VIDEO 2
# Read in data
setwd('C:/Users/daria.alekseeva/Documents/Edx/Trees/')
boston = read.csv("boston.csv")
str(boston)
## 'data.frame': 506 obs. of 16 variables:
## $ TOWN : Factor w/ 92 levels "Arlington","Ashland",..: 54 77 77 46 46 46 69 69 69 69 ...
## $ TRACT : int 2011 2021 2022 2031 2032 2033 2041 2042 2043 2044 ...
## $ LON : num -71 -71 -70.9 -70.9 -70.9 ...
## $ LAT : num 42.3 42.3 42.3 42.3 42.3 ...
## $ MEDV : num 24 21.6 34.7 33.4 36.2 28.7 22.9 22.1 16.5 18.9 ...
## $ CRIM : num 0.00632 0.02731 0.02729 0.03237 0.06905 ...
## $ ZN : num 18 0 0 0 0 0 12.5 12.5 12.5 12.5 ...
## $ INDUS : num 2.31 7.07 7.07 2.18 2.18 2.18 7.87 7.87 7.87 7.87 ...
## $ CHAS : int 0 0 0 0 0 0 0 0 0 0 ...
## $ NOX : num 0.538 0.469 0.469 0.458 0.458 0.458 0.524 0.524 0.524 0.524 ...
## $ RM : num 6.58 6.42 7.18 7 7.15 ...
## $ AGE : num 65.2 78.9 61.1 45.8 54.2 58.7 66.6 96.1 100 85.9 ...
## $ DIS : num 4.09 4.97 4.97 6.06 6.06 ...
## $ RAD : int 1 2 2 3 3 3 5 5 5 5 ...
## $ TAX : int 296 242 242 222 222 222 311 311 311 311 ...
## $ PTRATIO: num 15.3 17.8 17.8 18.7 18.7 18.7 15.2 15.2 15.2 15.2 ...
# Plot observations
plot(boston$LON, boston$LAT)
# Tracts alongside the Charles River
points(boston$LON[boston$CHAS==1], boston$LAT[boston$CHAS==1], col="blue", pch=19)
# Plot MIT
points(boston$LON[boston$TRACT==3531],boston$LAT[boston$TRACT==3531],col="red", pch=20)
# Plot polution
summary(boston$NOX)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.3850 0.4490 0.5380 0.5547 0.6240 0.8710
points(boston$LON[boston$NOX>=0.55], boston$LAT[boston$NOX>=0.55], col="green", pch=20)
# Plot prices
plot(boston$LON, boston$LAT)
summary(boston$MEDV)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 5.00 17.02 21.20 22.53 25.00 50.00
points(boston$LON[boston$MEDV>=21.2], boston$LAT[boston$MEDV>=21.2], col="red", pch=20)
# VIDEO 3
# Linear Regression using LAT and LON
plot(boston$LAT, boston$MEDV)
plot(boston$LON, boston$MEDV)
latlonlm = lm(MEDV ~ LAT + LON, data=boston)
summary(latlonlm)
##
## Call:
## lm(formula = MEDV ~ LAT + LON, data = boston)
##
## Residuals:
## Min 1Q Median 3Q Max
## -16.460 -5.590 -1.299 3.695 28.129
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3178.472 484.937 -6.554 1.39e-10 ***
## LAT 8.046 6.327 1.272 0.204
## LON -40.268 5.184 -7.768 4.50e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.693 on 503 degrees of freedom
## Multiple R-squared: 0.1072, Adjusted R-squared: 0.1036
## F-statistic: 30.19 on 2 and 503 DF, p-value: 4.159e-13
# Visualize regression output
plot(boston$LON, boston$LAT)
points(boston$LON[boston$MEDV>=21.2], boston$LAT[boston$MEDV>=21.2], col="red", pch=20)
latlonlm$fitted.values
## 1 2 3 4 5 6 7 8
## 18.75633 18.81648 18.21651 17.97483 17.77344 17.60024 18.32916 18.49416
## 9 10 11 12 13 14 15 16
## 18.32904 18.20015 18.44176 18.81222 19.00560 19.43658 19.69836 19.93589
## 17 18 19 20 21 22 23 24
## 20.39492 19.92388 20.48766 20.26703 20.08099 20.05277 19.85547 19.67426
## 25 26 27 28 29 30 31 32
## 19.54619 19.35208 19.20306 19.16685 19.03801 18.78031 19.43265 19.29173
## 33 34 35 36 37 38 39 40
## 19.61388 19.91187 19.79915 20.68910 21.04745 20.98293 21.63527 21.55856
## 41 42 43 44 45 46 47 48
## 22.33163 21.37316 21.24036 20.21512 19.75853 19.88344 19.58142 19.25924
## 49 50 51 52 53 54 55 56
## 19.25115 19.18508 19.23088 19.74790 19.60931 20.38652 22.21046 20.07213
## 57 58 59 60 61 62 63 64
## 18.70708 18.66683 18.82408 18.77184 18.40938 18.33295 18.02687 17.51943
## 65 66 67 68 69 70 71 72
## 15.65495 23.10462 24.13141 24.84590 25.60131 25.61752 25.93170 25.34631
## 73 74 75 76 77 78 79 80
## 26.20561 25.81913 25.29164 24.85675 24.42188 23.90640 24.53454 24.63514
## 81 82 83 84 85 86 87 88
## 23.75323 23.82969 23.85779 23.38269 22.72237 22.94390 22.29957 22.40842
## 89 90 91 92 93 94 95 96
## 22.45762 22.14675 21.91325 22.41258 22.92793 23.39494 23.27825 23.80985
## 97 98 99 100 101 102 103 104
## 24.17226 24.28506 24.63140 23.89449 23.25432 23.74970 23.81005 23.62081
## 105 106 107 108 109 110 111 112
## 23.29062 23.13361 22.97737 22.72687 22.74697 22.97647 22.86770 22.52944
## 113 114 115 116 117 118 119 120
## 22.52548 22.31604 22.13247 21.99392 22.06474 21.77238 21.74020 21.37777
## 121 122 123 124 125 126 127 128
## 21.49303 21.78858 22.02217 21.96582 21.72822 21.52770 21.78464 22.54575
## 129 130 131 132 133 134 135 136
## 22.74307 22.99111 23.22626 23.46786 23.45175 23.66916 23.51215 23.43729
## 137 138 139 140 141 142 143 144
## 23.12160 22.92429 22.84380 22.65451 22.46283 22.52568 22.23739 22.40088
## 145 146 147 148 149 150 151 152
## 22.34452 22.45326 22.67069 22.53941 22.60221 22.64652 22.81242 22.79553
## 153 154 155 156 157 158 159 160
## 22.63851 22.84389 22.92200 22.98483 22.97271 23.13372 23.02100 22.92276
## 161 162 163 164 165 166 167 168
## 23.11686 23.31252 23.42771 23.60892 24.03575 23.66526 23.47196 23.89072
## 169 170 171 172 173 174 175 176
## 23.37207 23.52911 23.68372 23.62894 23.96395 23.93091 23.86243 24.37376
## 177 178 179 180 181 182 183 184
## 25.09862 24.80630 24.38995 24.48101 24.41018 24.24272 24.40379 24.65586
## 185 186 187 188 189 190 191 192
## 24.87733 25.13904 24.97145 25.49323 26.23821 26.48860 25.58575 26.72127
## 193 194 195 196 197 198 199 200
## 26.15347 27.07142 27.53046 28.15904 29.56023 30.37365 29.78157 30.29335
## 201 202 203 204 205 206 207 208
## 30.89753 28.88834 28.88817 28.39678 28.18598 26.42353 26.41397 26.34152
## 209 210 211 212 213 214 215 216
## 26.35525 26.05888 26.04683 25.85673 25.70288 25.94843 25.52159 25.36218
## 217 218 219 220 221 222 223 224
## 25.00625 24.54316 24.05995 24.54320 24.66565 25.13194 25.26726 25.13756
## 225 226 227 228 229 230 231 232
## 24.60370 24.18094 25.03862 24.75439 24.43473 24.76255 25.26424 25.24407
## 233 234 235 236 237 238 239 240
## 25.72003 25.55405 25.55558 25.79638 26.19426 26.15406 28.30049 28.21593
## 241 242 243 244 245 246 247 248
## 27.75302 28.44966 28.80955 29.24691 29.63356 30.18767 30.42681 29.83324
## 249 250 251 252 253 254 255 256
## 30.20688 29.95153 29.63737 29.91678 30.88568 31.20960 31.44166 30.54133
## 257 258 259 260 261 262 263 264
## 28.66323 22.91885 23.11536 23.26677 23.37955 23.32319 23.48831 23.12993
## 265 266 267 268 269 270 271 272
## 23.00909 22.94468 23.01719 23.48836 23.91107 23.70209 23.15454 23.39217
## 273 274 275 276 277 278 279 280
## 23.63371 24.44305 25.11943 25.46811 25.48752 25.92879 25.59288 25.98907
## 281 282 283 284 285 286 287 288
## 26.70586 27.45326 27.06033 26.66993 26.65411 27.91862 26.91216 25.10000
## 289 290 291 292 293 294 295 296
## 24.60860 25.54682 25.08756 25.00528 23.87704 23.79102 24.24758 24.72601
## 297 298 299 300 301 302 303 304
## 24.56256 24.21390 23.93226 23.01827 23.27587 22.80456 21.85417 22.96544
## 305 306 307 308 309 310 311 312
## 21.55585 22.03901 21.60809 20.90341 20.32355 20.61345 20.57708 20.25089
## 313 314 315 316 317 318 319 320
## 20.46440 20.11653 19.74773 18.96246 19.22830 19.82432 20.12628 20.53701
## 321 322 323 324 325 326 327 328
## 19.89691 19.49419 19.21390 18.95456 19.11170 19.37440 19.44197 19.89697
## 329 330 331 332 333 334 335 336
## 20.53328 21.11313 20.31192 19.67577 19.07574 18.49177 17.91995 18.23393
## 337 338 339 340 341 342 343 344
## 18.58014 17.93585 18.14436 18.36659 18.31661 15.16523 16.38123 17.16657
## 345 346 347 348 349 350 351 352
## 16.78823 16.96581 17.17110 16.23690 16.11270 13.72375 12.71715 12.29463
## 353 354 355 356 357 358 359 360
## 11.34041 12.06130 13.01563 12.81849 23.60656 24.04794 24.26138 23.92718
## 361 362 363 364 365 366 367 368
## 23.79674 23.68957 23.45200 23.72980 22.58058 22.58221 22.34222 22.22785
## 369 370 371 372 373 374 375 376
## 22.14326 22.22781 21.94108 21.93382 21.87098 21.65754 21.66964 21.79684
## 377 378 379 380 381 382 383 384
## 21.70421 21.86931 21.93617 21.95789 22.21961 22.01023 21.28298 21.20890
## 385 386 387 388 389 390 391 392
## 21.30154 21.24358 21.22987 21.19120 21.11629 21.02849 20.80619 20.53234
## 393 394 395 396 397 398 399 400
## 21.09620 20.80642 20.92563 21.00858 21.16724 21.15191 21.12448 21.48050
## 401 402 403 404 405 406 407 408
## 21.44749 21.34601 21.32429 21.44671 21.51596 21.46034 21.85567 21.91777
## 409 410 411 412 413 414 415 416
## 21.92585 22.00638 22.04664 22.12558 22.04264 21.95407 21.80510 21.92029
## 417 418 419 420 421 422 423 424
## 22.01853 22.13689 22.23113 22.48482 22.60643 22.75782 22.77960 22.57667
## 425 426 427 428 429 430 431 432
## 22.43736 22.42283 22.32218 22.27706 22.17560 22.01454 22.24007 22.06290
## 433 434 435 436 437 438 439 440
## 22.10238 21.97033 21.91152 21.87123 21.87201 21.85105 21.86795 21.56755
## 441 442 443 444 445 446 447 448
## 21.35816 21.39446 21.40651 21.56114 21.69239 21.74879 21.59015 21.48709
## 449 450 451 452 453 454 455 456
## 21.59180 21.72467 21.82537 21.61196 21.32605 21.55157 21.77144 22.00257
## 457 458 459 460 461 462 463 464
## 21.99455 21.95834 21.78922 21.60801 21.63859 21.33012 21.12881 21.30601
## 465 466 467 468 469 470 471 472
## 21.64832 22.05905 22.08721 22.60660 22.68721 22.68315 22.84829 23.20505
## 473 474 475 476 477 478 479 480
## 23.27911 22.94481 22.20387 22.08625 22.30451 22.18770 22.30287 22.77962
## 481 482 483 484 485 486 487 488
## 23.97576 23.73415 23.48051 23.73667 22.99336 22.70752 22.64302 22.42955
## 489 490 491 492 493 494 495 496
## 21.16374 21.31355 21.40855 21.07754 21.68151 21.00096 21.03154 20.98882
## 497 498 499 500 501 502 503 504
## 20.58857 20.31154 20.69332 20.41146 20.10948 19.81316 19.98473 20.12569
## 505 506
## 19.81563 19.59015
points(boston$LON[latlonlm$fitted.values >= 21.2], boston$LAT[latlonlm$fitted.values >= 21.2], col="blue", pch="$")
# Video 4
# Load CART packages
library(rpart)
library(rpart.plot)
# CART model
latlontree = rpart(MEDV ~ LAT + LON, data=boston)
prp(latlontree)
# Visualize output
plot(boston$LON, boston$LAT)
points(boston$LON[boston$MEDV>=21.2], boston$LAT[boston$MEDV>=21.2], col="red", pch=20)
fittedvalues = predict(latlontree)
points(boston$LON[fittedvalues>21.2], boston$LAT[fittedvalues>=21.2], col="blue", pch="$")
# Simplify tree by increasing minbucket
latlontree = rpart(MEDV ~ LAT + LON, data=boston, minbucket=50)
plot(latlontree)
text(latlontree)
# Visualize Output
plot(boston$LON,boston$LAT)
abline(v=-71.07)
abline(h=42.21)
abline(h=42.17)
points(boston$LON[boston$MEDV>=21.2], boston$LAT[boston$MEDV>=21.2], col="red", pch=20)
# VIDEO 5
# Let's use all the variables
# Split the data
library(caTools)
set.seed(123)
split = sample.split(boston$MEDV, SplitRatio = 0.7)
train = subset(boston, split==TRUE)
test = subset(boston, split==FALSE)
# Create linear regression
linreg = lm(MEDV ~ LAT + LON + CRIM + ZN + INDUS + CHAS + NOX + RM + AGE + DIS + RAD + TAX + PTRATIO, data=train)
summary(linreg)
##
## Call:
## lm(formula = MEDV ~ LAT + LON + CRIM + ZN + INDUS + CHAS + NOX +
## RM + AGE + DIS + RAD + TAX + PTRATIO, data = train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -14.511 -2.712 -0.676 1.793 36.883
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.523e+02 4.367e+02 -0.578 0.5638
## LAT 1.544e+00 5.192e+00 0.297 0.7664
## LON -2.987e+00 4.786e+00 -0.624 0.5329
## CRIM -1.808e-01 4.390e-02 -4.118 4.77e-05 ***
## ZN 3.250e-02 1.877e-02 1.731 0.0843 .
## INDUS -4.297e-02 8.473e-02 -0.507 0.6124
## CHAS 2.904e+00 1.220e+00 2.380 0.0178 *
## NOX -2.161e+01 5.414e+00 -3.992 7.98e-05 ***
## RM 6.284e+00 4.827e-01 13.019 < 2e-16 ***
## AGE -4.430e-02 1.785e-02 -2.482 0.0135 *
## DIS -1.577e+00 2.842e-01 -5.551 5.63e-08 ***
## RAD 2.451e-01 9.728e-02 2.519 0.0122 *
## TAX -1.112e-02 5.452e-03 -2.040 0.0421 *
## PTRATIO -9.835e-01 1.939e-01 -5.072 6.38e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.595 on 350 degrees of freedom
## Multiple R-squared: 0.665, Adjusted R-squared: 0.6525
## F-statistic: 53.43 on 13 and 350 DF, p-value: < 2.2e-16
# Make predictions
linreg.pred = predict(linreg, newdata=test)
linreg.sse = sum((linreg.pred - test$MEDV)^2)
linreg.sse
## [1] 3037.088
# Create a CART model
tree = rpart(MEDV ~ LAT + LON + CRIM + ZN + INDUS + CHAS + NOX + RM + AGE + DIS + RAD + TAX + PTRATIO, data=train)
prp(tree)
# Make predictions
tree.pred = predict(tree, newdata=test)
tree.sse = sum((tree.pred - test$MEDV)^2)
tree.sse
## [1] 4328.988
# Video 7
# Load libraries for cross-validation
library(caret)
## Loading required package: lattice
## Loading required package: ggplot2
library(e1071)
# Number of folds
tr.control = trainControl(method = "cv", number = 10)
# cp values
cp.grid = expand.grid( .cp = (0:10)*0.001)
# What did we just do?
1*0.001
## [1] 0.001
10*0.001
## [1] 0.01
0:10
## [1] 0 1 2 3 4 5 6 7 8 9 10
0:10 * 0.001
## [1] 0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010
# Cross-validation
tr = train(MEDV ~ LAT + LON + CRIM + ZN + INDUS + CHAS + NOX + RM + AGE + DIS + RAD + TAX + PTRATIO, data = train, method = "rpart", trControl = tr.control, tuneGrid = cp.grid)
tr
## CART
##
## 364 samples
## 15 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 328, 327, 329, 328, 327, 328, ...
## Resampling results across tuning parameters:
##
## cp RMSE Rsquared RMSE SD Rsquared SD
## 0.000 4.795661 0.7251433 1.839513 0.1726678
## 0.001 4.808653 0.7241589 1.852793 0.1750635
## 0.002 4.843092 0.7203932 1.834373 0.1745897
## 0.003 4.855853 0.7187000 1.848917 0.1792498
## 0.004 4.992709 0.7032541 1.824035 0.1805318
## 0.005 4.984651 0.7008777 1.850695 0.1867995
## 0.006 5.018776 0.6955937 1.872769 0.1916284
## 0.007 4.994024 0.6980549 1.877489 0.1906712
## 0.008 5.017056 0.6951007 1.959210 0.1966926
## 0.009 4.989958 0.6965547 1.994557 0.1986186
## 0.010 4.989958 0.6965547 1.994557 0.1986186
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was cp = 0.
# Extract tree
best.tree = tr$finalModel
prp(best.tree)
# Make predictions
best.tree.pred = predict(best.tree, newdata=test)
best.tree.sse = sum((best.tree.pred - test$MEDV)^2)
best.tree.sse
## [1] 3660.149