Baitap 7
Thong
May 14, 2020
BAI TAP VE MO HINH HOI QUY TUYEN TINH DA BIEN (dataset = Boston-price)
Cau 1: Ve bieu do tan xa da bien cua cac bien rm, tax, lstat, nox, crim, age tu Boston-price
Tao dataset con tu Boston-price
setwd("D:/Rml")
q = read.csv('Boston-price.csv')
attach(q)
z = cbind(rm,tax,lstat,nox,crim,age)
dat = data.frame(z)
dat## rm tax lstat nox crim age
## 1 6.575 296 4.98 0.5380 0.00632 65.2
## 2 6.421 242 9.14 0.4690 0.02731 78.9
## 3 7.185 242 4.03 0.4690 0.02729 61.1
## 4 6.998 222 2.94 0.4580 0.03237 45.8
## 5 7.147 222 5.33 0.4580 0.06905 54.2
## 6 6.430 222 5.21 0.4580 0.02985 58.7
## 7 6.012 311 12.43 0.5240 0.08829 66.6
## 8 6.172 311 19.15 0.5240 0.14455 96.1
## 9 5.631 311 29.93 0.5240 0.21124 100.0
## 10 6.004 311 17.10 0.5240 0.17004 85.9
## 11 6.377 311 20.45 0.5240 0.22489 94.3
## 12 6.009 311 13.27 0.5240 0.11747 82.9
## 13 5.889 311 15.71 0.5240 0.09378 39.0
## 14 5.949 307 8.26 0.5380 0.62976 61.8
## 15 6.096 307 10.26 0.5380 0.63796 84.5
## 16 5.834 307 8.47 0.5380 0.62739 56.5
## 17 5.935 307 6.58 0.5380 1.05393 29.3
## 18 5.990 307 14.67 0.5380 0.78420 81.7
## 19 5.456 307 11.69 0.5380 0.80271 36.6
## 20 5.727 307 11.28 0.5380 0.72580 69.5
## 21 5.570 307 21.02 0.5380 1.25179 98.1
## 22 5.965 307 13.83 0.5380 0.85204 89.2
## 23 6.142 307 18.72 0.5380 1.23247 91.7
## 24 5.813 307 19.88 0.5380 0.98843 100.0
## 25 5.924 307 16.30 0.5380 0.75026 94.1
## 26 5.599 307 16.51 0.5380 0.84054 85.7
## 27 5.813 307 14.81 0.5380 0.67191 90.3
## 28 6.047 307 17.28 0.5380 0.95577 88.8
## 29 6.495 307 12.80 0.5380 0.77299 94.4
## 30 6.674 307 11.98 0.5380 1.00245 87.3
## 31 5.713 307 22.60 0.5380 1.13081 94.1
## 32 6.072 307 13.04 0.5380 1.35472 100.0
## 33 5.950 307 27.71 0.5380 1.38799 82.0
## 34 5.701 307 18.35 0.5380 1.15172 95.0
## 35 6.096 307 20.34 0.5380 1.61282 96.9
## 36 5.933 279 9.68 0.4990 0.06417 68.2
## 37 5.841 279 11.41 0.4990 0.09744 61.4
## 38 5.850 279 8.77 0.4990 0.08014 41.5
## 39 5.966 279 10.13 0.4990 0.17505 30.2
## 40 6.595 252 4.32 0.4280 0.02763 21.8
## 41 7.024 252 1.98 0.4280 0.03359 15.8
## 42 6.770 233 4.84 0.4480 0.12744 2.9
## 43 6.169 233 5.81 0.4480 0.14150 6.6
## 44 6.211 233 7.44 0.4480 0.15936 6.5
## 45 6.069 233 9.55 0.4480 0.12269 40.0
## 46 5.682 233 10.21 0.4480 0.17142 33.8
## 47 5.786 233 14.15 0.4480 0.18836 33.3
## 48 6.030 233 18.80 0.4480 0.22927 85.5
## 49 5.399 233 30.81 0.4480 0.25387 95.3
## 50 5.602 233 16.20 0.4480 0.21977 62.0
## 51 5.963 243 13.45 0.4390 0.08873 45.7
## 52 6.115 243 9.43 0.4390 0.04337 63.0
## 53 6.511 243 5.28 0.4390 0.05360 21.1
## 54 5.998 243 8.43 0.4390 0.04981 21.4
## 55 5.888 469 14.80 0.4100 0.01360 47.6
## 56 7.249 226 4.81 0.4030 0.01311 21.9
## 57 6.383 313 5.77 0.4100 0.02055 35.7
## 58 6.816 256 3.95 0.4110 0.01432 40.5
## 59 6.145 284 6.86 0.4530 0.15445 29.2
## 60 5.927 284 9.22 0.4530 0.10328 47.2
## 61 5.741 284 13.15 0.4530 0.14932 66.2
## 62 5.966 284 14.44 0.4530 0.17171 93.4
## 63 6.456 284 6.73 0.4530 0.11027 67.8
## 64 6.762 284 9.50 0.4530 0.12650 43.4
## 65 7.104 216 8.05 0.4161 0.01951 59.5
## 66 6.290 337 4.67 0.3980 0.03584 17.8
## 67 5.787 337 10.24 0.3980 0.04379 31.1
## 68 5.878 345 8.10 0.4090 0.05789 21.4
## 69 5.594 345 13.09 0.4090 0.13554 36.8
## 70 5.885 345 8.79 0.4090 0.12816 33.0
## 71 6.417 305 6.72 0.4130 0.08826 6.6
## 72 5.961 305 9.88 0.4130 0.15876 17.5
## 73 6.065 305 5.52 0.4130 0.09164 7.8
## 74 6.245 305 7.54 0.4130 0.19539 6.2
## 75 6.273 398 6.78 0.4370 0.07896 6.0
## 76 6.286 398 8.94 0.4370 0.09512 45.0
## 77 6.279 398 11.97 0.4370 0.10153 74.5
## 78 6.140 398 10.27 0.4370 0.08707 45.8
## 79 6.232 398 12.34 0.4370 0.05646 53.7
## 80 5.874 398 9.10 0.4370 0.08387 36.6
## 81 6.727 281 5.29 0.4260 0.04113 33.5
## 82 6.619 281 7.22 0.4260 0.04462 70.4
## 83 6.302 281 6.72 0.4260 0.03659 32.2
## 84 6.167 281 7.51 0.4260 0.03551 46.7
## 85 6.389 247 9.62 0.4490 0.05059 48.0
## 86 6.630 247 6.53 0.4490 0.05735 56.1
## 87 6.015 247 12.86 0.4490 0.05188 45.1
## 88 6.121 247 8.44 0.4490 0.07151 56.8
## 89 7.007 270 5.50 0.4890 0.05660 86.3
## 90 7.079 270 5.70 0.4890 0.05302 63.1
## 91 6.417 270 8.81 0.4890 0.04684 66.1
## 92 6.405 270 8.20 0.4890 0.03932 73.9
## 93 6.442 270 8.16 0.4640 0.04203 53.6
## 94 6.211 270 6.21 0.4640 0.02875 28.9
## 95 6.249 270 10.59 0.4640 0.04294 77.3
## 96 6.625 276 6.65 0.4450 0.12204 57.8
## 97 6.163 276 11.34 0.4450 0.11504 69.6
## 98 8.069 276 4.21 0.4450 0.12083 76.0
## 99 7.820 276 3.57 0.4450 0.08187 36.9
## 100 7.416 276 6.19 0.4450 0.06860 62.5
## 101 6.727 384 9.42 0.5200 0.14866 79.9
## 102 6.781 384 7.67 0.5200 0.11432 71.3
## 103 6.405 384 10.63 0.5200 0.22876 85.4
## 104 6.137 384 13.44 0.5200 0.21161 87.4
## 105 6.167 384 12.33 0.5200 0.13960 90.0
## 106 5.851 384 16.47 0.5200 0.13262 96.7
## 107 5.836 384 18.66 0.5200 0.17120 91.9
## 108 6.127 384 14.09 0.5200 0.13117 85.2
## 109 6.474 384 12.27 0.5200 0.12802 97.1
## 110 6.229 384 15.55 0.5200 0.26363 91.2
## 111 6.195 384 13.00 0.5200 0.10793 54.4
## 112 6.715 432 10.16 0.5470 0.10084 81.6
## 113 5.913 432 16.21 0.5470 0.12329 92.9
## 114 6.092 432 17.09 0.5470 0.22212 95.4
## 115 6.254 432 10.45 0.5470 0.14231 84.2
## 116 5.928 432 15.76 0.5470 0.17134 88.2
## 117 6.176 432 12.04 0.5470 0.13158 72.5
## 118 6.021 432 10.30 0.5470 0.15098 82.6
## 119 5.872 432 15.37 0.5470 0.13058 73.1
## 120 5.731 432 13.61 0.5470 0.14476 65.2
## 121 5.870 188 14.37 0.5810 0.06899 69.7
## 122 6.004 188 14.27 0.5810 0.07165 84.1
## 123 5.961 188 17.93 0.5810 0.09299 92.9
## 124 5.856 188 25.41 0.5810 0.15038 97.0
## 125 5.879 188 17.58 0.5810 0.09849 95.8
## 126 5.986 188 14.81 0.5810 0.16902 88.4
## 127 5.613 188 27.26 0.5810 0.38735 95.6
## 128 5.693 437 17.19 0.6240 0.25915 96.0
## 129 6.431 437 15.39 0.6240 0.32543 98.8
## 130 5.637 437 18.34 0.6240 0.88125 94.7
## 131 6.458 437 12.60 0.6240 0.34006 98.9
## 132 6.326 437 12.26 0.6240 1.19294 97.7
## 133 6.372 437 11.12 0.6240 0.59005 97.9
## 134 5.822 437 15.03 0.6240 0.32982 95.4
## 135 5.757 437 17.31 0.6240 0.97617 98.4
## 136 6.335 437 16.96 0.6240 0.55778 98.2
## 137 5.942 437 16.90 0.6240 0.32264 93.5
## 138 6.454 437 14.59 0.6240 0.35233 98.4
## 139 5.857 437 21.32 0.6240 0.24980 98.2
## 140 6.151 437 18.46 0.6240 0.54452 97.9
## 141 6.174 437 24.16 0.6240 0.29090 93.6
## 142 5.019 437 34.41 0.6240 1.62864 100.0
## 143 5.403 403 26.82 0.8710 3.32105 100.0
## 144 5.468 403 26.42 0.8710 4.09740 100.0
## 145 4.903 403 29.29 0.8710 2.77974 97.8
## 146 6.130 403 27.80 0.8710 2.37934 100.0
## 147 5.628 403 16.65 0.8710 2.15505 100.0
## 148 4.926 403 29.53 0.8710 2.36862 95.7
## 149 5.186 403 28.32 0.8710 2.33099 93.8
## 150 5.597 403 21.45 0.8710 2.73397 94.9
## 151 6.122 403 14.10 0.8710 1.65660 97.3
## 152 5.404 403 13.28 0.8710 1.49632 100.0
## 153 5.012 403 12.12 0.8710 1.12658 88.0
## 154 5.709 403 15.79 0.8710 2.14918 98.5
## 155 6.129 403 15.12 0.8710 1.41385 96.0
## 156 6.152 403 15.02 0.8710 3.53501 82.6
## 157 5.272 403 16.14 0.8710 2.44668 94.0
## 158 6.943 403 4.59 0.6050 1.22358 97.4
## 159 6.066 403 6.43 0.6050 1.34284 100.0
## 160 6.510 403 7.39 0.8710 1.42502 100.0
## 161 6.250 403 5.50 0.6050 1.27346 92.6
## 162 7.489 403 1.73 0.6050 1.46336 90.8
## 163 7.802 403 1.92 0.6050 1.83377 98.2
## 164 8.375 403 3.32 0.6050 1.51902 93.9
## 165 5.854 403 11.64 0.6050 2.24236 91.8
## 166 6.101 403 9.81 0.6050 2.92400 93.0
## 167 7.929 403 3.70 0.6050 2.01019 96.2
## 168 5.877 403 12.14 0.6050 1.80028 79.2
## 169 6.319 403 11.10 0.6050 2.30040 96.1
## 170 6.402 403 11.32 0.6050 2.44953 95.2
## 171 5.875 403 14.43 0.6050 1.20742 94.6
## 172 5.880 403 12.03 0.6050 2.31390 97.3
## 173 5.572 296 14.69 0.5100 0.13914 88.5
## 174 6.416 296 9.04 0.5100 0.09178 84.1
## 175 5.859 296 9.64 0.5100 0.08447 68.7
## 176 6.546 296 5.33 0.5100 0.06664 33.1
## 177 6.020 296 10.11 0.5100 0.07022 47.2
## 178 6.315 296 6.29 0.5100 0.05425 73.4
## 179 6.860 296 6.92 0.5100 0.06642 74.4
## 180 6.980 193 5.04 0.4880 0.05780 58.4
## 181 7.765 193 7.56 0.4880 0.06588 83.3
## 182 6.144 193 9.45 0.4880 0.06888 62.2
## 183 7.155 193 4.82 0.4880 0.09103 92.2
## 184 6.563 193 5.68 0.4880 0.10008 95.6
## 185 5.604 193 13.98 0.4880 0.08308 89.8
## 186 6.153 193 13.15 0.4880 0.06047 68.8
## 187 7.831 193 4.45 0.4880 0.05602 53.6
## 188 6.782 398 6.68 0.4370 0.07875 41.1
## 189 6.556 398 4.56 0.4370 0.12579 29.1
## 190 7.185 398 5.39 0.4370 0.08370 38.9
## 191 6.951 398 5.10 0.4370 0.09068 21.5
## 192 6.739 398 4.69 0.4370 0.06911 30.8
## 193 7.178 398 2.87 0.4370 0.08664 26.3
## 194 6.800 265 5.03 0.4010 0.02187 9.9
## 195 6.604 265 4.38 0.4010 0.01439 18.8
## 196 7.875 255 2.97 0.4220 0.01381 32.0
## 197 7.287 329 4.08 0.4040 0.04011 34.1
## 198 7.107 329 8.61 0.4040 0.04666 36.6
## 199 7.274 329 6.62 0.4040 0.03768 38.3
## 200 6.975 402 4.56 0.4030 0.03150 15.3
## 201 7.135 402 4.45 0.4030 0.01778 13.9
## 202 6.162 348 7.43 0.4150 0.03445 38.4
## 203 7.610 348 3.11 0.4150 0.02177 15.7
## 204 7.853 224 3.81 0.4161 0.03510 33.2
## 205 8.034 224 2.88 0.4161 0.02009 31.9
## 206 5.891 277 10.87 0.4890 0.13642 22.3
## 207 6.326 277 10.97 0.4890 0.22969 52.5
## 208 5.783 277 18.06 0.4890 0.25199 72.7
## 209 6.064 277 14.66 0.4890 0.13587 59.1
## 210 5.344 277 23.09 0.4890 0.43571 100.0
## 211 5.960 277 17.27 0.4890 0.17446 92.1
## 212 5.404 277 23.98 0.4890 0.37578 88.6
## 213 5.807 277 16.03 0.4890 0.21719 53.8
## 214 6.375 277 9.38 0.4890 0.14052 32.3
## 215 5.412 277 29.55 0.4890 0.28955 9.8
## 216 6.182 277 9.47 0.4890 0.19802 42.4
## 217 5.888 276 13.51 0.5500 0.04560 56.0
## 218 6.642 276 9.69 0.5500 0.07013 85.1
## 219 5.951 276 17.92 0.5500 0.11069 93.8
## 220 6.373 276 10.50 0.5500 0.11425 92.4
## 221 6.951 307 9.71 0.5070 0.35809 88.5
## 222 6.164 307 21.46 0.5070 0.40771 91.3
## 223 6.879 307 9.93 0.5070 0.62356 77.7
## 224 6.618 307 7.60 0.5070 0.61470 80.8
## 225 8.266 307 4.14 0.5040 0.31533 78.3
## 226 8.725 307 4.63 0.5040 0.52693 83.0
## 227 8.040 307 3.13 0.5040 0.38214 86.5
## 228 7.163 307 6.36 0.5040 0.41238 79.9
## 229 7.686 307 3.92 0.5040 0.29819 17.0
## 230 6.552 307 3.76 0.5040 0.44178 21.4
## 231 5.981 307 11.65 0.5040 0.53700 68.1
## 232 7.412 307 5.25 0.5040 0.46296 76.9
## 233 8.337 307 2.47 0.5070 0.57529 73.3
## 234 8.247 307 3.95 0.5070 0.33147 70.4
## 235 6.726 307 8.05 0.5070 0.44791 66.5
## 236 6.086 307 10.88 0.5070 0.33045 61.5
## 237 6.631 307 9.54 0.5070 0.52058 76.5
## 238 7.358 307 4.73 0.5070 0.51183 71.6
## 239 6.481 300 6.36 0.4280 0.08244 18.5
## 240 6.606 300 7.37 0.4280 0.09252 42.2
## 241 6.897 300 11.38 0.4280 0.11329 54.3
## 242 6.095 300 12.40 0.4280 0.10612 65.1
## 243 6.358 300 11.22 0.4280 0.10290 52.9
## 244 6.393 300 5.19 0.4280 0.12757 7.8
## 245 5.593 330 12.50 0.4310 0.20608 76.5
## 246 5.605 330 18.46 0.4310 0.19133 70.2
## 247 6.108 330 9.16 0.4310 0.33983 34.9
## 248 6.226 330 10.15 0.4310 0.19657 79.2
## 249 6.433 330 9.52 0.4310 0.16439 49.1
## 250 6.718 330 6.56 0.4310 0.19073 17.5
## 251 6.487 330 5.90 0.4310 0.14030 13.0
## 252 6.438 330 3.59 0.4310 0.21409 8.9
## 253 6.957 330 3.53 0.4310 0.08221 6.8
## 254 8.259 330 3.54 0.4310 0.36894 8.4
## 255 6.108 315 6.57 0.3920 0.04819 32.0
## 256 5.876 315 9.25 0.3920 0.03548 19.1
## 257 7.454 244 3.11 0.3940 0.01538 34.2
## 258 8.704 264 5.12 0.6470 0.61154 86.9
## 259 7.333 264 7.79 0.6470 0.66351 100.0
## 260 6.842 264 6.90 0.6470 0.65665 100.0
## 261 7.203 264 9.59 0.6470 0.54011 81.8
## 262 7.520 264 7.26 0.6470 0.53412 89.4
## 263 8.398 264 5.91 0.6470 0.52014 91.5
## 264 7.327 264 11.25 0.6470 0.82526 94.5
## 265 7.206 264 8.10 0.6470 0.55007 91.6
## 266 5.560 264 10.45 0.6470 0.76162 62.8
## 267 7.014 264 14.79 0.6470 0.78570 84.6
## 268 8.297 264 7.44 0.5750 0.57834 67.0
## 269 7.470 264 3.16 0.5750 0.54050 52.6
## 270 5.920 223 13.65 0.4640 0.09065 61.5
## 271 5.856 223 13.00 0.4640 0.29916 42.1
## 272 6.240 223 6.59 0.4640 0.16211 16.3
## 273 6.538 223 7.73 0.4640 0.11460 58.7
## 274 7.691 223 6.58 0.4640 0.22188 51.8
## 275 6.758 254 3.53 0.4470 0.05644 32.9
## 276 6.854 254 2.98 0.4470 0.09604 42.8
## 277 7.267 254 6.05 0.4470 0.10469 49.0
## 278 6.826 254 4.16 0.4470 0.06127 27.6
## 279 6.482 254 7.19 0.4470 0.07978 32.1
## 280 6.812 216 4.85 0.4429 0.21038 32.2
## 281 7.820 216 3.76 0.4429 0.03578 64.5
## 282 6.968 216 4.59 0.4429 0.03705 37.2
## 283 7.645 216 3.01 0.4429 0.06129 49.7
## 284 7.923 198 3.16 0.4010 0.01501 24.8
## 285 7.088 285 7.85 0.4000 0.00906 20.8
## 286 6.453 300 8.23 0.3890 0.01096 31.9
## 287 6.230 241 12.93 0.3850 0.01965 31.5
## 288 6.209 293 7.14 0.4050 0.03871 31.3
## 289 6.315 293 7.60 0.4050 0.04590 45.6
## 290 6.565 293 9.51 0.4050 0.04297 22.9
## 291 6.861 245 3.33 0.4110 0.03502 27.9
## 292 7.148 245 3.56 0.4110 0.07886 27.7
## 293 6.630 245 4.70 0.4110 0.03615 23.4
## 294 6.127 289 8.58 0.4370 0.08265 18.4
## 295 6.009 289 10.40 0.4370 0.08199 42.3
## 296 6.678 289 6.27 0.4370 0.12932 31.1
## 297 6.549 289 7.39 0.4370 0.05372 51.0
## 298 5.790 289 15.84 0.4370 0.14103 58.0
## 299 6.345 358 4.97 0.4000 0.06466 20.1
## 300 7.041 358 4.74 0.4000 0.05561 10.0
## 301 6.871 358 6.07 0.4000 0.04417 47.4
## 302 6.590 329 9.50 0.4330 0.03537 40.4
## 303 6.495 329 8.67 0.4330 0.09266 18.4
## 304 6.982 329 4.86 0.4330 0.10000 17.7
## 305 7.236 222 6.93 0.4720 0.05515 41.1
## 306 6.616 222 8.93 0.4720 0.05479 58.1
## 307 7.420 222 6.47 0.4720 0.07503 71.9
## 308 6.849 222 7.53 0.4720 0.04932 70.3
## 309 6.635 304 4.54 0.5440 0.49298 82.5
## 310 5.972 304 9.97 0.5440 0.34940 76.7
## 311 4.973 304 12.64 0.5440 2.63548 37.8
## 312 6.122 304 5.98 0.5440 0.79041 52.8
## 313 6.023 304 11.72 0.5440 0.26169 90.4
## 314 6.266 304 7.90 0.5440 0.26938 82.8
## 315 6.567 304 9.28 0.5440 0.36920 87.3
## 316 5.705 304 11.50 0.5440 0.25356 77.7
## 317 5.914 304 18.33 0.5440 0.31827 83.2
## 318 5.782 304 15.94 0.5440 0.24522 71.7
## 319 6.382 304 10.36 0.5440 0.40202 67.2
## 320 6.113 304 12.73 0.5440 0.47547 58.8
## 321 6.426 287 7.20 0.4930 0.16760 52.3
## 322 6.376 287 6.87 0.4930 0.18159 54.3
## 323 6.041 287 7.70 0.4930 0.35114 49.9
## 324 5.708 287 11.74 0.4930 0.28392 74.3
## 325 6.415 287 6.12 0.4930 0.34109 40.1
## 326 6.431 287 5.08 0.4930 0.19186 14.7
## 327 6.312 287 6.15 0.4930 0.30347 28.9
## 328 6.083 287 12.79 0.4930 0.24103 43.7
## 329 5.868 430 9.97 0.4600 0.06617 25.8
## 330 6.333 430 7.34 0.4600 0.06724 17.2
## 331 6.144 430 9.09 0.4600 0.04544 32.2
## 332 5.706 304 12.43 0.4379 0.05023 28.4
## 333 6.031 304 7.83 0.4379 0.03466 23.3
## 334 6.316 224 5.68 0.5150 0.05083 38.1
## 335 6.310 224 6.75 0.5150 0.03738 38.5
## 336 6.037 224 8.01 0.5150 0.03961 34.5
## 337 5.869 224 9.80 0.5150 0.03427 46.3
## 338 5.895 224 10.56 0.5150 0.03041 59.6
## 339 6.059 224 8.51 0.5150 0.03306 37.3
## 340 5.985 224 9.74 0.5150 0.05497 45.4
## 341 5.968 224 9.29 0.5150 0.06151 58.5
## 342 7.241 284 5.49 0.4420 0.01301 49.3
## 343 6.540 422 8.65 0.5180 0.02498 59.7
## 344 6.696 370 7.18 0.4840 0.02543 56.4
## 345 6.874 370 4.61 0.4840 0.03049 28.1
## 346 6.014 352 10.53 0.4420 0.03113 48.5
## 347 5.898 352 12.67 0.4420 0.06162 52.3
## 348 6.516 351 6.36 0.4290 0.01870 27.7
## 349 6.635 280 5.99 0.4350 0.01501 29.7
## 350 6.939 335 5.89 0.4290 0.02899 34.5
## 351 6.490 335 5.98 0.4290 0.06211 44.4
## 352 6.579 411 5.49 0.4110 0.07950 35.9
## 353 5.884 411 7.79 0.4110 0.07244 18.5
## 354 6.728 187 4.50 0.4100 0.01709 36.1
## 355 5.663 334 8.05 0.4130 0.04301 21.9
## 356 5.936 334 5.57 0.4130 0.10659 19.5
## 357 6.212 666 17.60 0.7700 8.98296 97.4
## 358 6.395 666 13.27 0.7700 3.84970 91.0
## 359 6.127 666 11.48 0.7700 5.20177 83.4
## 360 6.112 666 12.67 0.7700 4.26131 81.3
## 361 6.398 666 7.79 0.7700 4.54192 88.0
## 362 6.251 666 14.19 0.7700 3.83684 91.1
## 363 5.362 666 10.19 0.7700 3.67822 96.2
## 364 5.803 666 14.64 0.7700 4.22239 89.0
## 365 8.780 666 5.29 0.7180 3.47428 82.9
## 366 3.561 666 7.12 0.7180 4.55587 87.9
## 367 4.963 666 14.00 0.7180 3.69695 91.4
## 368 3.863 666 13.33 0.6310 13.52220 100.0
## 369 4.970 666 3.26 0.6310 4.89822 100.0
## 370 6.683 666 3.73 0.6310 5.66998 96.8
## 371 7.016 666 2.96 0.6310 6.53876 97.5
## 372 6.216 666 9.53 0.6310 9.23230 100.0
## 373 5.875 666 8.88 0.6680 8.26725 89.6
## 374 4.906 666 34.77 0.6680 11.10810 100.0
## 375 4.138 666 37.97 0.6680 18.49820 100.0
## 376 7.313 666 13.44 0.6710 19.60910 97.9
## 377 6.649 666 23.24 0.6710 15.28800 93.3
## 378 6.794 666 21.24 0.6710 9.82349 98.8
## 379 6.380 666 23.69 0.6710 23.64820 96.2
## 380 6.223 666 21.78 0.6710 17.86670 100.0
## 381 6.968 666 17.21 0.6710 88.97620 91.9
## 382 6.545 666 21.08 0.6710 15.87440 99.1
## 383 5.536 666 23.60 0.7000 9.18702 100.0
## 384 5.520 666 24.56 0.7000 7.99248 100.0
## 385 4.368 666 30.63 0.7000 20.08490 91.2
## 386 5.277 666 30.81 0.7000 16.81180 98.1
## 387 4.652 666 28.28 0.7000 24.39380 100.0
## 388 5.000 666 31.99 0.7000 22.59710 89.5
## 389 4.880 666 30.62 0.7000 14.33370 100.0
## 390 5.390 666 20.85 0.7000 8.15174 98.9
## 391 5.713 666 17.11 0.7000 6.96215 97.0
## 392 6.051 666 18.76 0.7000 5.29305 82.5
## 393 5.036 666 25.68 0.7000 11.57790 97.0
## 394 6.193 666 15.17 0.6930 8.64476 92.6
## 395 5.887 666 16.35 0.6930 13.35980 94.7
## 396 6.471 666 17.12 0.6930 8.71675 98.8
## 397 6.405 666 19.37 0.6930 5.87205 96.0
## 398 5.747 666 19.92 0.6930 7.67202 98.9
## 399 5.453 666 30.59 0.6930 38.35180 100.0
## 400 5.852 666 29.97 0.6930 9.91655 77.8
## 401 5.987 666 26.77 0.6930 25.04610 100.0
## 402 6.343 666 20.32 0.6930 14.23620 100.0
## 403 6.404 666 20.31 0.6930 9.59571 100.0
## 404 5.349 666 19.77 0.6930 24.80170 96.0
## 405 5.531 666 27.38 0.6930 41.52920 85.4
## 406 5.683 666 22.98 0.6930 67.92080 100.0
## 407 4.138 666 23.34 0.6590 20.71620 100.0
## 408 5.608 666 12.13 0.6590 11.95110 100.0
## 409 5.617 666 26.40 0.5970 7.40389 97.9
## 410 6.852 666 19.78 0.5970 14.43830 100.0
## 411 5.757 666 10.11 0.5970 51.13580 100.0
## 412 6.657 666 21.22 0.5970 14.05070 100.0
## 413 4.628 666 34.37 0.5970 18.81100 100.0
## 414 5.155 666 20.08 0.5970 28.65580 100.0
## 415 4.519 666 36.98 0.6930 45.74610 100.0
## 416 6.434 666 29.05 0.6790 18.08460 100.0
## 417 6.782 666 25.79 0.6790 10.83420 90.8
## 418 5.304 666 26.64 0.6790 25.94060 89.1
## 419 5.957 666 20.62 0.6790 73.53410 100.0
## 420 6.824 666 22.74 0.7180 11.81230 76.5
## 421 6.411 666 15.02 0.7180 11.08740 100.0
## 422 6.006 666 15.70 0.7180 7.02259 95.3
## 423 5.648 666 14.10 0.6140 12.04820 87.6
## 424 6.103 666 23.29 0.6140 7.05042 85.1
## 425 5.565 666 17.16 0.5840 8.79212 70.6
## 426 5.896 666 24.39 0.6790 15.86030 95.4
## 427 5.837 666 15.69 0.5840 12.24720 59.7
## 428 6.202 666 14.52 0.6790 37.66190 78.7
## 429 6.193 666 21.52 0.6790 7.36711 78.1
## 430 6.380 666 24.08 0.6790 9.33889 95.6
## 431 6.348 666 17.64 0.5840 8.49213 86.1
## 432 6.833 666 19.69 0.5840 10.06230 94.3
## 433 6.425 666 12.03 0.5840 6.44405 74.8
## 434 6.436 666 16.22 0.7130 5.58107 87.9
## 435 6.208 666 15.17 0.7130 13.91340 95.0
## 436 6.629 666 23.27 0.7400 11.16040 94.6
## 437 6.461 666 18.05 0.7400 14.42080 93.3
## 438 6.152 666 26.45 0.7400 15.17720 100.0
## 439 5.935 666 34.02 0.7400 13.67810 87.9
## 440 5.627 666 22.88 0.7400 9.39063 93.9
## 441 5.818 666 22.11 0.7400 22.05110 92.4
## 442 6.406 666 19.52 0.7400 9.72418 97.2
## 443 6.219 666 16.59 0.7400 5.66637 100.0
## 444 6.485 666 18.85 0.7400 9.96654 100.0
## 445 5.854 666 23.79 0.7400 12.80230 96.6
## 446 6.459 666 23.98 0.7400 10.67180 94.8
## 447 6.341 666 17.79 0.7400 6.28807 96.4
## 448 6.251 666 16.44 0.7400 9.92485 96.6
## 449 6.185 666 18.13 0.7130 9.32909 98.7
## 450 6.417 666 19.31 0.7130 7.52601 98.3
## 451 6.749 666 17.44 0.7130 6.71772 92.6
## 452 6.655 666 17.73 0.7130 5.44114 98.2
## 453 6.297 666 17.27 0.7130 5.09017 91.8
## 454 7.393 666 16.74 0.7130 8.24809 99.3
## 455 6.728 666 18.71 0.7130 9.51363 94.1
## 456 6.525 666 18.13 0.7130 4.75237 86.5
## 457 5.976 666 19.01 0.7130 4.66883 87.9
## 458 5.936 666 16.94 0.7130 8.20058 80.3
## 459 6.301 666 16.23 0.7130 7.75223 83.7
## 460 6.081 666 14.70 0.7130 6.80117 84.4
## 461 6.701 666 16.42 0.7130 4.81213 90.0
## 462 6.376 666 14.65 0.7130 3.69311 88.4
## 463 6.317 666 13.99 0.7130 6.65492 83.0
## 464 6.513 666 10.29 0.7130 5.82115 89.9
## 465 6.209 666 13.22 0.6550 7.83932 65.4
## 466 5.759 666 14.13 0.6550 3.16360 48.2
## 467 5.952 666 17.15 0.6550 3.77498 84.7
## 468 6.003 666 21.32 0.5840 4.42228 94.5
## 469 5.926 666 18.13 0.5800 15.57570 71.0
## 470 5.713 666 14.76 0.5800 13.07510 56.7
## 471 6.167 666 16.29 0.5800 4.34879 84.0
## 472 6.229 666 12.87 0.5320 4.03841 90.7
## 473 6.437 666 14.36 0.5800 3.56868 75.0
## 474 6.980 666 11.66 0.6140 4.64689 67.6
## 475 5.427 666 18.14 0.5840 8.05579 95.4
## 476 6.162 666 24.10 0.5840 6.39312 97.4
## 477 6.484 666 18.68 0.6140 4.87141 93.6
## 478 5.304 666 24.91 0.6140 15.02340 97.3
## 479 6.185 666 18.03 0.6140 10.23300 96.7
## 480 6.229 666 13.11 0.6140 14.33370 88.0
## 481 6.242 666 10.74 0.5320 5.82401 64.7
## 482 6.750 666 7.74 0.5320 5.70818 74.9
## 483 7.061 666 7.01 0.5320 5.73116 77.0
## 484 5.762 666 10.42 0.5320 2.81838 40.3
## 485 5.871 666 13.34 0.5830 2.37857 41.9
## 486 6.312 666 10.58 0.5830 3.67367 51.9
## 487 6.114 666 14.98 0.5830 5.69175 79.8
## 488 5.905 666 11.45 0.5830 4.83567 53.2
## 489 5.454 711 18.06 0.6090 0.15086 92.7
## 490 5.414 711 23.97 0.6090 0.18337 98.3
## 491 5.093 711 29.68 0.6090 0.20746 98.0
## 492 5.983 711 18.07 0.6090 0.10574 98.8
## 493 5.983 711 13.35 0.6090 0.11132 83.5
## 494 5.707 391 12.01 0.5850 0.17331 54.0
## 495 5.926 391 13.59 0.5850 0.27957 42.6
## 496 5.670 391 17.60 0.5850 0.17899 28.8
## 497 5.390 391 21.14 0.5850 0.28960 72.9
## 498 5.794 391 14.10 0.5850 0.26838 70.6
## 499 6.019 391 12.92 0.5850 0.23912 65.3
## 500 5.569 391 15.10 0.5850 0.17783 73.5
## 501 6.027 391 14.33 0.5850 0.22438 79.7
## 502 6.593 273 9.67 0.5730 0.06263 69.1
## 503 6.120 273 9.08 0.5730 0.04527 76.7
## 504 6.976 273 5.64 0.5730 0.06076 91.0
## 505 6.794 273 6.48 0.5730 0.10959 89.3
## 506 6.030 273 7.88 0.5730 0.04741 80.8Ve bieu do tan xa cua dataset = dat
library('psych')
pairs.panels(dat)
Nhan xet:
- Cac tuong quan lon la: cor(nox,age) = 0.73 cor(tax,nox) = 0.67 cor(rm,lstat) = -0.61
- Tuong quan nho nhat la: cor(rm,crim) = -0.22
Cau 2: Xet cac mo hinh hoi quy don bien medv~rm, medv~tax, medv~lstat
Mo hinh medv~rm:
summary(lm(medv~rm))##
## Call:
## lm(formula = medv ~ rm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -23.346 -2.547 0.090 2.986 39.433
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -34.671 2.650 -13.08 <2e-16 ***
## rm 9.102 0.419 21.72 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.616 on 504 degrees of freedom
## Multiple R-squared: 0.4835, Adjusted R-squared: 0.4825
## F-statistic: 471.8 on 1 and 504 DF, p-value: < 2.2e-16Nhan xet:
- rm co Pr < 0.05 => co y nghia thong ke doi voi medv
- R binh phuong = 48% => mo hinh du bao duoc 48% do dao dong cua medv thuc te
- Mo hinh co phuong trinh: medv = -34,67 + 9,102.rm
- Khi rm tang 1 don vi thi medv tang 9,102 don vi.
Mo hinh medv~tax:
summary(lm(medv~tax))##
## Call:
## lm(formula = medv ~ tax)
##
## Residuals:
## Min 1Q Median 3Q Max
## -14.091 -5.173 -2.085 3.158 34.058
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 32.970654 0.948296 34.77 <2e-16 ***
## tax -0.025568 0.002147 -11.91 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.133 on 504 degrees of freedom
## Multiple R-squared: 0.2195, Adjusted R-squared: 0.218
## F-statistic: 141.8 on 1 and 504 DF, p-value: < 2.2e-16Nhan xet:
- tax co Pr < 0.05 => co y nghia thong ke doi voi medv
- R binh phuong = 21% => mo hinh du bao duoc 21% do dao dong cua medv thuc te
- Mo hinh co phuong trinh: medv = 32,97 - 0,03.tax
- Khi tax tang 1 don vi thi medv giam 0,03 don vi.
Mo hinh medv~lstat:
summary(lm(medv~lstat))##
## Call:
## lm(formula = medv ~ lstat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.168 -3.990 -1.318 2.034 24.500
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 34.55384 0.56263 61.41 <2e-16 ***
## lstat -0.95005 0.03873 -24.53 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.216 on 504 degrees of freedom
## Multiple R-squared: 0.5441, Adjusted R-squared: 0.5432
## F-statistic: 601.6 on 1 and 504 DF, p-value: < 2.2e-16Nhan xet:
- lsat co Pr < 0.05 => co y nghia thong ke doi voi medv
- R binh phuong = 54% => mo hinh du bao duoc 54% do dao dong cua medv thuc te
- Mo hinh co phuong trinh: medv = 34,55 - 0,95.lstat
- Khi lstat tang 1 don vi thi medv giam 0,95 do vi. Nghia la o khu vuc co dia vi xa hoi thap (lstat cao), gia nha giam.
Cau 3: Xet mo hinh hoi quy da bien giua medv & cac bien da neu o cau 1
summary(lm(medv~rm+tax+lstat+nox+crim+age))##
## Call:
## lm(formula = medv ~ rm + tax + lstat + nox + crim + age)
##
## Residuals:
## Min 1Q Median 3Q Max
## -16.557 -3.381 -1.065 1.980 29.691
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.390107 3.394655 -0.409 0.68235
## rm 5.094850 0.448100 11.370 < 2e-16 ***
## tax -0.006326 0.002186 -2.895 0.00396 **
## lstat -0.585858 0.057036 -10.272 < 2e-16 ***
## nox 1.636011 3.589663 0.456 0.64876
## crim -0.059704 0.035523 -1.681 0.09344 .
## age 0.017608 0.013538 1.301 0.19398
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.45 on 499 degrees of freedom
## Multiple R-squared: 0.6531, Adjusted R-squared: 0.6489
## F-statistic: 156.6 on 6 and 499 DF, p-value: < 2.2e-16Nhan xet:
- rm, lstat & tax deu co Pr < 0.05 => co y nghia thong ke doi voi medv
- nox, crim & age deu co Pr > 0.05 => KHONG co y nghia thong ke doi voi medv
- Mo hinh co phuong trinh: medv = -1,39 + 5,09.rm - 0,006.tax - 0,59.lstat
- Khi co su dong gop cua cac bien co y nghia thong ke, R-squared = 65%, nghia la mo hinh giai thich duoc co 65% do dao dong cua medv thuc te.
Cau 4: Xet cac truong hop co da cong tuyen => Mo hinh du bao chinh xac la gi?
pairs.panels(dat)
Theo bieu do tan xa, ta thay:
Cac he so tuong quan kha lon nen giua cac bien co xay ra da cong tuyen:
- Cong tuyen giua rm & tax = -0.29
- Cong tuyen giua rm & lstat = -0.61
- Cong tuyen giua tax & lstat = 0.54
=> phuong trinh medv = -1,39 + 5,09.rm - 0,006.tax - 0,59.lstat KHONG THE du bao duoc chinh xac gia tri cua medv.
KET LUAN: Gia nha (medv) tang manh neu can nha co nhieu phong (rm), nguoc lai gia nha se giam o khu vuc co dia vi xa hoi cang thap (lstat).
Vi du: rm = 6.57, tax = 296, lstat = 4.98 thi:
medv = 27.3371
So voi gia tri thuc te la medv = 24.0—THE END—