single multi credit 8
## 425 14 16 lower single multi credit 8
## 426 16 17 lower multiple multi credit 8
## 427 15 18 lower multiple multi credit 8
## 428 22 24 lower multiple multi credit 8
## 429 17 20 upper multiple multi credit 8
## 430 85 120 lower multiple multi credit 6
## 431 67 155 lower multiple multi credit 6
## 432 11 38 lower multiple multi credit 1
## 433 28 70 lower multiple multi credit 1
## 434 61 149 lower multiple multi credit 1
## 435 49 137 lower multiple multi credit 1
## 436 13 29 upper multiple multi credit 1
## 437 28 55 lower multiple multi credit 1
## 438 67 136 lower multiple multi credit 1
## 439 60 96 lower multiple multi credit 7
## 440 20 60 lower multiple multi credit 7
## 441 43 108 lower multiple multi credit 7
## 442 27 39 lower multiple multi credit 3
## 443 13 15 lower multiple multi credit 3
## 444 61 111 lower multiple multi credit 4
## 445 14 17 lower multiple multi credit 4
## 446 19 19 lower multiple multi credit 4
## 447 23 27 upper multiple multi credit 4
## 448 18 19 upper multiple multi credit 4
## 449 11 13 upper multiple multi credit 4
## 450 18 19 upper multiple multi credit 4
## 451 11 22 upper multiple multi credit 4
## 452 7 20 upper multiple multi credit 4
## 453 24 27 upper multiple multi credit 4
## 454 98 132 lower multiple multi credit 6
## 455 111 127 lower multiple multi credit 6
## 456 62 85 upper multiple multi credit 6
## 457 76 101 lower multiple multi credit 6
## 458 9 21 lower multiple multi credit 6
## 459 52 86 upper multiple multi credit 6
## 460 48 84 upper multiple multi credit 3
## 461 52 67 upper multiple multi credit 3
## 462 54 66 upper multiple multi credit 3
## 463 28 35 lower multiple one credit 3
## bty_f1upper bty_f2upper bty_m1lower bty_m1upper bty_m2upper bty_avg
## 1 7 6 2 4 6 5.000
## 2 7 6 2 4 6 5.000
## 3 7 6 2 4 6 5.000
## 4 7 6 2 4 6 5.000
## 5 4 2 2 3 3 3.000
## 6 4 2 2 3 3 3.000
## 7 4 2 2 3 3 3.000
## 8 2 5 2 3 3 3.333
## 9 2 5 2 3 3 3.333
## 10 5 4 3 3 2 3.167
## 11 5 4 3 3 2 3.167
## 12 5 4 3 3 2 3.167
## 13 5 4 3 3 2 3.167
## 14 5 4 3 3 2 3.167
## 15 5 4 3 3 2 3.167
## 16 5 4 3 3 2 3.167
## 17 5 4 3 3 2 3.167
## 18 9 9 7 6 6 7.333
## 19 9 9 7 6 6 7.333
## 20 9 9 7 6 6 7.333
## 21 9 9 7 6 6 7.333
## 22 9 9 7 6 6 7.333
## 23 9 9 7 6 6 7.333
## 24 6 5 5 5 6 5.500
## 25 6 5 5 5 6 5.500
## 26 6 5 5 5 6 5.500
## 27 6 5 5 5 6 5.500
## 28 6 5 5 5 6 5.500
## 29 6 5 5 5 6 5.500
## 30 6 5 5 5 6 5.500
## 31 4 5 4 4 4 4.167
## 32 4 5 4 4 4 4.167
## 33 4 5 4 4 4 4.167
## 34 4 5 4 4 4 4.167
## 35 4 5 4 4 4 4.167
## 36 6 6 2 3 3 4.000
## 37 6 6 2 3 3 4.000
## 38 6 6 2 3 3 4.000
## 39 6 6 2 3 3 4.000
## 40 6 6 2 3 3 4.000
## 41 6 6 2 3 3 4.000
## 42 6 6 2 3 3 4.000
## 43 7 5 5 3 5 4.667
## 44 7 5 5 3 5 4.667
## 45 7 5 5 3 5 4.667
## 46 7 5 5 3 5 4.667
## 47 7 5 5 3 5 4.667
## 48 7 5 5 3 5 4.667
## 49 7 5 5 3 5 4.667
## 50 7 6 3 6 6 5.500
## 51 7 6 3 6 6 5.500
## 52 7 6 3 6 6 5.500
## 53 7 6 3 6 6 5.500
## 54 7 6 3 6 6 5.500
## 55 7 6 3 6 6 5.500
## 56 7 6 3 6 6 5.500
## 57 7 6 3 6 6 5.500
## 58 7 6 3 6 6 5.500
## 59 7 6 3 6 6 5.500
## 60 7 4 2 4 7 4.833
## 61 7 4 2 4 7 4.833
## 62 7 4 2 4 7 4.833
## 63 5 5 3 5 4 4.333
## 64 5 5 3 5 4 4.333
## 65 5 5 3 5 4 4.333
## 66 5 5 3 5 4 4.333
## 67 5 5 3 5 4 4.333
## 68 7 5 4 4 5 4.833
## 69 7 5 4 4 5 4.833
## 70 7 5 4 4 5 4.833
## 71 7 5 4 4 5 4.833
## 72 7 5 4 4 5 4.833
## 73 7 5 4 4 5 4.833
## 74 7 5 4 4 5 4.833
## 75 3 5 1 7 5 4.000
## 76 3 5 1 7 5 4.000
## 77 3 5 1 7 5 4.000
## 78 3 5 1 7 5 4.000
## 79 7 7 5 4 4 5.500
## 80 7 7 5 4 4 5.500
## 81 7 7 5 4 4 5.500
## 82 7 7 5 4 4 5.500
## 83 4 3 5 4 7 4.167
## 84 4 3 5 4 7 4.167
## 85 4 3 5 4 7 4.167
## 86 4 3 5 4 7 4.167
## 87 4 3 5 4 7 4.167
## 88 4 3 5 4 7 4.167
## 89 4 1 2 2 3 2.500
## 90 4 1 2 2 3 2.500
## 91 4 1 2 2 3 2.500
## 92 4 1 2 2 3 2.500
## 93 4 1 2 2 3 2.500
## 94 5 6 4 4 4 4.333
## 95 5 6 4 4 4 4.333
## 96 5 6 4 4 4 4.333
## 97 5 6 4 4 4 4.333
## 98 5 6 4 4 4 4.333
## 99 5 6 4 4 4 4.333
## 100 5 6 4 4 4 4.333
## 101 5 6 4 4 4 4.333
## 102 4 5 2 6 5 4.333
## 103 4 5 2 6 5 4.333
## 104 4 5 2 6 5 4.333
## 105 4 5 2 6 5 4.333
## 106 4 5 2 6 5 4.333
## 107 4 5 2 6 5 4.333
## 108 4 5 2 6 5 4.333
## 109 4 5 2 6 5 4.333
## 110 4 5 2 6 5 4.333
## 111 4 4 5 2 6 4.333
## 112 4 4 5 2 6 4.333
## 113 4 4 5 2 6 4.333
## 114 4 4 5 2 6 4.333
## 115 4 4 5 2 6 4.333
## 116 4 4 5 2 6 4.333
## 117 4 4 5 2 6 4.333
## 118 4 4 5 2 6 4.333
## 119 4 4 5 2 6 4.333
## 120 4 4 5 2 6 4.333
## 121 6 4 2 4 7 4.833
## 122 6 4 2 4 7 4.833
## 123 6 4 2 4 7 4.833
## 124 6 4 2 4 7 4.833
## 125 6 4 2 4 7 4.833
## 126 6 4 2 4 7 4.833
## 127 3 4 2 3 2 2.833
## 128 3 4 1 2 4 3.000
## 129 3 4 1 2 4 3.000
## 130 3 4 1 2 4 3.000
## 131 3 4 1 2 4 3.000
## 132 3 4 1 2 4 3.000
## 133 4 5 3 3 5 4.167
## 134 4 5 3 3 5 4.167
## 135 4 5 3 3 5 4.167
## 136 4 5 3 3 5 4.167
## 137 4 5 3 3 5 4.167
## 138 4 5 3 3 5 4.167
## 139 4 5 3 3 5 4.167
## 140 9 8 6 8 8 7.833
## 141 9 8 6 8 8 7.833
## 142 4 5 2 4 4 3.833
## 143 4 5 2 4 4 3.833
## 144 4 5 2 4 4 3.833
## 145 4 5 2 4 4 3.833
## 146 4 5 2 4 4 3.833
## 147 5 7 5 4 4 4.833
## 148 5 7 5 4 4 4.833
## 149 5 7 5 4 4 4.833
## 150 5 7 5 4 4 4.833
## 151 5 7 5 4 4 4.833
## 152 5 7 5 4 4 4.833
## 153 5 7 5 4 4 4.833
## 154 3 6 2 1 5 3.000
## 155 3 6 2 1 5 3.000
## 156 3 6 2 1 5 3.000
## 157 3 6 2 1 5 3.000
## 158 3 2 3 3 2 3.000
## 159 3 2 3 3 2 3.000
## 160 3 2 3 3 2 3.000
## 161 3 2 3 3 2 3.000
## 162 6 7 4 4 7 5.167
## 163 4 6 4 2 5 4.333
## 164 4 6 4 2 5 4.333
## 165 4 6 4 2 5 4.333
## 166 4 6 4 2 5 4.333
## 167 4 6 4 2 5 4.333
## 168 4 6 4 2 5 4.333
## 169 4 6 4 2 5 4.333
## 170 4 3 2 3 3 2.667
## 171 4 3 2 3 3 2.667
## 172 4 3 2 3 3 2.667
## 173 6 6 6 5 5 5.500
## 174 6 6 6 5 5 5.500
## 175 6 6 6 5 5 5.500
## 176 6 6 6 5 5 5.500
## 177 6 6 6 5 5 5.500
## 178 6 6 3 5 4 4.333
## 179 6 6 3 5 4 4.333
## 180 6 6 3 5 4 4.333
## 181 6 6 3 5 4 4.333
## 182 6 6 3 5 4 4.333
## 183 6 6 3 5 4 4.333
## 184 6 6 3 5 4 4.333
## 185 6 6 3 5 4 4.333
## 186 6 6 3 5 4 4.333
## 187 6 6 3 5 4 4.333
## 188 6 6 3 5 4 4.333
## 189 6 6 3 5 4 4.333
## 190 6 6 3 5 4 4.333
## 191 2 4 1 2 4 2.333
## 192 2 4 1 2 4 2.333
## 193 2 4 1 2 4 2.333
## 194 8 8 5 7 5 6.500
## 195 8 8 5 7 5 6.500
## 196 8 8 5 7 5 6.500
## 197 8 8 5 7 5 6.500
## 198 2 2 2 2 4 2.333
## 199 2 2 2 2 4 2.333
## 200 2 2 2 2 4 2.333
## 201 2 2 2 2 4 2.333
## 202 2 2 2 2 4 2.333
## 203 2 2 2 2 4 2.333
## 204 2 2 2 2 4 2.333
## 205 2 2 2 2 4 2.333
## 206 2 5 3 2 3 3.000
## 207 2 5 3 2 3 3.000
## 208 2 5 3 2 3 3.000
## 209 4 6 2 2 4 3.667
## 210 4 6 2 2 4 3.667
## 211 4 6 2 2 4 3.667
## 212 4 6 2 2 4 3.667
## 213 4 6 2 2 4 3.667
## 214 4 6 2 2 4 3.667
## 215 4 6 2 2 4 3.667
## 216 4 6 2 2 4 3.667
## 217 8 7 5 5 8 6.167
## 218 5 3 3 6 4 4.000
## 219 5 3 3 6 4 4.000
## 220 5 3 3 6 4 4.000
## 221 5 3 3 6 4 4.000
## 222 5 3 3 6 4 4.000
## 223 7 2 6 4 6 4.833
## 224 7 2 6 4 6 4.833
## 225 7 2 6 4 6 4.833
## 226 7 2 6 4 6 4.833
## 227 8 8 7 9 9 8.167
## 228 8 8 7 9 9 8.167
## 229 8 8 7 9 9 8.167
## 230 8 8 7 9 9 8.167
## 231 6 7 6 9 5 6.500
## 232 6 7 6 9 5 6.500
## 233 6 7 6 9 5 6.500
## 234 5 4 4 5 6 4.833
## 235 5 4 4 5 6 4.833
## 236 5 4 4 5 6 4.833
## 237 5 4 4 5 6 4.833
## 238 8 7 6 7 7 7.000
## 239 8 7 6 7 7 7.000
## 240 8 7 6 7 7 7.000
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## 301 3 5 3 3 4 3.333
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## 311 5 5 1 4 5 3.500
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## 339 4 4 2 4 4 3.500
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## 342 4 4 2 4 4 3.500
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## 351 5 4 1 4 5 3.333
## 352 5 4 1 4 5 3.333
## 353 5 4 1 4 5 3.333
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## 355 5 4 1 4 5 3.333
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## 362 6 6 5 5 6 5.833
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## 365 7 8 6 6 4 6.167
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## 382 4 2 1 3 2 2.500
## 383 4 5 4 4 5 4.333
## 384 4 5 4 4 5 4.333
## 385 4 5 4 4 5 4.333
## 386 4 5 4 4 5 4.333
## 387 4 3 2 3 3 3.000
## 388 4 3 2 3 3 3.000
## 389 4 3 2 3 3 3.000
## 390 8 5 6 8 6 6.333
## 391 8 5 6 8 6 6.333
## 392 8 5 6 8 6 6.333
## 393 8 5 6 8 6 6.333
## 394 4 2 5 4 4 3.333
## 395 4 2 5 4 4 3.333
## 396 4 2 5 4 4 3.333
## 397 4 2 5 4 4 3.333
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## 399 3 3 2 1 6 2.833
## 400 3 3 2 1 6 2.833
## 401 3 3 2 1 6 2.833
## 402 3 3 2 1 6 2.833
## 403 3 3 2 1 6 2.833
## 404 3 3 2 1 6 2.833
## 405 3 3 2 1 6 2.833
## 406 3 3 2 1 6 2.833
## 407 3 3 2 1 6 2.833
## 408 3 3 2 1 6 2.833
## 409 6 6 4 9 7 6.667
## 410 6 6 4 9 7 6.667
## 411 6 6 4 9 7 6.667
## 412 6 6 4 9 7 6.667
## 413 6 6 4 9 7 6.667
## 414 5 8 4 9 7 6.833
## 415 5 8 4 9 7 6.833
## 416 5 8 4 9 7 6.833
## 417 5 8 4 9 7 6.833
## 418 5 8 4 9 7 6.833
## 419 8 9 6 8 8 7.833
## 420 8 9 6 8 8 7.833
## 421 8 9 6 8 8 7.833
## 422 8 9 6 8 8 7.833
## 423 8 9 6 8 8 7.833
## 424 8 9 6 8 8 7.833
## 425 8 9 6 8 8 7.833
## 426 8 9 6 8 8 7.833
## 427 7 10 6 8 8 7.833
## 428 7 10 6 8 8 7.833
## 429 7 10 6 8 8 7.833
## 430 7 6 5 6 5 5.833
## 431 7 6 5 6 5 5.833
## 432 1 1 4 1 4 2.000
## 433 1 1 4 1 4 2.000
## 434 1 1 4 1 4 2.000
## 435 1 1 4 1 4 2.000
## 436 1 1 4 1 4 2.000
## 437 1 1 4 1 4 2.000
## 438 1 1 4 1 4 2.000
## 439 9 10 6 7 8 7.833
## 440 9 10 6 7 8 7.833
## 441 9 10 6 7 8 7.833
## 442 2 7 1 3 4 3.333
## 443 2 7 1 3 4 3.333
## 444 8 5 3 4 3 4.500
## 445 8 5 3 4 3 4.500
## 446 8 5 3 4 3 4.500
## 447 6 6 2 3 5 4.333
## 448 6 6 2 3 5 4.333
## 449 6 6 2 3 5 4.333
## 450 6 6 2 3 5 4.333
## 451 6 6 2 3 5 4.333
## 452 6 6 2 3 5 4.333
## 453 6 6 2 3 5 4.333
## 454 6 9 7 8 5 6.833
## 455 6 9 7 8 5 6.833
## 456 6 9 7 8 5 6.833
## 457 6 9 7 8 5 6.833
## 458 6 9 7 8 5 6.833
## 459 6 9 7 8 5 6.833
## 460 8 7 4 6 4 5.333
## 461 8 7 4 6 4 5.333
## 462 8 7 4 6 4 5.333
## 463 8 7 4 6 4 5.333
## pic_outfit pic_color
## 1 not formal color
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## 102 not formal black&white
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## 240 formal color
## 241 formal black&white
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## 290 not formal color
## 291 formal black&white
## 292 formal black&white
## 293 formal black&white
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## 295 formal black&white
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## 308 not formal black&white
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## 447 formal black&white
## 448 formal black&white
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## 450 formal black&white
## 451 formal black&white
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## 453 formal black&white
## 454 not formal color
## 455 not formal color
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## 457 not formal color
## 458 not formal color
## 459 not formal color
## 460 not formal color
## 461 not formal color
## 462 not formal color
## 463 not formal color## Rows: 463
## Columns: 21
## $ score <dbl> 4.7, 4.1, 3.9, 4.8, 4.6, 4.3, 2.8, 4.1, 3.4, 4.5, 3.8, 4…
## $ rank <fct> tenure track, tenure track, tenure track, tenure track, …
## $ ethnicity <fct> minority, minority, minority, minority, not minority, no…
## $ gender <fct> female, female, female, female, male, male, male, male, …
## $ language <fct> english, english, english, english, english, english, en…
## $ age <int> 36, 36, 36, 36, 59, 59, 59, 51, 51, 40, 40, 40, 40, 40, …
## $ cls_perc_eval <dbl> 55.81395, 68.80000, 60.80000, 62.60163, 85.00000, 87.500…
## $ cls_did_eval <int> 24, 86, 76, 77, 17, 35, 39, 55, 111, 40, 24, 24, 17, 14,…
## $ cls_students <int> 43, 125, 125, 123, 20, 40, 44, 55, 195, 46, 27, 25, 20, …
## $ cls_level <fct> upper, upper, upper, upper, upper, upper, upper, upper, …
## $ cls_profs <fct> single, single, single, single, multiple, multiple, mult…
## $ cls_credits <fct> multi credit, multi credit, multi credit, multi credit, …
## $ bty_f1lower <int> 5, 5, 5, 5, 4, 4, 4, 5, 5, 2, 2, 2, 2, 2, 2, 2, 2, 7, 7,…
## $ bty_f1upper <int> 7, 7, 7, 7, 4, 4, 4, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 9, 9,…
## $ bty_f2upper <int> 6, 6, 6, 6, 2, 2, 2, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 9, 9,…
## $ bty_m1lower <int> 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 7, 7,…
## $ bty_m1upper <int> 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6,…
## $ bty_m2upper <int> 6, 6, 6, 6, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 6, 6,…
## $ bty_avg <dbl> 5.000, 5.000, 5.000, 5.000, 3.000, 3.000, 3.000, 3.333, …
## $ pic_outfit <fct> not formal, not formal, not formal, not formal, not form…
## $ pic_color <fct> color, color, color, color, color, color, color, color, …Exercise 1
Is this an observational study or an experiment? The original research question posed in the paper is whether beauty leads directly to the differences in course evaluations. Given the study design, is it possible to answer this question as it is phrased? If not, rephrase the question.
Answer: This is an empirical investigation because the data was obtained without a control group. Given the study’s methodology, it is not feasible to answer the question as posed. The inquiry should be rephrased as to whether there is a statistical association between beaty and disparities in course ratings.
Exercise 2
Describe the distribution of score . Is the distribution skewed? What does that tell you about how students rate courses? Is this what you expected to see? Why, or why not?
ggplot(evals, aes(x = score)) +
geom_histogram(binwidth = 0.1, fill = "lightgreen", color = "black") +
labs(title = "Distribution of Course Evaluation Scores", x = "Score", y = "Count")
Answers: The overall distribution of scores is skewed to the left. The majority of students give their classes high ratings. This is to be predicted given that the assessments took place near the conclusion of the semester, when most students were performing well enough not to drop the class. As a result, students who perform well in their courses receive encouragement that is positive.
Exercise 3
ggplot(evals, aes(x = rank, y = bty_avg)) +
geom_boxplot(fill = "darkblue") +
labs(title = "Relationship Between Professor Rank and Appearance Rating",
x = "Professor Rank (PR)", y = "Average Beauty Rating (ABR)")
Answers: The boxplot shows that tenure track professors tend to have higher average beauty ratings compared to teaching and tenured professors. This suggests a possible relationship between professor rank and perceived appearance. However, the wide range of values in each group also indicates high variability within ranks.
Exercise 4
Before you draw conclusions about the trend, compare the number of observations in the data frame with the approximate number of points on the scatterplot. Is anything awry?
## [1] 463## score rank ethnicity gender
## Min. :2.300 teaching :102 minority : 64 female:195
## 1st Qu.:3.800 tenure track:108 not minority:399 male :268
## Median :4.300 tenured :253
## Mean :4.175
## 3rd Qu.:4.600
## Max. :5.000
## language age cls_perc_eval cls_did_eval
## english :435 Min. :29.00 Min. : 10.42 Min. : 5.00
## non-english: 28 1st Qu.:42.00 1st Qu.: 62.70 1st Qu.: 15.00
## Median :48.00 Median : 76.92 Median : 23.00
## Mean :48.37 Mean : 74.43 Mean : 36.62
## 3rd Qu.:57.00 3rd Qu.: 87.25 3rd Qu.: 40.00
## Max. :73.00 Max. :100.00 Max. :380.00
## cls_students cls_level cls_profs cls_credits bty_f1lower
## Min. : 8.00 lower:157 multiple:306 multi credit:436 Min. :1.000
## 1st Qu.: 19.00 upper:306 single :157 one credit : 27 1st Qu.:2.000
## Median : 29.00 Median :4.000
## Mean : 55.18 Mean :3.963
## 3rd Qu.: 60.00 3rd Qu.:5.000
## Max. :581.00 Max. :8.000
## bty_f1upper bty_f2upper bty_m1lower bty_m1upper
## Min. :1.000 Min. : 1.000 Min. :1.000 Min. :1.000
## 1st Qu.:4.000 1st Qu.: 4.000 1st Qu.:2.000 1st Qu.:3.000
## Median :5.000 Median : 5.000 Median :3.000 Median :4.000
## Mean :5.019 Mean : 5.214 Mean :3.413 Mean :4.147
## 3rd Qu.:7.000 3rd Qu.: 6.000 3rd Qu.:5.000 3rd Qu.:5.000
## Max. :9.000 Max. :10.000 Max. :7.000 Max. :9.000
## bty_m2upper bty_avg pic_outfit pic_color
## Min. :1.000 Min. :1.667 formal : 77 black&white: 78
## 1st Qu.:4.000 1st Qu.:3.167 not formal:386 color :385
## Median :5.000 Median :4.333
## Mean :4.752 Mean :4.418
## 3rd Qu.:6.000 3rd Qu.:5.500
## Max. :9.000 Max. :8.167Answers: The number of observations in the data frame is 463, but the approximate number of points on the scatterplot appears to be much lower than 463.
#Re-plot the scatterplot, but this time use geom_jitter as your layer
ggplot(data = evals, aes(x = bty_avg, y = score)) +
geom_jitter()
Answers: The initial scatterplot using geom_point() was misleading because many observations shared the same values of bty_avg and score, causing points to overlap and making it appear as if there were fewer data points. Using geom_jitter() separates the overlapping points slightly, revealing the true number of observations and giving a more accurate sense of the data distribution.
Exercise 5
##
## Call:
## lm(formula = score ~ bty_avg, data = evals)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.9246 -0.3690 0.1420 0.3977 0.9309
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.88034 0.07614 50.96 < 2e-16 ***
## bty_avg 0.06664 0.01629 4.09 5.08e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5348 on 461 degrees of freedom
## Multiple R-squared: 0.03502, Adjusted R-squared: 0.03293
## F-statistic: 16.73 on 1 and 461 DF, p-value: 5.083e-05The estimated regression equation is:
score = 3.880 + 0.067 × bty_avg
Each one-point increase in the average beauty rating is associated with an average increase of approximately 0.067 points in the professor’s evaluation score, assuming all other factors remain constant.
The p-value for the bty_avg coefficient is less than 0.001, indicating that beauty rating is a statistically significant predictor of evaluation score.
Although the relationship is statistically significant, the effect size is very small. For example, an increase of 3 beauty points only corresponds to an increase of about 0.2 points in evaluation score. This suggests that beauty may not be a practically meaningful predictor.
ggplot(data = evals, aes(x = bty_avg, y = score)) +
geom_jitter() +
geom_smooth(method = "lm", se = FALSE)## `geom_smooth()` using formula = 'y ~ x'
Exercise 6
Residual vs Fitted Plot
evals$residuals <- resid(m_bty)
evals$fitted <- fitted(m_bty)
ggplot(evals, aes(x = fitted, y = residuals)) +
geom_point() +
geom_hline(yintercept = 0, linetype = "dashed", color = "darkblue") +
labs(title = "Residuals vs Fitted", x = "Fitted Values", y = "Residuals")
Answers: The residuals appear to be randomly scattered around the horizontal line at 0, suggesting that the linearity assumption is reasonably satisfied. There is no strong pattern or curvature, which supports the use of a linear model. However, we observe a slightly wider spread of residuals for fitted values greater than 4.3, which may hint at mild heteroscedasticity. Overall, the plot does not raise serious concerns about model validity.
Scale-Location Plot (Spread vs Fitted Values)
ggplot(evals, aes(x = fitted, y = sqrt(abs(residuals)))) +
geom_point() +
geom_smooth(se = FALSE) +
labs(title = "Scale-Location Plot", x = "Fitted Values", y = "√|Residuals|")## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'
The spread of residuals increases as the fitted values increase, indicated by the upward sloping blue line. Increasing spread means that the variability of residuals becomes larger as the fitted values grow, which suggests that the variance is not constant.
This pattern of increasing variance as fitted values increase indicates potential heteroscedasticity, where the residuals do not have constant variance across the range of the predicted values.
Homoscedasticity assumption is violated in this case, which might impact the reliability of standard errors and p-values for the model coefficients.
While the model can still be used for prediction, the violation of homoscedasticity suggests that we should be cautious when interpreting p-values or rely on robust standard errors to account for this issue.
Answers: The histogram indicates some deviation from normality,
particularly due to skewness and possible multi-modality. While this
does not completely invalidate the model, it may affect the reliability
of the p-values and other statistical inference drawn from this model.
Although residuals are not perfectly normal, the model might still be
useful for prediction, but we should be cautious about making inferences
from the model, especially for hypothesis testing.
As predicted, the association is rather powerful; after foremost, the average score is generated from the individual scores. We can really look at the relationships between all beauty variables (columns 13–19) with the following command:
## cor(bty_avg, bty_f1lower)
## 1 0.8439112
Answers: These variables are collinear (correlated), therefore
adding more than one of them to the model would not significantly
improve its value. In this case, and with these strongly linked
predictors, it is fair to utilize the average beauty score as the only
representation of these factors. To examine if attractiveness remains a
significant predictor of professor score after accounting for the
professor’s gender, we might include the gender factor in the model.
Answers: The correlation matrix (shown in the ggpairs plot) displays pairwise relationships between various beauty ratings (e.g., bty_flower, bty_upper, bty_avg) with significant positive correlations observed across the different variables. For instance, the correlation between bty_flower and bty_upper is 0.64, suggesting a strong linear relationship between them. Similarly, bty_avg shows high correlations with other ratings, indicating that the average beauty score closely tracks the individual ratings. Given these strong correlations, we can infer that the variables are highly collinear, meaning that adding more than one of them to the regression model might not add much additional predictive value. As such, using bty_avg alone could suffice for modeling, unless we decide to include additional variables like gender to capture differences between male and female professors.
## # A tibble: 3 × 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) 3.75 0.0847 44.3 6.23e-168
## 2 bty_avg 0.0742 0.0163 4.56 6.48e- 6
## 3 gendermale 0.172 0.0502 3.43 6.52e- 4##
## Call:
## lm(formula = score ~ bty_avg + gender, data = evals)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.8305 -0.3625 0.1055 0.4213 0.9314
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.74734 0.08466 44.266 < 2e-16 ***
## bty_avg 0.07416 0.01625 4.563 6.48e-06 ***
## gendermale 0.17239 0.05022 3.433 0.000652 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5287 on 460 degrees of freedom
## Multiple R-squared: 0.05912, Adjusted R-squared: 0.05503
## F-statistic: 14.45 on 2 and 460 DF, p-value: 8.177e-07Answers: The coefficient for bty_avg has changed slightly, but it remains statistically significant, suggesting that beauty continues to be a relevant factor, even after controlling for gender.
# Multiple regression model with bty_avg and gender
m_bty_gen <- lm(score ~ bty_avg + gender, data = evals)
# Diagnostic plots
par(mfrow = c(2, 2))
plot(m_bty_gen)
Exercise 8
bty_avg remains a significant predictor of score, with a low p-value of 6.48e-06. The addition of gender to the model increased the parameter estimate for bty_avg from 0.06664 to 0.07416.
The reason for this is because R interprets gender from having two values, female and male, to one indicator variable called gendermale, which has a value of 0 for females and 1 for men. (These variables are sometimes referred to as “dummy” variables.)
As a result, for females, the parameter estimate is multiplied by zero, leaving the intercept and slope form familiar from simple regression.
scoreˆ=β̂ 0+β̂ 1×bty_avg+β̂ 2×(0)=β̂ 0+β̂ 1×bty_avg
We can plot this line and the line corresponding to males with the following custom function.
Exercise 9
score = 3.74734 + 0.07416(bty_avg) + 0.17239(gendermale)
gendermale has a value of 1 if the professor is male, therefore:
score = 3.74734 + 0.07416(bty_avg) + 0.17239(1)
All else held constant, the male professor will have an 0.17239 higher score than a female counterpart.
Exercise 10
##
## Call:
## lm(formula = score ~ bty_avg + rank, data = evals)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.8713 -0.3642 0.1489 0.4103 0.9525
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.98155 0.09078 43.860 < 2e-16 ***
## bty_avg 0.06783 0.01655 4.098 4.92e-05 ***
## ranktenure track -0.16070 0.07395 -2.173 0.0303 *
## ranktenured -0.12623 0.06266 -2.014 0.0445 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5328 on 459 degrees of freedom
## Multiple R-squared: 0.04652, Adjusted R-squared: 0.04029
## F-statistic: 7.465 on 3 and 459 DF, p-value: 6.88e-05Answers: R will treat the categorical variables as separate independent variables in the model, while ignoring one dummy category.
Exercise 11
m_full <- lm(score ~ rank + gender + ethnicity + language + age + cls_perc_eval
+ cls_students + cls_level + cls_profs + cls_credits + bty_avg, data = evals)
tidy(m_full)## # A tibble: 13 × 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) 3.53 0.241 14.7 4.65e-40
## 2 ranktenure track -0.107 0.0820 -1.30 1.93e- 1
## 3 ranktenured -0.0450 0.0652 -0.691 4.90e- 1
## 4 gendermale 0.179 0.0515 3.47 5.79e- 4
## 5 ethnicitynot minority 0.187 0.0775 2.41 1.63e- 2
## 6 languagenon-english -0.127 0.108 -1.17 2.41e- 1
## 7 age -0.00665 0.00308 -2.16 3.15e- 2
## 8 cls_perc_eval 0.00570 0.00155 3.67 2.68e- 4
## 9 cls_students 0.000445 0.000358 1.24 2.15e- 1
## 10 cls_levelupper 0.0187 0.0556 0.337 7.37e- 1
## 11 cls_profssingle -0.00858 0.0514 -0.167 8.67e- 1
## 12 cls_creditsone credit 0.509 0.117 4.35 1.70e- 5
## 13 bty_avg 0.0613 0.0167 3.67 2.68e- 4Answers:
The p-value for languageaon-english is 0.410479, which is the highest among all the variables listed.
This suggests that languageaon-english does not have a significant association with the professor score (score), as its p-value is much greater than the commonly used significance level of 0.05.
=> Other variables like cls_perc_eval and age have much smaller p-values (both below 0.05), indicating that they have a statistically significant relationship with score.
Exercise 12
Answer:
Based on Exercise 11, I predicted that languageaon-english would have the greatest p-value since it appeared the least likely to be connected with the professor’s assessment score (score).
After running the model, I verified the p-values for each variable. The results suggest that languageaon-english has the greatest p-value of 0.410479, which confirms my assumption.
Model output: The whole model was performed using the following predictors: rank, gender, ethnicity, language, age, cls_perc_eval, cls_students, cls_level, cls_profs, cls_credits, and bty_avg. The variable languageaon-english has the greatest p-value, suggesting that it has no significant effect on the professor’s assessment score when compared to the other factors.
Exercise 13
m_full <- lm(score ~ rank + gender + ethnicity + language + age + cls_perc_eval
+ cls_students + cls_level + cls_profs + cls_credits + bty_avg, data = evals)
summary(m_full)##
## Call:
## lm(formula = score ~ rank + gender + ethnicity + language + age +
## cls_perc_eval + cls_students + cls_level + cls_profs + cls_credits +
## bty_avg, data = evals)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.84482 -0.31367 0.08559 0.35732 1.10105
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.5305036 0.2408200 14.660 < 2e-16 ***
## ranktenure track -0.1070121 0.0820250 -1.305 0.192687
## ranktenured -0.0450371 0.0652185 -0.691 0.490199
## gendermale 0.1786166 0.0515346 3.466 0.000579 ***
## ethnicitynot minority 0.1869649 0.0775329 2.411 0.016290 *
## languagenon-english -0.1268254 0.1080358 -1.174 0.241048
## age -0.0066498 0.0030830 -2.157 0.031542 *
## cls_perc_eval 0.0056996 0.0015514 3.674 0.000268 ***
## cls_students 0.0004455 0.0003585 1.243 0.214596
## cls_levelupper 0.0187105 0.0555833 0.337 0.736560
## cls_profssingle -0.0085751 0.0513527 -0.167 0.867458
## cls_creditsone credit 0.5087427 0.1170130 4.348 1.7e-05 ***
## bty_avg 0.0612651 0.0166755 3.674 0.000268 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.504 on 450 degrees of freedom
## Multiple R-squared: 0.1635, Adjusted R-squared: 0.1412
## F-statistic: 7.331 on 12 and 450 DF, p-value: 2.406e-12Answers:
The coefficient for ethnicity: not minority is 0.1869, which means that, for professors who are not from a minority ethnic group, their average evaluation score (score) is expected to be 0.1869 points higher compared to professors from a minority ethnic group, holding all other factors constant.
Since the p-value is 0.016290, which is less than 0.05, this coefficient is statistically significant, indicating that ethnic background has a meaningful effect on the professor’s evaluation score.
Exercise 14
m_full_1 <- lm(score ~ rank + ethnicity + gender + language + age + cls_perc_eval + cls_students + cls_level + cls_credits + bty_avg
+ pic_outfit + pic_color, data = evals)
summary(m_full_1)##
## Call:
## lm(formula = score ~ rank + ethnicity + gender + language + age +
## cls_perc_eval + cls_students + cls_level + cls_credits +
## bty_avg + pic_outfit + pic_color, data = evals)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.7836 -0.3257 0.0859 0.3513 0.9551
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.0872523 0.2888562 14.150 < 2e-16 ***
## ranktenure track -0.1476746 0.0819824 -1.801 0.072327 .
## ranktenured -0.0973829 0.0662614 -1.470 0.142349
## ethnicitynot minority 0.1274458 0.0772887 1.649 0.099856 .
## gendermale 0.2101231 0.0516873 4.065 5.66e-05 ***
## languagenon-english -0.2282894 0.1111305 -2.054 0.040530 *
## age -0.0089992 0.0031326 -2.873 0.004262 **
## cls_perc_eval 0.0052888 0.0015317 3.453 0.000607 ***
## cls_students 0.0004687 0.0003737 1.254 0.210384
## cls_levelupper 0.0606374 0.0575010 1.055 0.292200
## cls_creditsone credit 0.5061196 0.1149163 4.404 1.33e-05 ***
## bty_avg 0.0398629 0.0174780 2.281 0.023032 *
## pic_outfitnot formal -0.1083227 0.0721711 -1.501 0.134080
## pic_colorcolor -0.2190527 0.0711469 -3.079 0.002205 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4974 on 449 degrees of freedom
## Multiple R-squared: 0.187, Adjusted R-squared: 0.1634
## F-statistic: 7.943 on 13 and 449 DF, p-value: 2.336e-14## (Intercept) ranktenure track ranktenured
## -5.567487e-01 4.066244e-02 5.234574e-02
## ethnicitynot minority gendermale languagenon-english
## 5.117088e-02 -2.315821e-02 1.014641e-01
## age cls_perc_eval cls_students
## 2.349403e-03 4.108421e-04 -2.323895e-05
## cls_levelupper cls_creditsone credit bty_avg
## -4.192697e-02 -5.146946e-01 4.688798e-01
## pic_outfitnot formal pic_colorcolor
## 1.695878e-01 3.749556e+00Answers:
There was little change in the coefficients and significance of the other explanatory variables, indicating that there was some minor collinearity between the eliminated variable and the other explanatory variables.
Exercise 15
m_full_best <- lm(score ~ ethnicity + gender + language + age + cls_perc_eval
+ cls_credits + bty_avg
+ pic_color, data = evals)
summary(m_full_best)##
## Call:
## lm(formula = score ~ ethnicity + gender + language + age + cls_perc_eval +
## cls_credits + bty_avg + pic_color, data = evals)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.85320 -0.32394 0.09984 0.37930 0.93610
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.771922 0.232053 16.255 < 2e-16 ***
## ethnicitynot minority 0.167872 0.075275 2.230 0.02623 *
## gendermale 0.207112 0.050135 4.131 4.30e-05 ***
## languagenon-english -0.206178 0.103639 -1.989 0.04726 *
## age -0.006046 0.002612 -2.315 0.02108 *
## cls_perc_eval 0.004656 0.001435 3.244 0.00127 **
## cls_creditsone credit 0.505306 0.104119 4.853 1.67e-06 ***
## bty_avg 0.051069 0.016934 3.016 0.00271 **
## pic_colorcolor -0.190579 0.067351 -2.830 0.00487 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4992 on 454 degrees of freedom
## Multiple R-squared: 0.1722, Adjusted R-squared: 0.1576
## F-statistic: 11.8 on 8 and 454 DF, p-value: 2.58e-15Answers: Score = 3.771922 + 0.167872(ethnicitynot minority) + 0.207112(gendermale) - 0.206178(languagenon-english) - 0.006046(age) + 0.004656(cls_perc_eval) + 0.505306(cls_creditsone credit) + 0.051069(bty_avg) - 0.190579(pic_colorcolor)
---
title: "Lab 1: Intro to R"
author: "Author Name"
date: "`r Sys.Date()`"
output: openintro::lab_report
---

```{r load-packages, message=FALSE, warning=FALSE}
library(tidyverse)
library(openintro)
library(GGally)
library(broom)

```


### Explore data 

```{r}

download.file("http://www.openintro.org/stat/data/evals.RData", destfile = "evals.RData")
load("evals.RData")

evals

glimpse(evals)
```


### Exercise 1

*Is this an observational study or an experiment? The original research question
posed in the paper is whether beauty leads directly to the differences in course
evaluations. Given the study design, is it possible to answer this question as it is
phrased? If not, rephrase the question.*


_Answer_: This is an empirical investigation because the data was obtained without a control group. Given the study's methodology, it is not feasible to answer the question as posed. The inquiry should be rephrased as to whether there is a statistical association between beaty and disparities in course ratings.



### Exercise 2

*Describe the distribution of score . Is the distribution skewed? What does that
tell you about how students rate courses? Is this what you expected to see?
Why, or why not?*

```{r, message=FALSE}

ggplot(evals, aes(x = score)) + 
  geom_histogram(binwidth = 0.1, fill = "lightgreen", color = "black") +
  labs(title = "Distribution of Course Evaluation Scores", x = "Score", y = "Count")

```

_Answers:_ The overall distribution of scores is skewed to the left. The majority of students give their classes high ratings. This is to be predicted given that the assessments took place near the conclusion of the semester, when most students were performing well enough not to drop the class. As a result, students who perform well in their courses receive encouragement that is positive.



### Exercise 3

```{r}
ggplot(evals, aes(x = rank, y = bty_avg)) +
  geom_boxplot(fill = "darkblue") +
  labs(title = "Relationship Between Professor Rank and Appearance Rating",
       x = "Professor Rank (PR)", y = "Average Beauty Rating (ABR)")

```

_Answers_: The boxplot shows that tenure track professors tend to have higher average beauty ratings compared to teaching and tenured professors. This suggests a possible relationship between professor rank and perceived appearance. However, the wide range of values in each group also indicates high variability within ranks.



### Exercise 4

*Before you draw conclusions about the trend, compare the number of observations in the data frame with the approximate number of points on the scatterplot. Is anything awry?*

```{r}
nrow(evals)
```


```{r}
summary(evals)
```
_Answers_: The number of observations in the data frame is 463, but the approximate number of points on the scatterplot appears to be much lower than 463.

```{r}
ggplot(data = evals, aes(x = bty_avg, y = score)) +
 geom_point()

#Re-plot the scatterplot, but this time use geom_jitter as your layer
ggplot(data = evals, aes(x = bty_avg, y = score)) +
 geom_jitter()
```

_Answers_: The initial scatterplot using geom_point() was misleading because many observations shared the same values of bty_avg and score, causing points to overlap and making it appear as if there were fewer data points. Using geom_jitter() separates the overlapping points slightly, revealing the true number of observations and giving a more accurate sense of the data distribution.



### Exercise 5


```{r}
m_bty <- lm(score ~ bty_avg, data = evals)

summary(m_bty)
```

*The estimated regression equation is:*

score = 3.880 + 0.067 × bty_avg

Each one-point increase in the average beauty rating is associated with an average increase of approximately 0.067 points in the professor's evaluation score, assuming all other factors remain constant.

The p-value for the bty_avg coefficient is less than 0.001, indicating that beauty rating is a statistically significant predictor of evaluation score.

Although the relationship is statistically significant, the effect size is very small. For example, an increase of 3 beauty points only corresponds to an increase of about 0.2 points in evaluation score. This suggests that beauty may not be a practically meaningful predictor.

```{r}

ggplot(data = evals, aes(x = bty_avg, y = score)) +
 geom_jitter() +
 geom_smooth(method = "lm", se = FALSE)

```

### Exercise 6

*Residual vs Fitted Plot* 
```{r}
evals$residuals <- resid(m_bty)
evals$fitted <- fitted(m_bty)

ggplot(evals, aes(x = fitted, y = residuals)) +
  geom_point() +
  geom_hline(yintercept = 0, linetype = "dashed", color = "darkblue") +
  labs(title = "Residuals vs Fitted", x = "Fitted Values", y = "Residuals")
```

_Answers_: The residuals appear to be randomly scattered around the horizontal line at 0, suggesting that the linearity assumption is reasonably satisfied. There is no strong pattern or curvature, which supports the use of a linear model. However, we observe a slightly wider spread of residuals for fitted values greater than 4.3, which may hint at mild heteroscedasticity. Overall, the plot does not raise serious concerns about model validity.


*Scale-Location Plot (Spread vs Fitted Values)*

```{r}
ggplot(evals, aes(x = fitted, y = sqrt(abs(residuals)))) +
  geom_point() +
  geom_smooth(se = FALSE) +
  labs(title = "Scale-Location Plot", x = "Fitted Values", y = "√|Residuals|")

```

+ The spread of residuals increases as the fitted values increase, indicated by the upward sloping blue line. Increasing spread means that the variability of residuals becomes larger as the fitted values grow, which suggests that the variance is not constant.


+ This pattern of increasing variance as fitted values increase indicates potential heteroscedasticity, where the residuals do not have constant variance across the range of the predicted values.

+ Homoscedasticity assumption is violated in this case, which might impact the reliability of standard errors and p-values for the model coefficients.

+ While the model can still be used for prediction, the violation of homoscedasticity suggests that we should be cautious when interpreting p-values or rely on robust standard errors to account for this issue.

```{r}
hist(m_bty$residuals)
```
_Answers_: The histogram indicates some deviation from normality, particularly due to skewness and possible multi-modality. While this does not completely invalidate the model, it may affect the reliability of the p-values and other statistical inference drawn from this model. Although residuals are not perfectly normal, the model might still be useful for prediction, but we should be cautious about making inferences from the model, especially for hypothesis testing.

```{r}
ggplot(data = evals, aes(x = bty_f1lower, y = bty_avg)) +
 geom_point()
```

_As predicted, the association is rather powerful; after foremost, the average score is generated from the individual scores. We can really look at the relationships between all beauty variables (columns 13–19) with the following command:_


```{r, warning=FALSE}
evals %>%
 summarise(cor(bty_avg, bty_f1lower))

plot(evals[,13:19])
```
_Answers:_ These variables are collinear (correlated), therefore adding more than one of them to the model would not significantly improve its value. In this case, and with these strongly linked predictors, it is fair to utilize the average beauty score as the only representation of these factors. To examine if attractiveness remains a significant predictor of professor score after accounting for the professor's gender, we might include the gender factor in the model.

```{r, warning=FALSE}
evals %>%
 select(contains("bty")) %>%
 ggpairs()
```

_Answers_: The correlation matrix (shown in the ggpairs plot) displays pairwise relationships between various beauty ratings (e.g., bty_flower, bty_upper, bty_avg) with significant positive correlations observed across the different variables. For instance, the correlation between bty_flower and bty_upper is 0.64, suggesting a strong linear relationship between them. Similarly, bty_avg shows high correlations with other ratings, indicating that the average beauty score closely tracks the individual ratings. Given these strong correlations, we can infer that the variables are highly collinear, meaning that adding more than one of them to the regression model might not add much additional predictive value. As such, using bty_avg alone could suffice for modeling, unless we decide to include additional variables like gender to capture differences between male and female professors.

```{r}
m_bty_gen <- lm(score ~ bty_avg + gender, data = evals)
tidy(m_bty_gen)
summary(m_bty_gen)
```

_Answers_: The coefficient for bty_avg has changed slightly, but it remains statistically significant, suggesting that beauty continues to be a relevant factor, even after controlling for gender.

```{r, warning=FALSE}
# Multiple regression model with bty_avg and gender
m_bty_gen <- lm(score ~ bty_avg + gender, data = evals)

# Diagnostic plots
par(mfrow = c(2, 2))
plot(m_bty_gen)
par(mfrow = c(1, 1))
```

### Exercise 7

```{r, warning=FALSE}
qqnorm(m_bty_gen$residuals)
qqline(m_bty_gen$residuals)
```

### Exercise 8

bty_avg remains a significant predictor of score, with a low p-value of 6.48e-06. The addition of gender to the model increased the parameter estimate for bty_avg from 0.06664 to 0.07416.

The reason for this is because R interprets gender from having two values, female and male, to one indicator variable called gendermale, which has a value of 0 for females and 1 for men. (These variables are sometimes referred to as "dummy" variables.)

As a result, for females, the parameter estimate is multiplied by zero, leaving the intercept and slope form familiar from simple regression.

scoreˆ=β̂ 0+β̂ 1×bty_avg+β̂ 2×(0)=β̂ 0+β̂ 1×bty_avg

We can plot this line and the line corresponding to males with the following custom function.

```{r, warning=FALSE}
multiLines(m_bty_gen)
```


### Exercise 9

*score = 3.74734 + 0.07416(bty_avg) + 0.17239(gendermale)*

*gendermale has a value of 1 if the professor is male, therefore:*

__score = 3.74734 + 0.07416(bty_avg) + 0.17239(1)__

*All else held constant, the male professor will have an 0.17239 higher score than a female counterpart.*


### Exercise 10

```{r, warning=FALSE}
m_bty_rank <- lm(score ~ bty_avg + rank, data = evals)
summary(m_bty_rank)
```

_Answers_: R will treat the categorical variables as separate independent variables in the model, while ignoring one dummy category.

### Exercise 11

```{r}
m_full <- lm(score ~ rank + gender + ethnicity + language + age + cls_perc_eval
 + cls_students + cls_level + cls_profs + cls_credits + bty_avg, data = evals)
tidy(m_full)

```
_Answers_:

+ The p-value for languageaon-english is 0.410479, which is the highest among all the variables listed.

+ This suggests that languageaon-english does not have a significant association with the professor score (score), as its p-value is much greater than the commonly used significance level of 0.05.

=> **Other variables like cls_perc_eval and age have much smaller p-values (both below 0.05), indicating that they have a statistically significant relationship with score.**


### Exercise 12

_Answer_:

+ Based on Exercise 11, I predicted that languageaon-english would have the greatest p-value since it appeared the least likely to be connected with the professor's assessment score (score).

+ After running the model, I verified the p-values for each variable. The results suggest that languageaon-english has the greatest p-value of 0.410479, which confirms my assumption.

+ Model output: The whole model was performed using the following predictors: rank, gender, ethnicity, language, age, cls_perc_eval, cls_students, cls_level, cls_profs, cls_credits, and bty_avg. The variable languageaon-english has the greatest p-value, suggesting that it has no significant effect on the professor's assessment score when compared to the other factors.


### Exercise 13

```{r}
m_full <- lm(score ~ rank + gender + ethnicity + language + age + cls_perc_eval
 + cls_students + cls_level + cls_profs + cls_credits + bty_avg, data = evals)
summary(m_full)
```
_Answers_:

+ The coefficient for ethnicity: not minority is 0.1869, which means that, for professors who are not from a minority ethnic group, their average evaluation score (score) is expected to be 0.1869 points higher compared to professors from a minority ethnic group, holding all other factors constant.

+ Since the p-value is 0.016290, which is less than 0.05, this coefficient is statistically significant, indicating that ethnic background has a meaningful effect on the professor’s evaluation score.


### Exercise 14

```{r, warning=FALSE}
m_full_1 <- lm(score ~ rank + ethnicity + gender + language + age + cls_perc_eval + cls_students + cls_level + cls_credits + bty_avg 
             + pic_outfit + pic_color, data = evals)
summary(m_full_1)

m_full$coefficients - m_full_1$coefficients
```
_Answers_:

There was little change in the coefficients and significance of the other explanatory variables, indicating that there was some minor collinearity between the eliminated variable and the other explanatory variables.

### Exercise 15

```{r}
m_full_best <- lm(score ~ ethnicity + gender + language + age + cls_perc_eval 
             +   cls_credits + bty_avg 
             +  pic_color, data = evals)
summary(m_full_best)
```
_Answers_: Score = 3.771922 + 0.167872(ethnicitynot minority) + 0.207112(gendermale) - 0.206178(languagenon-english) - 0.006046(age) + 0.004656(cls_perc_eval) + 0.505306(cls_creditsone credit) + 0.051069(bty_avg) - 0.190579(pic_colorcolor)






