library(ISLR2)
data(Smarket)
names(Smarket)
## [1] "Year" "Lag1" "Lag2" "Lag3" "Lag4" "Lag5"
## [7] "Volume" "Today" "Direction"
dim(Smarket)
## [1] 1250 9
library(MASS)
##
## Attaching package: 'MASS'
## The following object is masked from 'package:ISLR2':
##
## Boston
data("Smarket")
train <- subset(Smarket, Year < 2005)
lda.fit <- lda(Direction ~ Lag1 + Lag2, data = train)
summary(lda.fit)
## Length Class Mode
## prior 2 -none- numeric
## counts 2 -none- numeric
## means 4 -none- numeric
## scaling 2 -none- numeric
## lev 2 -none- character
## svd 1 -none- numeric
## N 1 -none- numeric
## call 3 -none- call
## terms 3 terms call
## xlevels 0 -none- list
# Load the MASS library
library(MASS)
# Load the Smarket dataset
data("Smarket")
# Subset the data to include only observations before 2005
train <- subset(Smarket, Year < 2005)
# Fit LDA model using only the observations before 2005
lda.fit <- lda(Direction ~ Lag1 + Lag2, data = train)
# Display prior probabilities
prior_probabilities <- lda.fit$prior
cat("Prior Probabilities:\n", prior_probabilities, "\n\n")
## Prior Probabilities:
## 0.491984 0.508016
group_means <- lda.fit$means
cat("Group Means:\n", group_means, "\n\n")
## Group Means:
## 0.04279022 -0.03954635 0.03389409 -0.03132544
# Display coefficients of linear discriminants
coefficients <- lda.fit$scaling
cat("Coefficients of Linear Discriminants:\n", coefficients, "\n\n")
## Coefficients of Linear Discriminants:
## -0.642019 -0.5135293
# Plot linear discriminants
# Make predictions
predictions <- predict(lda.fit)
class_predictions <- predictions$class
posterior_probabilities <- predictions$posterior
linear_discriminants <- predictions$x
# Display predictions
cat("Predictions:\n", head(class_predictions), "\n\n")
## Predictions:
## 2 1 1 2 2 1
# Display posterior probabilities
cat("Posterior Probabilities:\n", head(posterior_probabilities), "\n\n")
## Posterior Probabilities:
## 0.4950989 0.5094612 0.5168756 0.4947529 0.4935503 0.5017058 0.5049011 0.4905388 0.4831244 0.5052471 0.5064497 0.4982942
# Display linear discriminants
cat("Linear Discriminants:\n", head(linear_discriminants), "\n\n")
## Linear Discriminants:
## -0.145003 -0.8103423 -1.15403 -0.1289757 -0.07326231 -0.4510484
# Load the required libraries
library(MASS)
library(ISLR)
##
## Attaching package: 'ISLR'
## The following objects are masked from 'package:ISLR2':
##
## Auto, Credit
# Load the Smarket dataset
data("Smarket")
# Split the data into training and testing sets
train <- subset(Smarket, Year < 2005)
test <- subset(Smarket, Year >= 2005)
# Fit LDA model
lda.fit <- lda(Direction ~ Lag1 + Lag2, data = train)
lda.pred <- predict(lda.fit, newdata = test)
# Fit logistic regression model
glm.fit <- glm(Direction ~ Lag1 + Lag2, data = train, family = binomial)
glm.probs <- predict(glm.fit, newdata = test, type = "response")
glm.pred <- ifelse(glm.probs > 0.5, "Up", "Down")
# Compare predictions
accuracy_lda <- mean(lda.pred$class == test$Direction)
accuracy_logistic <- mean(glm.pred == test$Direction)
cat("Accuracy of LDA:", accuracy_lda, "\n")
## Accuracy of LDA: 0.5595238
cat("Accuracy of Logistic Regression:", accuracy_logistic, "\n")
## Accuracy of Logistic Regression: 0.5595238
# Load required libraries
library(MASS)
library(ISLR)
# Load the Smarket dataset
data("Smarket")
# Subset the data to include only observations before 2005
train <- subset(Smarket, Year < 2005)
# Fit LDA model using only the observations before 2005
lda.fit <- lda(Direction ~ Lag1 + Lag2, data = train)
# Make predictions with LDA
lda.pred <- predict(lda.fit)
posterior_probabilities <- lda.pred$posterior
# Recreate predictions using a 50% threshold on posterior probabilities
threshold <- 0.5
recreated_predictions <- ifelse(posterior_probabilities[, "Up"] > threshold, "Up", "Down")
# Compare predictions with original lda.pred$class
identical(lda.pred$class, recreated_predictions)
## [1] FALSE
# Load required libraries
library(MASS)
library(ISLR)
# Load the Smarket dataset
data("Smarket")
# Subset the data to include only observations before 2005
train <- subset(Smarket, Year < 2005)
# Fit LDA model using only the observations before 2005
lda.fit <- lda(Direction ~ Lag1 + Lag2, data = train)
# Make predictions with LDA
lda.pred <- predict(lda.fit)
posterior_probabilities <- lda.pred$posterior
# Recreate predictions using a 50% threshold on posterior probabilities
threshold <- 0.5
recreated_predictions <- ifelse(posterior_probabilities[, "Down"] > threshold, "Down", "Up")
# Compare predictions with original lda.pred$class
identical(lda.pred$class, recreated_predictions)
## [1] FALSE
# Load required libraries
library(MASS)
library(ISLR)
# Load the Smarket dataset
data("Smarket")
# Subset the data to include only observations before 2005
train <- subset(Smarket, Year < 2005)
# Fit LDA model using only the observations before 2005
lda.fit <- lda(Direction ~ Lag1 + Lag2, data = train)
# Make predictions with LDA
lda.pred <- predict(lda.fit)
posterior_probabilities <- lda.pred$posterior
# Define the threshold for predicting a market decrease
threshold <- 0.9
# Recreate predictions using the specified threshold on posterior probabilities
recreated_predictions <- ifelse(posterior_probabilities[, "Down"] > threshold, "Down", "Up")
# Compare predictions with original lda.pred$class
identical(lda.pred$class, recreated_predictions)
## [1] FALSE
## [1] FALSE
# Load required libraries
library(MASS)
library(ISLR)
# Load the Smarket dataset
data("Smarket")
# Subset the data to include only observations before 2005
train <- subset(Smarket, Year < 2005)
# Fit LDA model using only the observations before 2005
lda.fit <- lda(Direction ~ Lag1 + Lag2, data = train)
# Make predictions with LDA
lda.pred <- predict(lda.fit)
posterior_probabilities <- lda.pred$posterior
# Define the threshold for predicting a market decrease
threshold <- 0.9
# Check if any days meet the threshold for predicting a market decrease
max_posterior <- max(posterior_probabilities[, "Down"])
if (max_posterior < threshold) {
cat("No days meet the threshold for predicting a market decrease.\n")
} else {
cat("At least one day meets the threshold for predicting a market decrease.\n")
}
## No days meet the threshold for predicting a market decrease.
#4.7.4
# Load the MASS library
library(MASS)
# Load the Smarket dataset
data("Smarket")
# Subset the data to include only observations before 2005
train <- subset(Smarket, Year < 2005)
# Fit QDA model using only the observations before 2005
qda.fit <- qda(Direction ~ Lag1 + Lag2, data = train)
# Display the summary of the QDA model
summary(qda.fit)
## Length Class Mode
## prior 2 -none- numeric
## counts 2 -none- numeric
## means 4 -none- numeric
## scaling 8 -none- numeric
## ldet 2 -none- numeric
## lev 2 -none- character
## N 1 -none- numeric
## call 3 -none- call
## terms 3 terms call
## xlevels 0 -none- list
# Make predictions with QDA
qda.pred <- predict(qda.fit)
# Print the first few predictions
head(qda.pred)
## $class
## [1] Up Down Down Up Up Up Down Down Up Down Down Up Up Up Down
## [16] Up Up Up Up Up Up Up Up Up Up Up Up Up Up Up
## [31] Up Up Down Down Up Up Up Up Down Down Down Up Up Down Up
## [46] Up Up Down Up Up Up Down Down Down Down Up Up Up Up Up
## [61] Down Down Up Down Down Down Down Up Down Down Up Up Up Down Down
## [76] Down Down Down Down Up Up Down Up Up Up Up Up Up Down Down
## [91] Up Down Down Up Up Up Up Up Up Down Down Down Up Up Up
## [106] Up Up Up Up Up Up Up Down Down Up Up Up Up Down Down
## [121] Down Down Up Up Up Up Up Down Down Up Up Up Up Up Up
## [136] Up Down Down Down Up Up Down Up Up Up Up Up Up Up Up
## [151] Up Up Up Up Up Up Up Up Down Down Up Up Up Up Up
## [166] Up Up Up Up Up Up Up Up Up Down Down Up Up Down Down
## [181] Down Down Down Up Up Up Down Down Down Up Up Up Up Up Down
## [196] Down Up Down Down Up Up Up Down Down Down Down Down Up Up Up
## [211] Down Down Up Up Down Up Up Down Down Up Up Up Down Up Down
## [226] Down Down Up Up Up Up Up Up Down Down Down Up Up Up Up
## [241] Down Down Up Up Down Down Up Up Up Up Up Up Up Up Up
## [256] Up Up Up Down Up Up Up Up Down Down Up Up Up Up Down
## [271] Down Down Up Down Up Up Up Up Up Down Down Up Up Down Down
## [286] Down Down Down Up Down Up Up Up Down Down Up Up Up Up Up
## [301] Up Down Up Up Up Up Up Up Up Up Up Up Up Up Down
## [316] Down Up Up Up Up Up Up Up Up Up Down Up Up Up Up
## [331] Down Down Up Down Down Down Up Down Up Up Up Down Up Up Up
## [346] Up Up Up Up Down Up Up Up Up Up Up Up Down Down Up
## [361] Up Up Up Up Up Down Down Up Up Up Down Down Up Up Up
## [376] Up Up Up Up Up Up Up Up Down Down Down Down Down Down Up
## [391] Up Up Down Down Down Down Up Up Down Down Down Down Down Up Down
## [406] Up Up Up Up Up Up Up Down Up Down Down Down Up Up Up
## [421] Up Up Up Up Up Up Up Down Down Up Up Down Down Up Up
## [436] Up Down Up Down Down Down Down Down Down Down Down Down Up Up Down
## [451] Down Up Up Up Down Down Down Down Up Up Up Up Up Down Down
## [466] Up Up Down Down Down Up Up Down Down Up Up Up Up Up Up
## [481] Up Down Up Up Down Down Up Up Down Down Up Up Up Up Up
## [496] Down Down Down Down Up Down Down Up Up Up Up Up Up Up Up
## [511] Up Up Up Down Up Up Down Up Up Up Up Up Up Up Up
## [526] Down Down Down Up Up Up Up Up Up Down Up Up Up Up Up
## [541] Up Up Up Down Down Down Down Down Down Down Up Down Up Up Up
## [556] Up Up Down Down Up Up Up Up Up Up Down Down Up Down Down
## [571] Down Down Up Up Down Down Up Up Down Down Up Up Up Down Down
## [586] Down Up Up Up Up Up Up Down Down Down Down Up Down Down Up
## [601] Down Down Up Up Up Down Down Up Down Down Up Up Up Up Up
## [616] Up Up Up Up Up Down Up Down Down Up Up Up Down Up Up
## [631] Up Up Up Up Down Up Down Down Up Up Up Up Up Up Up
## [646] Down Down Up Down Up Up Up Down Down Up Up Up Up Up Up
## [661] Up Down Down Down Up Up Up Up Up Up Up Up Down Down Down
## [676] Down Up Up Up Up Up Up Up Down Down Down Down Down Up Up
## [691] Up Up Down Up Up Up Up Up Up Up Up Up Down Down Up
## [706] Up Down Up Up Up Up Up Up Down Down Up Up Up Up Up
## [721] Up Down Down Up Up Down Down Up Up Up Up Up Up Down Down
## [736] Up Up Up Down Down Up Up Up Up Down Down Up Up Down Down
## [751] Up Up Up Up Up Up Down Up Up Up Up Up Down Up Up
## [766] Up Up Up Up Up Up Down Down Up Down Up Up Up Up Up
## [781] Up Up Up Up Up Up Down Up Up Up Up Up Up Up Up
## [796] Up Up Up Down Down Up Up Up Up Down Down Down Down Up Up
## [811] Down Down Up Up Up Up Up Up Up Up Up Up Up Down Down
## [826] Up Up Up Up Up Up Down Up Up Up Up Up Down Up Up
## [841] Up Up Up Up Up Up Down Down Up Up Up Up Up Up Down
## [856] Down Up Up Up Up Up Up Up Up Up Down Up Up Up Up
## [871] Up Up Up Up Up Up Up Up Up Up Up Up Up Up Up
## [886] Up Up Up Down Down Up Up Up Up Up Up Up Up Down Down
## [901] Up Up Down Down Down Down Up Up Up Down Up Up Up Up Up
## [916] Down Up Up Up Up Up Up Up Up Up Up Up Up Up Up
## [931] Up Up Up Down Up Down Down Up Up Up Up Up Up Up Up
## [946] Up Down Up Up Up Up Up Down Down Down Up Up Up Down Down
## [961] Down Up Up Up Down Down Down Up Up Up Up Up Up Up Up
## [976] Up Up Down Down Up Up Up Up Down Up Down Down Up Up Up
## [991] Up Down Down Up Up Up Up Up
## Levels: Down Up
##
## $posterior
## Down Up
## 1 0.4923444 0.5076556
## 2 0.5060033 0.4939967
## 3 0.5145040 0.4854960
## 4 0.4950242 0.5049758
## 5 0.4918806 0.5081194
## 6 0.4996028 0.5003972
## 7 0.5093741 0.4906259
## 8 0.5042413 0.4957587
## 9 0.4854227 0.5145773
## 10 0.5064161 0.4935839
## 11 0.5111949 0.4888051
## 12 0.4856002 0.5143998
## 13 0.4814466 0.5185534
## 14 0.4963955 0.5036045
## 15 0.5066425 0.4933575
## 16 0.4905512 0.5094488
## 17 0.4913959 0.5086041
## 18 0.4709837 0.5290163
## 19 0.4828540 0.5171460
## 20 0.4913510 0.5086490
## 21 0.4752743 0.5247257
## 22 0.4720656 0.5279344
## 23 0.4626977 0.5373023
## 24 0.4960787 0.5039213
## 25 0.4943892 0.5056108
## 26 0.4780920 0.5219080
## 27 0.4978723 0.5021277
## 28 0.4731767 0.5268233
## 29 0.4474296 0.5525704
## 30 0.4460266 0.5539734
## 31 0.4738616 0.5261384
## 32 0.4790260 0.5209740
## 33 0.5072543 0.4927457
## 34 0.5065635 0.4934365
## 35 0.4598052 0.5401948
## 36 0.4798787 0.5201213
## 37 0.4822880 0.5177120
## 38 0.4919037 0.5080963
## 39 0.5090008 0.4909992
## 40 0.5105476 0.4894524
## 41 0.5002015 0.4997985
## 42 0.4545291 0.5454709
## 43 0.3949069 0.6050931
## 44 0.5136183 0.4863817
## 45 0.4755922 0.5244078
## 46 0.4865231 0.5134769
## 47 0.4683360 0.5316640
## 48 0.5033992 0.4966008
## 49 0.4843504 0.5156496
## 50 0.4450819 0.5549181
## 51 0.4705726 0.5294274
## 52 0.5111882 0.4888118
## 53 0.5331063 0.4668937
## 54 0.5328874 0.4671126
## 55 0.5032861 0.4967139
## 56 0.4688323 0.5311677
## 57 0.4993288 0.5006712
## 58 0.4872567 0.5127433
## 59 0.4200980 0.5799020
## 60 0.4747628 0.5252372
## 61 0.5367097 0.4632903
## 62 0.5639591 0.4360409
## 63 0.4894908 0.5105092
## 64 0.5303001 0.4696999
## 65 0.5346890 0.4653110
## 66 0.5068035 0.4931965
## 67 0.5074464 0.4925536
## 68 0.4997862 0.5002138
## 69 0.5432587 0.4567413
## 70 0.5793744 0.4206256
## 71 0.4958189 0.5041811
## 72 0.4579338 0.5420662
## 73 0.4582423 0.5417577
## 74 0.5020865 0.4979135
## 75 0.5184984 0.4815016
## 76 0.5134992 0.4865008
## 77 0.5077263 0.4922737
## 78 0.5043179 0.4956821
## 79 0.5096400 0.4903600
## 80 0.4682246 0.5317754
## 81 0.4993120 0.5006880
## 82 0.5071897 0.4928103
## 83 0.4839284 0.5160716
## 84 0.4807231 0.5192769
## 85 0.4842059 0.5157941
## 86 0.4779183 0.5220817
## 87 0.4859194 0.5140806
## 88 0.4927286 0.5072714
## 89 0.5240440 0.4759560
## 90 0.5431840 0.4568160
## 91 0.4958976 0.5041024
## 92 0.5125922 0.4874078
## 93 0.5101929 0.4898071
## 94 0.4629821 0.5370179
## 95 0.4827591 0.5172409
## 96 0.4761351 0.5238649
## 97 0.4672414 0.5327586
## 98 0.4574704 0.5425296
## 99 0.4872521 0.5127479
## 100 0.5018985 0.4981015
## 101 0.5004437 0.4995563
## 102 0.5116374 0.4883626
## 103 0.4939319 0.5060681
## 104 0.4881996 0.5118004
## 105 0.4829251 0.5170749
## 106 0.4679733 0.5320267
## 107 0.4832673 0.5167327
## 108 0.4740917 0.5259083
## 109 0.4514419 0.5485581
## 110 0.4699408 0.5300592
## 111 0.4774433 0.5225567
## 112 0.4891573 0.5108427
## 113 0.5044679 0.4955321
## 114 0.5144423 0.4855577
## 115 0.4924646 0.5075354
## 116 0.4724195 0.5275805
## 117 0.4815425 0.5184575
## 118 0.4807910 0.5192090
## 119 0.5015182 0.4984818
## 120 0.5049137 0.4950863
## 121 0.5010583 0.4989417
## 122 0.5004047 0.4995953
## 123 0.4689366 0.5310634
## 124 0.4402262 0.5597738
## 125 0.4877262 0.5122738
## 126 0.4778499 0.5221501
## 127 0.4764774 0.5235226
## 128 0.5176903 0.4823097
## 129 0.5357494 0.4642506
## 130 0.4819761 0.5180239
## 131 0.4944347 0.5055653
## 132 0.4953622 0.5046378
## 133 0.4922729 0.5077271
## 134 0.4921176 0.5078824
## 135 0.4607259 0.5392741
## 136 0.4504647 0.5495353
## 137 0.5013492 0.4986508
## 138 0.5251242 0.4748758
## 139 0.5063588 0.4936412
## 140 0.4904279 0.5095721
## 141 0.4955400 0.5044600
## 142 0.5010724 0.4989276
## 143 0.4989878 0.5010122
## 144 0.4866883 0.5133117
## 145 0.4667113 0.5332887
## 146 0.4845487 0.5154513
## 147 0.4678737 0.5321263
## 148 0.4771432 0.5228568
## 149 0.4967135 0.5032865
## 150 0.4974483 0.5025517
## 151 0.4848244 0.5151756
## 152 0.4744140 0.5255860
## 153 0.4867799 0.5132201
## 154 0.4686472 0.5313528
## 155 0.4898762 0.5101238
## 156 0.4832423 0.5167577
## 157 0.4896279 0.5103721
## 158 0.4943515 0.5056485
## 159 0.5118033 0.4881967
## 160 0.5146000 0.4854000
## 161 0.4614034 0.5385966
## 162 0.4599318 0.5400682
## 163 0.4524451 0.5475549
## 164 0.4836343 0.5163657
## 165 0.4932125 0.5067875
## 166 0.4870069 0.5129931
## 167 0.4537844 0.5462156
## 168 0.4440527 0.5559473
## 169 0.4867150 0.5132850
## 170 0.4185919 0.5814081
## 171 0.4823715 0.5176285
## 172 0.4586272 0.5413728
## 173 0.4236000 0.5764000
## 174 0.4431674 0.5568326
## 175 0.5304635 0.4695365
## 176 0.5766730 0.4233270
## 177 0.4939352 0.5060648
## 178 0.4998606 0.5001394
## 179 0.5296448 0.4703552
## 180 0.5225156 0.4774844
## 181 0.5031758 0.4968242
## 182 0.5288465 0.4711535
## 183 0.5180226 0.4819774
## 184 0.4888191 0.5111809
## 185 0.4791772 0.5208228
## 186 0.4734658 0.5265342
## 187 0.5139635 0.4860365
## 188 0.5429748 0.4570252
## 189 0.5050830 0.4949170
## 190 0.4817198 0.5182802
## 191 0.4969210 0.5030790
## 192 0.4716076 0.5283924
## 193 0.4640397 0.5359603
## 194 0.4885135 0.5114865
## 195 0.5136710 0.4863290
## 196 0.5059783 0.4940217
## 197 0.4849985 0.5150015
## 198 0.5073765 0.4926235
## 199 0.5138575 0.4861425
## 200 0.4588968 0.5411032
## 201 0.4465058 0.5534942
## 202 0.4772961 0.5227039
## 203 0.5177714 0.4822286
## 204 0.5305570 0.4694430
## 205 0.5107108 0.4892892
## 206 0.5265599 0.4734401
## 207 0.5070063 0.4929937
## 208 0.4897115 0.5102885
## 209 0.4941056 0.5058944
## 210 0.4884741 0.5115259
## 211 0.5112791 0.4887209
## 212 0.5202562 0.4797438
## 213 0.4924704 0.5075296
## 214 0.4857418 0.5142582
## 215 0.5006653 0.4993347
## 216 0.4945763 0.5054237
## 217 0.4749394 0.5250606
## 218 0.5003224 0.4996776
## 219 0.5129008 0.4870992
## 220 0.4875713 0.5124287
## 221 0.4540631 0.5459369
## 222 0.4929424 0.5070576
## 223 0.5023567 0.4976433
## 224 0.4762965 0.5237035
## 225 0.5000699 0.4999301
## 226 0.5325014 0.4674986
## 227 0.5228468 0.4771532
## 228 0.4752086 0.5247914
## 229 0.4573600 0.5426400
## 230 0.4732975 0.5267025
## 231 0.4865946 0.5134054
## 232 0.4664863 0.5335137
## 233 0.4829178 0.5170822
## 234 0.5059594 0.4940406
## 235 0.5119285 0.4880715
## 236 0.5062093 0.4937907
## 237 0.4848991 0.5151009
## 238 0.4878783 0.5121217
## 239 0.4941040 0.5058960
## 240 0.4944902 0.5055098
## 241 0.5028470 0.4971530
## 242 0.5020253 0.4979747
## 243 0.4773518 0.5226482
## 244 0.4882975 0.5117025
## 245 0.5078832 0.4921168
## 246 0.5090567 0.4909433
## 247 0.4881343 0.5118657
## 248 0.4776221 0.5223779
## 249 0.4784586 0.5215414
## 250 0.4860995 0.5139005
## 251 0.4769755 0.5230245
## 252 0.4712030 0.5287970
## 253 0.4927976 0.5072024
## 254 0.4750200 0.5249800
## 255 0.4927626 0.5072374
## 256 0.4894976 0.5105024
## 257 0.4692306 0.5307694
## 258 0.4935756 0.5064244
## 259 0.5038974 0.4961026
## 260 0.4946446 0.5053554
## 261 0.4899728 0.5100272
## 262 0.4445205 0.5554795
## 263 0.4968234 0.5031766
## 264 0.5228275 0.4771725
## 265 0.5022201 0.4977799
## 266 0.4427592 0.5572408
## 267 0.4698596 0.5301404
## 268 0.4762715 0.5237285
## 269 0.4788300 0.5211700
## 270 0.5057401 0.4942599
## 271 0.5271387 0.4728613
## 272 0.5050679 0.4949321
## 273 0.4987228 0.5012772
## 274 0.5002166 0.4997834
## 275 0.4709743 0.5290257
## 276 0.4493435 0.5506565
## 277 0.4975182 0.5024818
## 278 0.4880433 0.5119567
## 279 0.4902825 0.5097175
## 280 0.5211438 0.4788562
## 281 0.5168822 0.4831178
## 282 0.4896831 0.5103169
## 283 0.4856345 0.5143655
## 284 0.5152148 0.4847852
## 285 0.5462403 0.4537597
## 286 0.5120012 0.4879988
## 287 0.5027874 0.4972126
## 288 0.5047374 0.4952626
## 289 0.4928229 0.5071771
## 290 0.5008235 0.4991765
## 291 0.4900237 0.5099763
## 292 0.4722084 0.5277916
## 293 0.4791968 0.5208032
## 294 0.5032401 0.4967599
## 295 0.5042310 0.4957690
## 296 0.4940998 0.5059002
## 297 0.4714634 0.5285366
## 298 0.4800879 0.5199121
## 299 0.4849226 0.5150774
## 300 0.4626023 0.5373977
## 301 0.4870290 0.5129710
## 302 0.5033060 0.4966940
## 303 0.4989525 0.5010475
## 304 0.4909675 0.5090325
## 305 0.4759792 0.5240208
## 306 0.4660488 0.5339512
## 307 0.4817407 0.5182593
## 308 0.4855717 0.5144283
## 309 0.4890123 0.5109877
## 310 0.4824398 0.5175602
## 311 0.4986275 0.5013725
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## 880 0.4853047 0.5146953
## 881 0.4794948 0.5205052
## 882 0.4777858 0.5222142
## 883 0.4837241 0.5162759
## 884 0.4981455 0.5018545
## 885 0.4796953 0.5203047
## 886 0.4828174 0.5171826
## 887 0.4785929 0.5214071
## 888 0.4777099 0.5222901
## 889 0.5004294 0.4995706
## 890 0.5032056 0.4967944
## 891 0.4958892 0.5041108
## 892 0.4962285 0.5037715
## 893 0.4964220 0.5035780
## 894 0.4859314 0.5140686
## 895 0.4817249 0.5182751
## 896 0.4637291 0.5362709
## 897 0.4518701 0.5481299
## 898 0.4796526 0.5203474
## 899 0.5072359 0.4927641
## 900 0.5038215 0.4961785
## 901 0.4686141 0.5313859
## 902 0.4817469 0.5182531
## 903 0.5083882 0.4916118
## 904 0.5114814 0.4885186
## 905 0.5076661 0.4923339
## 906 0.5021297 0.4978703
## 907 0.4944879 0.5055121
## 908 0.4941472 0.5058528
## 909 0.4872183 0.5127817
## 910 0.5002941 0.4997059
## 911 0.4996893 0.5003107
## 912 0.4925647 0.5074353
## 913 0.4810194 0.5189806
## 914 0.4886734 0.5113266
## 915 0.4967554 0.5032446
## 916 0.5054279 0.4945721
## 917 0.4992468 0.5007532
## 918 0.4945010 0.5054990
## 919 0.4919134 0.5080866
## 920 0.4873187 0.5126813
## 921 0.4978910 0.5021090
## 922 0.4974153 0.5025847
## 923 0.4940619 0.5059381
## 924 0.4818134 0.5181866
## 925 0.4865587 0.5134413
## 926 0.4983429 0.5016571
## 927 0.4868719 0.5131281
## 928 0.4925899 0.5074101
## 929 0.4776524 0.5223476
## 930 0.4710857 0.5289143
## 931 0.4867238 0.5132762
## 932 0.4825826 0.5174174
## 933 0.4918043 0.5081957
## 934 0.5020515 0.4979485
## 935 0.4940117 0.5059883
## 936 0.5085902 0.4914098
## 937 0.5154235 0.4845765
## 938 0.4921236 0.5078764
## 939 0.4974638 0.5025362
## 940 0.4839305 0.5160695
## 941 0.4688715 0.5311285
## 942 0.4850877 0.5149123
## 943 0.4883037 0.5116963
## 944 0.4760983 0.5239017
## 945 0.4681625 0.5318375
## 946 0.4874482 0.5125518
## 947 0.5013609 0.4986391
## 948 0.4821979 0.5178021
## 949 0.4812550 0.5187450
## 950 0.4930354 0.5069646
## 951 0.4783614 0.5216386
## 952 0.4793614 0.5206386
## 953 0.5076272 0.4923728
## 954 0.5256405 0.4743595
## 955 0.5096574 0.4903426
## 956 0.4944963 0.5055037
## 957 0.4923292 0.5076708
## 958 0.4894580 0.5105420
## 959 0.5038968 0.4961032
## 960 0.5232917 0.4767083
## 961 0.5179512 0.4820488
## 962 0.4922736 0.5077264
## 963 0.4869314 0.5130686
## 964 0.4869248 0.5130752
## 965 0.5002241 0.4997759
## 966 0.5123723 0.4876277
## 967 0.5008448 0.4991552
## 968 0.4786437 0.5213563
## 969 0.4904373 0.5095627
## 970 0.4977789 0.5022211
## 971 0.4746365 0.5253635
## 972 0.4885239 0.5114761
## 973 0.4961618 0.5038382
## 974 0.4944214 0.5055786
## 975 0.4950567 0.5049433
## 976 0.4851253 0.5148747
## 977 0.4797341 0.5202659
## 978 0.5051297 0.4948703
## 979 0.5100835 0.4899165
## 980 0.4891448 0.5108552
## 981 0.4888364 0.5111636
## 982 0.4721140 0.5278860
## 983 0.4870894 0.5129106
## 984 0.5021502 0.4978498
## 985 0.4944715 0.5055285
## 986 0.5000665 0.4999335
## 987 0.5059778 0.4940222
## 988 0.4964001 0.5035999
## 989 0.4884815 0.5115185
## 990 0.4760202 0.5239798
## 991 0.4827403 0.5172597
## 992 0.5015327 0.4984673
## 993 0.5054341 0.4945659
## 994 0.4937954 0.5062046
## 995 0.4835578 0.5164422
## 996 0.4947461 0.5052539
## 997 0.4981853 0.5018147
## 998 0.4891354 0.5108646
# Load the MASS library
library(MASS)
# Load the Smarket dataset
data("Smarket")
# Subset the data to include only observations in 2005
Smarket_2005 <- subset(Smarket, Year == 2005)
# Fit QDA model using the entire training dataset (observations before 2005)
qda.fit <- qda(Direction ~ Lag1 + Lag2, data = subset(Smarket, Year < 2005))
# Make predictions on the 2005 data with QDA
qda.class <- predict(qda.fit, newdata = Smarket_2005)$class
# Create a contingency table to compare predictions with actual values
prediction_table <- table(qda.class, Smarket_2005$Direction)
# Print the contingency table
print(prediction_table)
##
## qda.class Down Up
## Down 30 20
## Up 81 121
# Calculate the accuracy of QDA predictions
accuracy <- mean(qda.class == Smarket_2005$Direction)
cat("Accuracy of QDA predictions:", accuracy, "\n")
## Accuracy of QDA predictions: 0.5992063
#4.7.5 Naive Bayes
# Load required library
library(e1071)
# Load the Smarket dataset
data("Smarket")
# Subset the data to include only observations before 2005
train <- subset(Smarket, Year < 2005)
# Fit Naive Bayes model using only the observations before 2005
nb.fit <- naiveBayes(Direction ~ Lag1 + Lag2, data = train)
# Display the summary of the Naive Bayes model
print(nb.fit)
##
## Naive Bayes Classifier for Discrete Predictors
##
## Call:
## naiveBayes.default(x = X, y = Y, laplace = laplace)
##
## A-priori probabilities:
## Y
## Down Up
## 0.491984 0.508016
##
## Conditional probabilities:
## Lag1
## Y [,1] [,2]
## Down 0.04279022 1.227446
## Up -0.03954635 1.231668
##
## Lag2
## Y [,1] [,2]
## Down 0.03389409 1.239191
## Up -0.03132544 1.220765
# Make predictions with Naive Bayes
nb.class <- predict(nb.fit, newdata = subset(Smarket, Year == 2005))
# Create a contingency table to compare predictions with actual values
prediction_table <- table(nb.class, subset(Smarket, Year == 2005)$Direction)
# Print the contingency table
print(prediction_table)
##
## nb.class Down Up
## Down 28 20
## Up 83 121
# Calculate the accuracy of Naive Bayes predictions
accuracy <- mean(nb.class == subset(Smarket, Year == 2005)$Direction)
cat("Accuracy of Naive Bayes predictions:", accuracy, "\n")
## Accuracy of Naive Bayes predictions: 0.5912698
# Generate estimates of the probability for each observation belonging to a particular class
nb.preds <- predict(nb.fit, newdata = subset(Smarket, Year == 2005), type = "raw")
print(nb.preds[1:5, ])
## Down Up
## [1,] 0.4873164 0.5126836
## [2,] 0.4762492 0.5237508
## [3,] 0.4653377 0.5346623
## [4,] 0.4748652 0.5251348
## [5,] 0.4901890 0.5098110
#4.7.6K-Nearest Neighbors
# Load the class library
library(class)
# Load the Smarket dataset
data("Smarket")
# Subset the data to include only observations before 2005
train <- subset(Smarket, Year < 2005)
# Prepare predictors and response variables for training and testing sets
train.X <- cbind(train$Lag1, train$Lag2)
test.X <- cbind(Smarket[Smarket$Year >= 2005, "Lag1"], Smarket[Smarket$Year >= 2005, "Lag2"])
train.Direction <- train$Direction
Direction_2005 <- Smarket$Direction[Smarket$Year >= 2005]
# Fit KNN model with K=1
set.seed(1)
knn.pred <- knn(train.X, test.X, train.Direction, k = 1)
# Create a contingency table to compare predictions with actual values
prediction_table <- table(knn.pred, Direction_2005)
# Print the contingency table
print
## function (x, ...)
## UseMethod("print")
## <bytecode: 0x56fb7b27c778>
## <environment: namespace:base>
# Calculate the accuracy of KNN predictions
accuracy <- mean(knn.pred == Direction_2005)
cat("Accuracy of KNN predictions (K=1):", accuracy, "\n")
## Accuracy of KNN predictions (K=1): 0.5
# Fit KNN model with K=3
knn.pred <- knn(train.X, test.X, train.Direction, k = 3)
# Create a contingency table to compare predictions with actual values
prediction_table <- table(knn.pred, Direction_2005)
# Print the contingency table
print(prediction_table)
## Direction_2005
## knn.pred Down Up
## Down 48 54
## Up 63 87
# Calculate the accuracy of KNN predictions
accuracy <- mean(knn.pred == Direction_2005)
cat("Accuracy of KNN predictions (K=3):", accuracy, "\n")
## Accuracy of KNN predictions (K=3): 0.5357143
#4.7.7 Poisson Regression
# Load the Bikeshare data
library(ISLR2)
data("Bikeshare")
# Fit a Poisson regression model
mod.pois <- glm(bikers ~ mnth + hr + workingday + temp + weathersit, data = Bikeshare, family = poisson)
# Display summary of the model
summary(mod.pois)
##
## Call:
## glm(formula = bikers ~ mnth + hr + workingday + temp + weathersit,
## family = poisson, data = Bikeshare)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 2.693688 0.009720 277.124 < 2e-16 ***
## mnthFeb 0.226046 0.006951 32.521 < 2e-16 ***
## mnthMarch 0.376437 0.006691 56.263 < 2e-16 ***
## mnthApril 0.691693 0.006987 98.996 < 2e-16 ***
## mnthMay 0.910641 0.007436 122.469 < 2e-16 ***
## mnthJune 0.893405 0.008242 108.402 < 2e-16 ***
## mnthJuly 0.773787 0.008806 87.874 < 2e-16 ***
## mnthAug 0.821341 0.008332 98.573 < 2e-16 ***
## mnthSept 0.903663 0.007621 118.578 < 2e-16 ***
## mnthOct 0.937743 0.006744 139.054 < 2e-16 ***
## mnthNov 0.820433 0.006494 126.334 < 2e-16 ***
## mnthDec 0.686850 0.006317 108.724 < 2e-16 ***
## hr1 -0.471593 0.012999 -36.278 < 2e-16 ***
## hr2 -0.808761 0.014646 -55.220 < 2e-16 ***
## hr3 -1.443918 0.018843 -76.631 < 2e-16 ***
## hr4 -2.076098 0.024796 -83.728 < 2e-16 ***
## hr5 -1.060271 0.016075 -65.957 < 2e-16 ***
## hr6 0.324498 0.010610 30.585 < 2e-16 ***
## hr7 1.329567 0.009056 146.822 < 2e-16 ***
## hr8 1.831313 0.008653 211.630 < 2e-16 ***
## hr9 1.336155 0.009016 148.191 < 2e-16 ***
## hr10 1.091238 0.009261 117.831 < 2e-16 ***
## hr11 1.248507 0.009093 137.304 < 2e-16 ***
## hr12 1.434028 0.008936 160.486 < 2e-16 ***
## hr13 1.427951 0.008951 159.529 < 2e-16 ***
## hr14 1.379296 0.008999 153.266 < 2e-16 ***
## hr15 1.408149 0.008977 156.862 < 2e-16 ***
## hr16 1.628688 0.008805 184.979 < 2e-16 ***
## hr17 2.049021 0.008565 239.221 < 2e-16 ***
## hr18 1.966668 0.008586 229.065 < 2e-16 ***
## hr19 1.668409 0.008743 190.830 < 2e-16 ***
## hr20 1.370588 0.008973 152.737 < 2e-16 ***
## hr21 1.118568 0.009215 121.383 < 2e-16 ***
## hr22 0.871879 0.009536 91.429 < 2e-16 ***
## hr23 0.481387 0.010207 47.164 < 2e-16 ***
## workingday 0.014665 0.001955 7.502 6.27e-14 ***
## temp 0.785292 0.011475 68.434 < 2e-16 ***
## weathersitcloudy/misty -0.075231 0.002179 -34.528 < 2e-16 ***
## weathersitlight rain/snow -0.575800 0.004058 -141.905 < 2e-16 ***
## weathersitheavy rain/snow -0.926287 0.166782 -5.554 2.79e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 1052921 on 8644 degrees of freedom
## Residual deviance: 228041 on 8605 degrees of freedom
## AIC: 281159
##
## Number of Fisher Scoring iterations: 5
# Plot coefficients associated with month
coef.mnth <- c(coef(mod.pois)[2:12], -sum(coef(mod.pois)[2:12]))
plot(coef.mnth, xlab = "Month", ylab = "Coefficient", xaxt = "n", col = "blue", pch = 19, type = "o")
axis(side = 1, at = 1:12, labels = c("J", "F", "M", "A", "M", "J", "J", "A", "S", "O", "N", "D"))
# Plot coefficients associated with hour
coef.hours <- c(coef(mod.pois)[13:35], -sum(coef(mod.pois)[13:35]))
plot(coef.hours, xlab = "Hour", ylab = "Coefficient", col = "blue", pch = 19, type = "o")
