Lab 5
INFO-H 415/515
2024-02-20
Lab 5
library(ISLR2)## Warning: package 'ISLR2' was built under R version 4.3.2library(corrplot)## Warning: package 'corrplot' was built under R version 4.3.2## corrplot 0.92 loadeddata(Weekly)
weekly = as.data.frame(Weekly)
# Removing missing values
# weekly <- na.omit(weekly)
summary(weekly)## Year Lag1 Lag2 Lag3
## Min. :1990 Min. :-18.1950 Min. :-18.1950 Min. :-18.1950
## 1st Qu.:1995 1st Qu.: -1.1540 1st Qu.: -1.1540 1st Qu.: -1.1580
## Median :2000 Median : 0.2410 Median : 0.2410 Median : 0.2410
## Mean :2000 Mean : 0.1506 Mean : 0.1511 Mean : 0.1472
## 3rd Qu.:2005 3rd Qu.: 1.4050 3rd Qu.: 1.4090 3rd Qu.: 1.4090
## Max. :2010 Max. : 12.0260 Max. : 12.0260 Max. : 12.0260
## Lag4 Lag5 Volume Today
## Min. :-18.1950 Min. :-18.1950 Min. :0.08747 Min. :-18.1950
## 1st Qu.: -1.1580 1st Qu.: -1.1660 1st Qu.:0.33202 1st Qu.: -1.1540
## Median : 0.2380 Median : 0.2340 Median :1.00268 Median : 0.2410
## Mean : 0.1458 Mean : 0.1399 Mean :1.57462 Mean : 0.1499
## 3rd Qu.: 1.4090 3rd Qu.: 1.4050 3rd Qu.:2.05373 3rd Qu.: 1.4050
## Max. : 12.0260 Max. : 12.0260 Max. :9.32821 Max. : 12.0260
## Direction
## Down:484
## Up :605
##
##
##
## Complete the following exercises from Introduction to Statistical Learning
Chapter 4: (13) and (14)
Question 13
pairs(weekly)
The pairplot shows:
- Year and Volume have a high correlation
b.
logmodel = glm(as.factor(Direction) ~ Lag1 + Lag2 + Lag3 + Lag4 + Lag5 + Volume, data = weekly, family = "binomial")
summary(logmodel)##
## Call:
## glm(formula = as.factor(Direction) ~ Lag1 + Lag2 + Lag3 + Lag4 +
## Lag5 + Volume, family = "binomial", data = weekly)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.26686 0.08593 3.106 0.0019 **
## Lag1 -0.04127 0.02641 -1.563 0.1181
## Lag2 0.05844 0.02686 2.175 0.0296 *
## Lag3 -0.01606 0.02666 -0.602 0.5469
## Lag4 -0.02779 0.02646 -1.050 0.2937
## Lag5 -0.01447 0.02638 -0.549 0.5833
## Volume -0.02274 0.03690 -0.616 0.5377
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1496.2 on 1088 degrees of freedom
## Residual deviance: 1486.4 on 1082 degrees of freedom
## AIC: 1500.4
##
## Number of Fisher Scoring iterations: 4Only Lag2 is statistically significant (p = 0.0296). All other are statistically non-significant including Volume.
c.
probs = predict(logmodel, type="response")
preds = rep("Down", 1089)
preds[probs > 0.5] = "Up"
table(preds, Weekly$Direction)##
## preds Down Up
## Down 54 48
## Up 430 557The confusion matrix shows that there is a good prediction on UP and a bad prediction for DOWN.
d.
datatrain = weekly[weekly$Year<2009,]
model = glm(Direction ~ Lag2, data= datatrain, family = "binomial")
summary(model)
##
## Call:
## glm(formula = Direction ~ Lag2, family = "binomial", data = datatrain)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.20326 0.06428 3.162 0.00157 **
## Lag2 0.05810 0.02870 2.024 0.04298 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1354.7 on 984 degrees of freedom
## Residual deviance: 1350.5 on 983 degrees of freedom
## AIC: 1354.5
##
## Number of Fisher Scoring iterations: 4
datatest = weekly[weekly$Year>=2009, ]
probs = predict(model, newdata = datatest, type="response")
direction = ifelse(probs>0.5, "Up", "Down")
direction_test = datatest$Direction
confusionmatrix = table(direction, direction_test)
confusionmatrix
## direction_test
## direction Down Up
## Down 9 5
## Up 34 56
accuracy = mean(direction == direction_test)
accuracy
## [1] 0.625Accuracy = Diagonals/Total = 0.625
e.
library(MASS)
##
## Attaching package: 'MASS'
## The following object is masked from 'package:ISLR2':
##
## Boston
datatrain = weekly[weekly$Year<2009,]
model = lda(Direction ~ Lag2, data= datatrain, family=binomial, subset = (Year < 2005))
model
## Call:
## lda(Direction ~ Lag2, data = datatrain, family = binomial, subset = (Year <
## 2005))
##
## Prior probabilities of groups:
## Down Up
## 0.4420103 0.5579897
##
## Group means:
## Lag2
## Down 0.05883965
## Up 0.29473441
##
## Coefficients of linear discriminants:
## LD1
## Lag2 0.4675613
datatest = weekly[weekly$Year>=2009, ]
probs = predict(model, newdata = datatest, type="response")
direction = probs$class
direction_test = datatest$Direction
confusionmatrix = table(direction, direction_test)
confusionmatrix
## direction_test
## direction Down Up
## Down 6 3
## Up 37 58
accuracy = mean(direction == direction_test)
accuracy
## [1] 0.6153846f.
datatrain = weekly[weekly$Year<2009,]
model = qda(Direction ~ Lag2, data= datatrain, subset = (Year < 2009))
model
## Call:
## qda(Direction ~ Lag2, data = datatrain, subset = (Year < 2009))
##
## Prior probabilities of groups:
## Down Up
## 0.4477157 0.5522843
##
## Group means:
## Lag2
## Down -0.03568254
## Up 0.26036581
datatest = weekly[weekly$Year>=2009, ]
probs = predict(model, newdata = datatest, type="response")
direction = probs$class
direction_test = datatest$Direction
confusionmatrix = table(direction, direction_test)
confusionmatrix
## direction_test
## direction Down Up
## Down 0 0
## Up 43 61
accuracy = mean(direction == direction_test)
accuracy
## [1] 0.5865385g.
library(class)
datatrain = weekly[weekly$Year<2009,]$Lag2
datatest = weekly[weekly$Year>=2009, ]$Lag2
train.Direction = weekly[weekly$Year<2009,]$Direction
cat(dim(datatrain), dim(datatest), dim(train.Direction))
model = knn(train = matrix(datatrain), test = matrix(datatest), cl = train.Direction, k = 1)
model
## [1] Up Up Down Down Down Up Up Down Up Down Up Down Up Up Up
## [16] Down Down Down Down Up Down Down Up Down Down Down Up Down Down Up
## [31] Up Up Up Down Up Up Up Down Down Up Down Down Down Down Up
## [46] Down Down Up Down Up Up Up Down Down Up Up Down Up Down Down
## [61] Up Down Down Down Down Down Down Up Up Up Up Up Down Up Up
## [76] Up Up Up Down Up Up Up Down Down Down Up Up Up Up Up
## [91] Up Up Down Down Down Up Down Up Down Up Up Down Down Up
## Levels: Down Up
direction_test = weekly[weekly$Year>=2009, ]$Direction
confusionmatrix = table(model, direction_test)
confusionmatrix
## direction_test
## model Down Up
## Down 21 29
## Up 22 32
accuracy = mean(direction == direction_test)
accuracy
## [1] 0.5865385h.
library(e1071)
## Warning: package 'e1071' was built under R version 4.3.2
datatrain = weekly[weekly$Year<2009,]
model = naiveBayes(Direction ~ Lag2, data= datatrain, subset = (Year < 2009))
model
##
## Naive Bayes Classifier for Discrete Predictors
##
## Call:
## naiveBayes.default(x = X, y = Y, laplace = laplace)
##
## A-priori probabilities:
## Y
## Down Up
## 0.4477157 0.5522843
##
## Conditional probabilities:
## Lag2
## Y [,1] [,2]
## Down -0.03568254 2.199504
## Up 0.26036581 2.317485
datatest = weekly[weekly$Year>=2009, ]
probs = predict(model, newdata = datatest)
direction_test = datatest$Direction
confusionmatrix = table(probs, direction_test)
confusionmatrix
## direction_test
## probs Down Up
## Down 0 0
## Up 43 61
accuracy = mean(direction == direction_test)
accuracy
## [1] 0.5865385i.
Logistic Regression = 62.50% is the highest accuracy from all the model. Logistic regression is the best for this use case.
j.
Sticking to Logistic regression We add more predictors. Given that Lag2 is the strongest predictor with Lag1 being close, we try them first.
datatrain = weekly[weekly$Year<2009,]
model = glm(Direction ~ Lag2 + Lag1, data= datatrain, family = "binomial")
summary(model)
##
## Call:
## glm(formula = Direction ~ Lag2 + Lag1, family = "binomial", data = datatrain)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.21109 0.06456 3.269 0.00108 **
## Lag2 0.05384 0.02905 1.854 0.06379 .
## Lag1 -0.05421 0.02886 -1.878 0.06034 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1354.7 on 984 degrees of freedom
## Residual deviance: 1347.0 on 982 degrees of freedom
## AIC: 1353
##
## Number of Fisher Scoring iterations: 4
datatest = weekly[weekly$Year>=2009, ]
probs = predict(model, newdata = datatest, type="response")
direction = ifelse(probs>0.5, "Up", "Down")
direction_test = datatest$Direction
confusionmatrix = table(direction, direction_test)
confusionmatrix
## direction_test
## direction Down Up
## Down 7 8
## Up 36 53
accuracy = mean(direction == direction_test)
accuracy
## [1] 0.5769231That reduced accuracy. Next we try QDA.
datatrain = weekly[weekly$Year<2009,]
model = qda(Direction ~ Lag2 + Lag1, data= datatrain, subset = (Year < 2009))
model
## Call:
## qda(Direction ~ Lag2 + Lag1, data = datatrain, subset = (Year <
## 2009))
##
## Prior probabilities of groups:
## Down Up
## 0.4477157 0.5522843
##
## Group means:
## Lag2 Lag1
## Down -0.03568254 0.289444444
## Up 0.26036581 -0.009213235
datatest = weekly[weekly$Year>=2009, ]
probs = predict(model, newdata = datatest, type="response")
direction = probs$class
direction_test = datatest$Direction
confusionmatrix = table(direction, direction_test)
confusionmatrix
## direction_test
## direction Down Up
## Down 7 10
## Up 36 51
accuracy = mean(direction == direction_test)
accuracy
## [1] 0.5576923This also does not result in a better solution. Next we try K = 3
datatrain = weekly[weekly$Year<2009,]$Lag2
datatest = weekly[weekly$Year>=2009, ]$Lag2
train.Direction = weekly[weekly$Year<2009,]$Direction
cat(dim(datatrain), dim(datatest), dim(train.Direction))
model = knn(train = matrix(datatrain), test = matrix(datatest), cl = train.Direction, k = 3)
direction_test = weekly[weekly$Year>=2009, ]$Direction
confusionmatrix = table(model, direction_test)
confusionmatrix
## direction_test
## model Down Up
## Down 15 19
## Up 28 42
accuracy = mean(direction == direction_test)
accuracy
## [1] 0.5576923This also does not result in a higher accuracy. Accuracy becomes constant or minimally different with increase in K.
Question 14
data(Auto)
auto = as.data.frame(Auto)
auto## mpg cylinders displacement horsepower weight acceleration year origin
## 1 18.0 8 307.0 130 3504 12.0 70 1
## 2 15.0 8 350.0 165 3693 11.5 70 1
## 3 18.0 8 318.0 150 3436 11.0 70 1
## 4 16.0 8 304.0 150 3433 12.0 70 1
## 5 17.0 8 302.0 140 3449 10.5 70 1
## 6 15.0 8 429.0 198 4341 10.0 70 1
## 7 14.0 8 454.0 220 4354 9.0 70 1
## 8 14.0 8 440.0 215 4312 8.5 70 1
## 9 14.0 8 455.0 225 4425 10.0 70 1
## 10 15.0 8 390.0 190 3850 8.5 70 1
## 11 15.0 8 383.0 170 3563 10.0 70 1
## 12 14.0 8 340.0 160 3609 8.0 70 1
## 13 15.0 8 400.0 150 3761 9.5 70 1
## 14 14.0 8 455.0 225 3086 10.0 70 1
## 15 24.0 4 113.0 95 2372 15.0 70 3
## 16 22.0 6 198.0 95 2833 15.5 70 1
## 17 18.0 6 199.0 97 2774 15.5 70 1
## 18 21.0 6 200.0 85 2587 16.0 70 1
## 19 27.0 4 97.0 88 2130 14.5 70 3
## 20 26.0 4 97.0 46 1835 20.5 70 2
## 21 25.0 4 110.0 87 2672 17.5 70 2
## 22 24.0 4 107.0 90 2430 14.5 70 2
## 23 25.0 4 104.0 95 2375 17.5 70 2
## 24 26.0 4 121.0 113 2234 12.5 70 2
## 25 21.0 6 199.0 90 2648 15.0 70 1
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## 217 31.5 4 98.0 68 2045 18.5 77 3
## 218 30.0 4 111.0 80 2155 14.8 77 1
## 219 36.0 4 79.0 58 1825 18.6 77 2
## 220 25.5 4 122.0 96 2300 15.5 77 1
## 221 33.5 4 85.0 70 1945 16.8 77 3
## 222 17.5 8 305.0 145 3880 12.5 77 1
## 223 17.0 8 260.0 110 4060 19.0 77 1
## 224 15.5 8 318.0 145 4140 13.7 77 1
## 225 15.0 8 302.0 130 4295 14.9 77 1
## 226 17.5 6 250.0 110 3520 16.4 77 1
## 227 20.5 6 231.0 105 3425 16.9 77 1
## 228 19.0 6 225.0 100 3630 17.7 77 1
## 229 18.5 6 250.0 98 3525 19.0 77 1
## 230 16.0 8 400.0 180 4220 11.1 77 1
## 231 15.5 8 350.0 170 4165 11.4 77 1
## 232 15.5 8 400.0 190 4325 12.2 77 1
## 233 16.0 8 351.0 149 4335 14.5 77 1
## 234 29.0 4 97.0 78 1940 14.5 77 2
## 235 24.5 4 151.0 88 2740 16.0 77 1
## 236 26.0 4 97.0 75 2265 18.2 77 3
## 237 25.5 4 140.0 89 2755 15.8 77 1
## 238 30.5 4 98.0 63 2051 17.0 77 1
## 239 33.5 4 98.0 83 2075 15.9 77 1
## 240 30.0 4 97.0 67 1985 16.4 77 3
## 241 30.5 4 97.0 78 2190 14.1 77 2
## 242 22.0 6 146.0 97 2815 14.5 77 3
## 243 21.5 4 121.0 110 2600 12.8 77 2
## 244 21.5 3 80.0 110 2720 13.5 77 3
## 245 43.1 4 90.0 48 1985 21.5 78 2
## 246 36.1 4 98.0 66 1800 14.4 78 1
## 247 32.8 4 78.0 52 1985 19.4 78 3
## 248 39.4 4 85.0 70 2070 18.6 78 3
## 249 36.1 4 91.0 60 1800 16.4 78 3
## 250 19.9 8 260.0 110 3365 15.5 78 1
## 251 19.4 8 318.0 140 3735 13.2 78 1
## 252 20.2 8 302.0 139 3570 12.8 78 1
## 253 19.2 6 231.0 105 3535 19.2 78 1
## 254 20.5 6 200.0 95 3155 18.2 78 1
## 255 20.2 6 200.0 85 2965 15.8 78 1
## 256 25.1 4 140.0 88 2720 15.4 78 1
## 257 20.5 6 225.0 100 3430 17.2 78 1
## 258 19.4 6 232.0 90 3210 17.2 78 1
## 259 20.6 6 231.0 105 3380 15.8 78 1
## 260 20.8 6 200.0 85 3070 16.7 78 1
## 261 18.6 6 225.0 110 3620 18.7 78 1
## 262 18.1 6 258.0 120 3410 15.1 78 1
## 263 19.2 8 305.0 145 3425 13.2 78 1
## 264 17.7 6 231.0 165 3445 13.4 78 1
## 265 18.1 8 302.0 139 3205 11.2 78 1
## 266 17.5 8 318.0 140 4080 13.7 78 1
## 267 30.0 4 98.0 68 2155 16.5 78 1
## 268 27.5 4 134.0 95 2560 14.2 78 3
## 269 27.2 4 119.0 97 2300 14.7 78 3
## 270 30.9 4 105.0 75 2230 14.5 78 1
## 271 21.1 4 134.0 95 2515 14.8 78 3
## 272 23.2 4 156.0 105 2745 16.7 78 1
## 273 23.8 4 151.0 85 2855 17.6 78 1
## 274 23.9 4 119.0 97 2405 14.9 78 3
## 275 20.3 5 131.0 103 2830 15.9 78 2
## 276 17.0 6 163.0 125 3140 13.6 78 2
## 277 21.6 4 121.0 115 2795 15.7 78 2
## 278 16.2 6 163.0 133 3410 15.8 78 2
## 279 31.5 4 89.0 71 1990 14.9 78 2
## 280 29.5 4 98.0 68 2135 16.6 78 3
## 281 21.5 6 231.0 115 3245 15.4 79 1
## 282 19.8 6 200.0 85 2990 18.2 79 1
## 283 22.3 4 140.0 88 2890 17.3 79 1
## 284 20.2 6 232.0 90 3265 18.2 79 1
## 285 20.6 6 225.0 110 3360 16.6 79 1
## 286 17.0 8 305.0 130 3840 15.4 79 1
## 287 17.6 8 302.0 129 3725 13.4 79 1
## 288 16.5 8 351.0 138 3955 13.2 79 1
## 289 18.2 8 318.0 135 3830 15.2 79 1
## 290 16.9 8 350.0 155 4360 14.9 79 1
## 291 15.5 8 351.0 142 4054 14.3 79 1
## 292 19.2 8 267.0 125 3605 15.0 79 1
## 293 18.5 8 360.0 150 3940 13.0 79 1
## 294 31.9 4 89.0 71 1925 14.0 79 2
## 295 34.1 4 86.0 65 1975 15.2 79 3
## 296 35.7 4 98.0 80 1915 14.4 79 1
## 297 27.4 4 121.0 80 2670 15.0 79 1
## 298 25.4 5 183.0 77 3530 20.1 79 2
## 299 23.0 8 350.0 125 3900 17.4 79 1
## 300 27.2 4 141.0 71 3190 24.8 79 2
## 301 23.9 8 260.0 90 3420 22.2 79 1
## 302 34.2 4 105.0 70 2200 13.2 79 1
## 303 34.5 4 105.0 70 2150 14.9 79 1
## 304 31.8 4 85.0 65 2020 19.2 79 3
## 305 37.3 4 91.0 69 2130 14.7 79 2
## 306 28.4 4 151.0 90 2670 16.0 79 1
## 307 28.8 6 173.0 115 2595 11.3 79 1
## 308 26.8 6 173.0 115 2700 12.9 79 1
## 309 33.5 4 151.0 90 2556 13.2 79 1
## 310 41.5 4 98.0 76 2144 14.7 80 2
## 311 38.1 4 89.0 60 1968 18.8 80 3
## 312 32.1 4 98.0 70 2120 15.5 80 1
## 313 37.2 4 86.0 65 2019 16.4 80 3
## 314 28.0 4 151.0 90 2678 16.5 80 1
## 315 26.4 4 140.0 88 2870 18.1 80 1
## 316 24.3 4 151.0 90 3003 20.1 80 1
## 317 19.1 6 225.0 90 3381 18.7 80 1
## 318 34.3 4 97.0 78 2188 15.8 80 2
## 319 29.8 4 134.0 90 2711 15.5 80 3
## 320 31.3 4 120.0 75 2542 17.5 80 3
## 321 37.0 4 119.0 92 2434 15.0 80 3
## 322 32.2 4 108.0 75 2265 15.2 80 3
## 323 46.6 4 86.0 65 2110 17.9 80 3
## 324 27.9 4 156.0 105 2800 14.4 80 1
## 325 40.8 4 85.0 65 2110 19.2 80 3
## 326 44.3 4 90.0 48 2085 21.7 80 2
## 327 43.4 4 90.0 48 2335 23.7 80 2
## 328 36.4 5 121.0 67 2950 19.9 80 2
## 329 30.0 4 146.0 67 3250 21.8 80 2
## 330 44.6 4 91.0 67 1850 13.8 80 3
## 332 33.8 4 97.0 67 2145 18.0 80 3
## 333 29.8 4 89.0 62 1845 15.3 80 2
## 334 32.7 6 168.0 132 2910 11.4 80 3
## 335 23.7 3 70.0 100 2420 12.5 80 3
## 336 35.0 4 122.0 88 2500 15.1 80 2
## 338 32.4 4 107.0 72 2290 17.0 80 3
## 339 27.2 4 135.0 84 2490 15.7 81 1
## 340 26.6 4 151.0 84 2635 16.4 81 1
## 341 25.8 4 156.0 92 2620 14.4 81 1
## 342 23.5 6 173.0 110 2725 12.6 81 1
## 343 30.0 4 135.0 84 2385 12.9 81 1
## 344 39.1 4 79.0 58 1755 16.9 81 3
## 345 39.0 4 86.0 64 1875 16.4 81 1
## 346 35.1 4 81.0 60 1760 16.1 81 3
## 347 32.3 4 97.0 67 2065 17.8 81 3
## 348 37.0 4 85.0 65 1975 19.4 81 3
## 349 37.7 4 89.0 62 2050 17.3 81 3
## 350 34.1 4 91.0 68 1985 16.0 81 3
## 351 34.7 4 105.0 63 2215 14.9 81 1
## 352 34.4 4 98.0 65 2045 16.2 81 1
## 353 29.9 4 98.0 65 2380 20.7 81 1
## 354 33.0 4 105.0 74 2190 14.2 81 2
## 356 33.7 4 107.0 75 2210 14.4 81 3
## 357 32.4 4 108.0 75 2350 16.8 81 3
## 358 32.9 4 119.0 100 2615 14.8 81 3
## 359 31.6 4 120.0 74 2635 18.3 81 3
## 360 28.1 4 141.0 80 3230 20.4 81 2
## 361 30.7 6 145.0 76 3160 19.6 81 2
## 362 25.4 6 168.0 116 2900 12.6 81 3
## 363 24.2 6 146.0 120 2930 13.8 81 3
## 364 22.4 6 231.0 110 3415 15.8 81 1
## 365 26.6 8 350.0 105 3725 19.0 81 1
## 366 20.2 6 200.0 88 3060 17.1 81 1
## 367 17.6 6 225.0 85 3465 16.6 81 1
## 368 28.0 4 112.0 88 2605 19.6 82 1
## 369 27.0 4 112.0 88 2640 18.6 82 1
## 370 34.0 4 112.0 88 2395 18.0 82 1
## 371 31.0 4 112.0 85 2575 16.2 82 1
## 372 29.0 4 135.0 84 2525 16.0 82 1
## 373 27.0 4 151.0 90 2735 18.0 82 1
## 374 24.0 4 140.0 92 2865 16.4 82 1
## 375 36.0 4 105.0 74 1980 15.3 82 2
## 376 37.0 4 91.0 68 2025 18.2 82 3
## 377 31.0 4 91.0 68 1970 17.6 82 3
## 378 38.0 4 105.0 63 2125 14.7 82 1
## 379 36.0 4 98.0 70 2125 17.3 82 1
## 380 36.0 4 120.0 88 2160 14.5 82 3
## 381 36.0 4 107.0 75 2205 14.5 82 3
## 382 34.0 4 108.0 70 2245 16.9 82 3
## 383 38.0 4 91.0 67 1965 15.0 82 3
## 384 32.0 4 91.0 67 1965 15.7 82 3
## 385 38.0 4 91.0 67 1995 16.2 82 3
## 386 25.0 6 181.0 110 2945 16.4 82 1
## 387 38.0 6 262.0 85 3015 17.0 82 1
## 388 26.0 4 156.0 92 2585 14.5 82 1
## 389 22.0 6 232.0 112 2835 14.7 82 1
## 390 32.0 4 144.0 96 2665 13.9 82 3
## 391 36.0 4 135.0 84 2370 13.0 82 1
## 392 27.0 4 151.0 90 2950 17.3 82 1
## 393 27.0 4 140.0 86 2790 15.6 82 1
## 394 44.0 4 97.0 52 2130 24.6 82 2
## 395 32.0 4 135.0 84 2295 11.6 82 1
## 396 28.0 4 120.0 79 2625 18.6 82 1
## 397 31.0 4 119.0 82 2720 19.4 82 1
## name
## 1 chevrolet chevelle malibu
## 2 buick skylark 320
## 3 plymouth satellite
## 4 amc rebel sst
## 5 ford torino
## 6 ford galaxie 500
## 7 chevrolet impala
## 8 plymouth fury iii
## 9 pontiac catalina
## 10 amc ambassador dpl
## 11 dodge challenger se
## 12 plymouth 'cuda 340
## 13 chevrolet monte carlo
## 14 buick estate wagon (sw)
## 15 toyota corona mark ii
## 16 plymouth duster
## 17 amc hornet
## 18 ford maverick
## 19 datsun pl510
## 20 volkswagen 1131 deluxe sedan
## 21 peugeot 504
## 22 audi 100 ls
## 23 saab 99e
## 24 bmw 2002
## 25 amc gremlin
## 26 ford f250
## 27 chevy c20
## 28 dodge d200
## 29 hi 1200d
## 30 datsun pl510
## 31 chevrolet vega 2300
## 32 toyota corona
## 34 amc gremlin
## 35 plymouth satellite custom
## 36 chevrolet chevelle malibu
## 37 ford torino 500
## 38 amc matador
## 39 chevrolet impala
## 40 pontiac catalina brougham
## 41 ford galaxie 500
## 42 plymouth fury iii
## 43 dodge monaco (sw)
## 44 ford country squire (sw)
## 45 pontiac safari (sw)
## 46 amc hornet sportabout (sw)
## 47 chevrolet vega (sw)
## 48 pontiac firebird
## 49 ford mustang
## 50 mercury capri 2000
## 51 opel 1900
## 52 peugeot 304
## 53 fiat 124b
## 54 toyota corolla 1200
## 55 datsun 1200
## 56 volkswagen model 111
## 57 plymouth cricket
## 58 toyota corona hardtop
## 59 dodge colt hardtop
## 60 volkswagen type 3
## 61 chevrolet vega
## 62 ford pinto runabout
## 63 chevrolet impala
## 64 pontiac catalina
## 65 plymouth fury iii
## 66 ford galaxie 500
## 67 amc ambassador sst
## 68 mercury marquis
## 69 buick lesabre custom
## 70 oldsmobile delta 88 royale
## 71 chrysler newport royal
## 72 mazda rx2 coupe
## 73 amc matador (sw)
## 74 chevrolet chevelle concours (sw)
## 75 ford gran torino (sw)
## 76 plymouth satellite custom (sw)
## 77 volvo 145e (sw)
## 78 volkswagen 411 (sw)
## 79 peugeot 504 (sw)
## 80 renault 12 (sw)
## 81 ford pinto (sw)
## 82 datsun 510 (sw)
## 83 toyouta corona mark ii (sw)
## 84 dodge colt (sw)
## 85 toyota corolla 1600 (sw)
## 86 buick century 350
## 87 amc matador
## 88 chevrolet malibu
## 89 ford gran torino
## 90 dodge coronet custom
## 91 mercury marquis brougham
## 92 chevrolet caprice classic
## 93 ford ltd
## 94 plymouth fury gran sedan
## 95 chrysler new yorker brougham
## 96 buick electra 225 custom
## 97 amc ambassador brougham
## 98 plymouth valiant
## 99 chevrolet nova custom
## 100 amc hornet
## 101 ford maverick
## 102 plymouth duster
## 103 volkswagen super beetle
## 104 chevrolet impala
## 105 ford country
## 106 plymouth custom suburb
## 107 oldsmobile vista cruiser
## 108 amc gremlin
## 109 toyota carina
## 110 chevrolet vega
## 111 datsun 610
## 112 maxda rx3
## 113 ford pinto
## 114 mercury capri v6
## 115 fiat 124 sport coupe
## 116 chevrolet monte carlo s
## 117 pontiac grand prix
## 118 fiat 128
## 119 opel manta
## 120 audi 100ls
## 121 volvo 144ea
## 122 dodge dart custom
## 123 saab 99le
## 124 toyota mark ii
## 125 oldsmobile omega
## 126 plymouth duster
## 128 amc hornet
## 129 chevrolet nova
## 130 datsun b210
## 131 ford pinto
## 132 toyota corolla 1200
## 133 chevrolet vega
## 134 chevrolet chevelle malibu classic
## 135 amc matador
## 136 plymouth satellite sebring
## 137 ford gran torino
## 138 buick century luxus (sw)
## 139 dodge coronet custom (sw)
## 140 ford gran torino (sw)
## 141 amc matador (sw)
## 142 audi fox
## 143 volkswagen dasher
## 144 opel manta
## 145 toyota corona
## 146 datsun 710
## 147 dodge colt
## 148 fiat 128
## 149 fiat 124 tc
## 150 honda civic
## 151 subaru
## 152 fiat x1.9
## 153 plymouth valiant custom
## 154 chevrolet nova
## 155 mercury monarch
## 156 ford maverick
## 157 pontiac catalina
## 158 chevrolet bel air
## 159 plymouth grand fury
## 160 ford ltd
## 161 buick century
## 162 chevroelt chevelle malibu
## 163 amc matador
## 164 plymouth fury
## 165 buick skyhawk
## 166 chevrolet monza 2+2
## 167 ford mustang ii
## 168 toyota corolla
## 169 ford pinto
## 170 amc gremlin
## 171 pontiac astro
## 172 toyota corona
## 173 volkswagen dasher
## 174 datsun 710
## 175 ford pinto
## 176 volkswagen rabbit
## 177 amc pacer
## 178 audi 100ls
## 179 peugeot 504
## 180 volvo 244dl
## 181 saab 99le
## 182 honda civic cvcc
## 183 fiat 131
## 184 opel 1900
## 185 capri ii
## 186 dodge colt
## 187 renault 12tl
## 188 chevrolet chevelle malibu classic
## 189 dodge coronet brougham
## 190 amc matador
## 191 ford gran torino
## 192 plymouth valiant
## 193 chevrolet nova
## 194 ford maverick
## 195 amc hornet
## 196 chevrolet chevette
## 197 chevrolet woody
## 198 vw rabbit
## 199 honda civic
## 200 dodge aspen se
## 201 ford granada ghia
## 202 pontiac ventura sj
## 203 amc pacer d/l
## 204 volkswagen rabbit
## 205 datsun b-210
## 206 toyota corolla
## 207 ford pinto
## 208 volvo 245
## 209 plymouth volare premier v8
## 210 peugeot 504
## 211 toyota mark ii
## 212 mercedes-benz 280s
## 213 cadillac seville
## 214 chevy c10
## 215 ford f108
## 216 dodge d100
## 217 honda accord cvcc
## 218 buick opel isuzu deluxe
## 219 renault 5 gtl
## 220 plymouth arrow gs
## 221 datsun f-10 hatchback
## 222 chevrolet caprice classic
## 223 oldsmobile cutlass supreme
## 224 dodge monaco brougham
## 225 mercury cougar brougham
## 226 chevrolet concours
## 227 buick skylark
## 228 plymouth volare custom
## 229 ford granada
## 230 pontiac grand prix lj
## 231 chevrolet monte carlo landau
## 232 chrysler cordoba
## 233 ford thunderbird
## 234 volkswagen rabbit custom
## 235 pontiac sunbird coupe
## 236 toyota corolla liftback
## 237 ford mustang ii 2+2
## 238 chevrolet chevette
## 239 dodge colt m/m
## 240 subaru dl
## 241 volkswagen dasher
## 242 datsun 810
## 243 bmw 320i
## 244 mazda rx-4
## 245 volkswagen rabbit custom diesel
## 246 ford fiesta
## 247 mazda glc deluxe
## 248 datsun b210 gx
## 249 honda civic cvcc
## 250 oldsmobile cutlass salon brougham
## 251 dodge diplomat
## 252 mercury monarch ghia
## 253 pontiac phoenix lj
## 254 chevrolet malibu
## 255 ford fairmont (auto)
## 256 ford fairmont (man)
## 257 plymouth volare
## 258 amc concord
## 259 buick century special
## 260 mercury zephyr
## 261 dodge aspen
## 262 amc concord d/l
## 263 chevrolet monte carlo landau
## 264 buick regal sport coupe (turbo)
## 265 ford futura
## 266 dodge magnum xe
## 267 chevrolet chevette
## 268 toyota corona
## 269 datsun 510
## 270 dodge omni
## 271 toyota celica gt liftback
## 272 plymouth sapporo
## 273 oldsmobile starfire sx
## 274 datsun 200-sx
## 275 audi 5000
## 276 volvo 264gl
## 277 saab 99gle
## 278 peugeot 604sl
## 279 volkswagen scirocco
## 280 honda accord lx
## 281 pontiac lemans v6
## 282 mercury zephyr 6
## 283 ford fairmont 4
## 284 amc concord dl 6
## 285 dodge aspen 6
## 286 chevrolet caprice classic
## 287 ford ltd landau
## 288 mercury grand marquis
## 289 dodge st. regis
## 290 buick estate wagon (sw)
## 291 ford country squire (sw)
## 292 chevrolet malibu classic (sw)
## 293 chrysler lebaron town @ country (sw)
## 294 vw rabbit custom
## 295 maxda glc deluxe
## 296 dodge colt hatchback custom
## 297 amc spirit dl
## 298 mercedes benz 300d
## 299 cadillac eldorado
## 300 peugeot 504
## 301 oldsmobile cutlass salon brougham
## 302 plymouth horizon
## 303 plymouth horizon tc3
## 304 datsun 210
## 305 fiat strada custom
## 306 buick skylark limited
## 307 chevrolet citation
## 308 oldsmobile omega brougham
## 309 pontiac phoenix
## 310 vw rabbit
## 311 toyota corolla tercel
## 312 chevrolet chevette
## 313 datsun 310
## 314 chevrolet citation
## 315 ford fairmont
## 316 amc concord
## 317 dodge aspen
## 318 audi 4000
## 319 toyota corona liftback
## 320 mazda 626
## 321 datsun 510 hatchback
## 322 toyota corolla
## 323 mazda glc
## 324 dodge colt
## 325 datsun 210
## 326 vw rabbit c (diesel)
## 327 vw dasher (diesel)
## 328 audi 5000s (diesel)
## 329 mercedes-benz 240d
## 330 honda civic 1500 gl
## 332 subaru dl
## 333 vokswagen rabbit
## 334 datsun 280-zx
## 335 mazda rx-7 gs
## 336 triumph tr7 coupe
## 338 honda accord
## 339 plymouth reliant
## 340 buick skylark
## 341 dodge aries wagon (sw)
## 342 chevrolet citation
## 343 plymouth reliant
## 344 toyota starlet
## 345 plymouth champ
## 346 honda civic 1300
## 347 subaru
## 348 datsun 210 mpg
## 349 toyota tercel
## 350 mazda glc 4
## 351 plymouth horizon 4
## 352 ford escort 4w
## 353 ford escort 2h
## 354 volkswagen jetta
## 356 honda prelude
## 357 toyota corolla
## 358 datsun 200sx
## 359 mazda 626
## 360 peugeot 505s turbo diesel
## 361 volvo diesel
## 362 toyota cressida
## 363 datsun 810 maxima
## 364 buick century
## 365 oldsmobile cutlass ls
## 366 ford granada gl
## 367 chrysler lebaron salon
## 368 chevrolet cavalier
## 369 chevrolet cavalier wagon
## 370 chevrolet cavalier 2-door
## 371 pontiac j2000 se hatchback
## 372 dodge aries se
## 373 pontiac phoenix
## 374 ford fairmont futura
## 375 volkswagen rabbit l
## 376 mazda glc custom l
## 377 mazda glc custom
## 378 plymouth horizon miser
## 379 mercury lynx l
## 380 nissan stanza xe
## 381 honda accord
## 382 toyota corolla
## 383 honda civic
## 384 honda civic (auto)
## 385 datsun 310 gx
## 386 buick century limited
## 387 oldsmobile cutlass ciera (diesel)
## 388 chrysler lebaron medallion
## 389 ford granada l
## 390 toyota celica gt
## 391 dodge charger 2.2
## 392 chevrolet camaro
## 393 ford mustang gl
## 394 vw pickup
## 395 dodge rampage
## 396 ford ranger
## 397 chevy s-10a.
auto = as.data.frame(Auto)
cat(c("Median",median(auto$mpg)))## Median 22.75auto$mpg01 = ifelse(auto$mpg > median(auto$mpg), 1 , 0)b.
pairs(auto)
par(mfrow=c(2,3))
boxplot(cylinders ~ mpg01, data = auto)
boxplot(displacement ~ mpg01, data = auto)
boxplot(horsepower ~ mpg01, data = auto)
boxplot(weight ~ mpg01, data = auto)
boxplot(acceleration ~ mpg01, data = auto)
boxplot(year ~ mpg01, data = auto)
# cor(auto)The plots indicate relationships between mpg01 and the following predictors: cylinders, displacement, weight.
c.
subset = sample(1:nrow(auto), nrow(auto)*0.8)
datatrain = auto[subset,]
datatest = auto[-subset,]d.
model <- lda(mpg01 ~ cylinders + weight + displacement, data = datatrain)
model## Call:
## lda(mpg01 ~ cylinders + weight + displacement, data = datatrain)
##
## Prior probabilities of groups:
## 0 1
## 0.5111821 0.4888179
##
## Group means:
## cylinders weight displacement
## 0 6.718750 3594.981 269.6125
## 1 4.196078 2342.575 116.9183
##
## Coefficients of linear discriminants:
## LD1
## cylinders -0.4578779851
## weight -0.0008711951
## displacement -0.0004520353probs = predict(model, newdata = datatest, type="response")
direction = probs$class
direction_test = datatest$mpg01
confusionmatrix = table(direction, direction_test)
confusionmatrix## direction_test
## direction 0 1
## 0 34 1
## 1 2 42accuracy = mean(direction == direction_test)
accuracy## [1] 0.9620253cat(c("Test Error = ",(1-accuracy)))## Test Error = 0.0379746835443038Test Error rate = 10.12%
e.
model = qda(mpg01 ~ cylinders + weight + displacement, data = datatrain)
model
## Call:
## qda(mpg01 ~ cylinders + weight + displacement, data = datatrain)
##
## Prior probabilities of groups:
## 0 1
## 0.5111821 0.4888179
##
## Group means:
## cylinders weight displacement
## 0 6.718750 3594.981 269.6125
## 1 4.196078 2342.575 116.9183
probs = predict(model, newdata = datatest, type="response")
direction = probs$class
direction_test = datatest$mpg01
confusionmatrix = table(direction, direction_test)
confusionmatrix
## direction_test
## direction 0 1
## 0 35 4
## 1 1 39
accuracy = mean(direction == direction_test)
accuracy
## [1] 0.9367089
cat(c("Test Error = ",(1-accuracy)))
## Test Error = 0.0632911392405063Test Error = 8.86%
f.
model = glm(mpg01 ~ cylinders + weight + displacement, data= datatrain, family = "binomial")
model
##
## Call: glm(formula = mpg01 ~ cylinders + weight + displacement, family = "binomial",
## data = datatrain)
##
## Coefficients:
## (Intercept) cylinders weight displacement
## 9.266452 -0.256955 -0.002227 -0.009864
##
## Degrees of Freedom: 312 Total (i.e. Null); 309 Residual
## Null Deviance: 433.8
## Residual Deviance: 190.7 AIC: 198.7
probs = predict(model, newdata = datatest, type="response")
direction = ifelse(probs>0.5, 1, 0)
direction_test = datatest$mpg01
confusionmatrix = table(direction, direction_test)
confusionmatrix
## direction_test
## direction 0 1
## 0 35 2
## 1 1 41
accuracy = mean(direction == direction_test)
accuracy
## [1] 0.9620253
cat(c("Test Error = ",(1-accuracy)))
## Test Error = 0.0379746835443038Test Error = 8.86%
g.
model = naiveBayes(mpg01 ~ cylinders + weight + displacement, data= datatrain)
model
##
## Naive Bayes Classifier for Discrete Predictors
##
## Call:
## naiveBayes.default(x = X, y = Y, laplace = laplace)
##
## A-priori probabilities:
## Y
## 0 1
## 0.5111821 0.4888179
##
## Conditional probabilities:
## cylinders
## Y [,1] [,2]
## 0 6.718750 1.4457566
## 1 4.196078 0.7260095
##
## weight
## Y [,1] [,2]
## 0 3594.981 700.3103
## 1 2342.575 406.5323
##
## displacement
## Y [,1] [,2]
## 0 269.6125 90.13456
## 1 116.9183 41.28386
probs = predict(model, newdata = datatest)
direction_test = datatest$mpg01
confusionmatrix = table(probs, direction_test)
confusionmatrix
## direction_test
## probs 0 1
## 0 34 2
## 1 2 41
accuracy = mean(direction == direction_test)
accuracy
## [1] 0.9620253
cat(c("Test Error = ",(1-accuracy)))
## Test Error = 0.0379746835443038Test Error = 8.86%
h. Testing for K = 1, 2, 3, 5, 7
predictors = c("cylinders", "horsepower", "weight")
k = c(1,2,3,5,7)
for (kval in k) {
model = knn(train = datatrain[predictors], test = datatest[predictors], cl = datatrain$mpg01, k = kval)
direction_test = datatest$mpg01
confusionmatrix
accuracy = mean(model == direction_test)
cat(c("K = ",kval," | Test Error = ",(1-accuracy),"\n\n"))
}
## K = 1 | Test Error = 0.126582278481013
##
## K = 2 | Test Error = 0.139240506329114
##
## K = 3 | Test Error = 0.0506329113924051
##
## K = 5 | Test Error = 0.0886075949367089
##
## K = 7 | Test Error = 0.0759493670886076K = 3 has the highest accuracy and lowest test error.