Heart Disease
Arthur ‘Rich’ Richardson
12/25/2024
#1. Introduction
In this project, I am exploring heart disease dataset for a university hospital. The results from my analysis will be used to develop predictive models that assess an individual’s risk of heart disease.
Installation:
Note: Due to known loading issues, load the following package(s) dependency(ies), if needed
library(hms)
library(ResourceSelection)
library(pROC)
library(rpart)
library(rpart.plot)
library(caret)
library(randomForest)
file_path <- '/Users/arthurrichardson/Documents/Documents - Arthur’s MacBook Pro/College/MAT 303/CSV/heart_disease.csv'
heart_data <- read.csv(file_path)
str(heart_data)#2. Data Preparation
## Rows: 303## Columns: 14#3. Model #1 - First Logistic Regression Model
Logistic multiple regression model for heart disease (target) using variables age (age), resting blood pressure (trestbps), exercised induced angina (exang), and maximum heart rate achieved (thalach).
log_model1 <- glm(target ~ age + trestbps + exang + thalach, data = heart_data, family = "binomial")
summary(log_model1)##
## Call:
## glm(formula = target ~ age + trestbps + exang + thalach, family = "binomial",
## data = heart_data)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.021121 1.784194 -0.572 0.5671
## age -0.017549 0.017144 -1.024 0.3060
## trestbps -0.014888 0.008337 -1.786 0.0741 .
## exang1 -1.624981 0.305774 -5.314 1.07e-07 ***
## thalach 0.031095 0.007275 4.274 1.92e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 417.64 on 302 degrees of freedom
## Residual deviance: 323.14 on 298 degrees of freedom
## AIC: 333.14
##
## Number of Fisher Scoring iterations: 4##Hosmer-Lemeshow test. Convert Target variable to numeric since its a factor.
print(hoslem_test)##
## Hosmer and Lemeshow goodness of fit (GOF) test
##
## data: heart_data$target_numeric, fitted(log_model1)
## X-squared = 9.192, df = 8, p-value = 0.3264Multiple Logistic Regression Model ROC Curve
Multiple Logistic Regression Prediction Model
Predicted_Results_Multi <- predict(log_model1, newdata = heart_data, type = "response")Round Predicted Results to 4 Decimal Places
## [1] "Multiple Logistic Regression Prediction Model Results"## 1 2 3 4 5 6 7 8 9 10 11
## 0.6213 0.5247 0.7330 0.2045 0.0800 0.7706 0.7872 0.9233 0.5583 0.8103 0.5395
## 12 13 14 15 16 17 18 19 20 21 22
## 0.4505 0.7853 0.6279 0.2941 0.5065 0.7922 0.5044 0.0587 0.7283 0.2634 0.7734
## 23 24 25 26 27 28 29 30 31 32 33
## 0.6364 0.6825 0.9018 0.3953 0.6764 0.8122 0.5343 0.7191 0.6398 0.2102 0.2119
## 34 35 36 37 38 39 40 41 42 43 44
## 0.6933 0.0402 0.2994 0.8106 0.6599 0.8068 0.7945 0.6861 0.8445 0.3334 0.4768
## 45 46 47 48 49 50 51 52 53 54 55
## 0.5331 0.5876 0.1353 0.7768 0.6614 0.7853 0.1941 0.8940 0.1741 0.1866 0.2851
## 56 57 58 59 60 61 62 63 64 65 66
## 0.0798 0.6264 0.3056 0.8227 0.3021 0.7557 0.2571 0.0862 0.2666 0.7280 0.5361
## 67 68 69 70 71 72 73 74 75 76 77
## 0.1604 0.7772 0.2831 0.8762 0.3921 0.7989 0.3393 0.1319 0.7549 0.6735 0.8581
## 78 79 80 81 82 83 84 85 86 87 88
## 0.4056 0.8623 0.5782 0.3510 0.9306 0.3655 0.1545 0.8423 0.7244 0.5696 0.3255
## 89 90 91 92 93 94 95 96 97 98 99
## 0.2031 0.4291 0.6364 0.7812 0.8204 0.7252 0.8049 0.2407 0.8246 0.3582 0.6868
## 100 101 102 103 104 105 106 107 108 109 110
## 0.6264 0.3875 0.7869 0.7777 0.6984 0.4290 0.7212 0.6584 0.7675 0.8277 0.5378
## 111 112 113 114 115 116 117 118 119 120 121
## 0.9029 0.7105 0.0791 0.5557 0.7997 0.1047 0.7982 0.6538 0.8617 0.6216 0.6040
## 122 123 124 125 126 127 128 129 130 131 132
## 0.1780 0.7091 0.2028 0.6247 0.8034 0.7368 0.8913 0.0792 0.3680 0.8449 0.8371
## 133 134 135 136 137 138 139 140 141 142 143
## 0.2770 0.4043 0.5936 0.1793 0.4446 0.8926 0.1830 0.8497 0.0824 0.4622 0.7648
## 144 145 146 147 148 149 150 151 152 153 154
## 0.5673 0.0710 0.1597 0.5936 0.6656 0.1448 0.3032 0.8513 0.2681 0.8563 0.6647
## 155 156 157 158 159 160 161 162 163 164 165
## 0.2353 0.6023 0.2957 0.1558 0.6721 0.6860 0.0779 0.8845 0.8359 0.4507 0.3561
## 166 167 168 169 170 171 172 173 174 175 176
## 0.7616 0.0959 0.4739 0.7103 0.8679 0.2429 0.3178 0.7902 0.1411 0.7471 0.7330
## 177 178 179 180 181 182 183 184 185 186 187
## 0.1225 0.9214 0.1802 0.5661 0.4328 0.2794 0.6549 0.8103 0.8233 0.2392 0.8165
## 188 189 190 191 192 193 194 195 196 197 198
## 0.3856 0.1481 0.8060 0.7815 0.7606 0.4881 0.6405 0.5529 0.8850 0.2033 0.8775
## 199 200 201 202 203 204 205 206 207 208 209
## 0.7325 0.7735 0.1891 0.7032 0.0658 0.6596 0.1810 0.7476 0.8177 0.4099 0.5923
## 210 211 212 213 214 215 216 217 218 219 220
## 0.0887 0.2083 0.6707 0.4388 0.7168 0.5999 0.2883 0.1684 0.5509 0.1912 0.8664
## 221 222 223 224 225 226 227 228 229 230 231
## 0.8464 0.1380 0.3140 0.5256 0.8948 0.7439 0.7749 0.8378 0.7528 0.6439 0.4687
## 232 233 234 235 236 237 238 239 240 241 242
## 0.8485 0.3493 0.4302 0.8371 0.8764 0.4399 0.7554 0.3110 0.2957 0.8579 0.3258
## 243 244 245 246 247 248 249 250 251 252 253
## 0.0963 0.1415 0.8343 0.8283 0.7250 0.7177 0.7595 0.3014 0.8419 0.3187 0.5959
## 254 255 256 257 258 259 260 261 262 263 264
## 0.1704 0.1784 0.6325 0.8247 0.8310 0.7897 0.2405 0.1388 0.8964 0.2731 0.7980
## 265 266 267 268 269 270 271 272 273 274 275
## 0.8882 0.4621 0.8210 0.1332 0.7527 0.5882 0.7344 0.2358 0.9435 0.3513 0.9010
## 276 277 278 279 280 281 282 283 284 285 286
## 0.6927 0.6581 0.6056 0.1847 0.7331 0.8165 0.1140 0.6245 0.1348 0.5838 0.6496
## 287 288 289 290 291 292 293 294 295 296 297
## 0.0549 0.7994 0.0834 0.7155 0.8722 0.7871 0.1294 0.1914 0.1862 0.7802 0.6747
## 298 299 300 301 302 303
## 0.7086 0.1186 0.7703 0.1916 0.8481 0.7949AUC
## [1] "Area Under the Curve (AUC)"## [1] 0.8007## Area under the curve: 0.8007Confusion Matrix
## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 89 31
## 1 49 134
##
## Accuracy : 0.736
## 95% CI : (0.6825, 0.7847)
## No Information Rate : 0.5446
## P-Value [Acc > NIR] : 5.29e-12
##
## Kappa : 0.462
##
## Mcnemar's Test P-Value : 0.05735
##
## Sensitivity : 0.8121
## Specificity : 0.6449
## Pos Pred Value : 0.7322
## Neg Pred Value : 0.7417
## Prevalence : 0.5446
## Detection Rate : 0.4422
## Detection Prevalence : 0.6040
## Balanced Accuracy : 0.7285
##
## 'Positive' Class : 1
## Preductive Model One
What is the probability of an individual having heart disease who is 50 years old, has a resting blood pressure of 122, has exercise induced angina, and has maximum heart rate of 140?
log_model2 <- glm(target ~ age + trestbps + exang + thalach, data = heart_data, family = "binomial")
new_data <- data.frame(age = 50, trestbps = 122, exang = factor(1, levels = levels(heart_data$exang)), thalach = 140)Predicted Probs
## Probability of having Heart Disease: 0.2716## Odds of Having Heart Disease: 0.3728Preductive Model Two
What is the probability of an individual having heart disease who is 50 years old, has a resting blood pressure of 130, does not have an exercise induced angina, and has maximum heart rate of 165?
log_model3 <- glm(target ~ age + trestbps + exang + thalach, data = heart_data, family = "binomial")
new_data <- data.frame(age = 50, trestbps = 130, exang = factor(0, levels = levels(heart_data$exang)), thalach = 165)Predicted Probs
predicted_probability2 <- predict(log_model3, newdata = new_data, type = "response")
predicted_odds2 <- predicted_probability2 / (1 - predicted_probability2)Results
## Probability of having Heart Disease: 0.7853## Odds of Having Heart Disease: 3.6571#4. Model #2 - Second Logistic Regression Model
log_model4 <- glm(target ~ age + trestbps + cp + thalach, data = heart_data, family = "binomial")Summary of the Multiple Logistic Regression Model
##
## Call:
## glm(formula = target ~ age + trestbps + cp + thalach, family = "binomial",
## data = heart_data)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.265458 1.811989 -1.250 0.211204
## age -0.012846 0.017656 -0.728 0.466873
## trestbps -0.019373 0.008899 -2.177 0.029476 *
## cp1 1.998672 0.439940 4.543 5.54e-06 ***
## cp2 2.098584 0.345310 6.077 1.22e-09 ***
## cp3 1.786071 0.542572 3.292 0.000995 ***
## thalach 0.031350 0.007559 4.147 3.36e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 417.64 on 302 degrees of freedom
## Residual deviance: 300.05 on 296 degrees of freedom
## AIC: 314.05
##
## Number of Fisher Scoring iterations: 4Hosmer-Lemeshow test.
‘Convert Target variable to numeric since its a factor.’
##
## Hosmer and Lemeshow goodness of fit (GOF) test
##
## data: heart_data$target_numeric, fitted(log_model1)
## X-squared = 9.192, df = 8, p-value = 0.3264Multiple Logistic Regression Model ROC Curve
Multiple Logistic Regression Prediction Model
Predicted_Results_Multi1 <- predict(log_model4, newdata = heart_data, type = "response")Round Predicted Results to 4 Decimal Places
## 1 2 3 4 5 6 7 8 9 10 11
## 0.7494 0.1943 0.7694 0.2188 0.0925 0.8582 0.4102 0.9548 0.6974 0.4799 0.5494
## 12 13 14 15 16 17 18 19 20 21 22
## 0.1470 0.4492 0.7418 0.4371 0.1812 0.8158 0.1658 0.3419 0.7765 0.3915 0.8605
## 23 24 25 26 27 28 29 30 31 32 33
## 0.9178 0.7208 0.9257 0.5597 0.7898 0.8794 0.7038 0.3563 0.2650 0.1996 0.2423
## 34 35 36 37 38 39 40 41 42 43 44
## 0.8058 0.0398 0.0807 0.8741 0.7537 0.4779 0.8635 0.3190 0.5157 0.4603 0.6150
## 45 46 47 48 49 50 51 52 53 54 55
## 0.6536 0.6747 0.5436 0.8256 0.7499 0.8616 0.2414 0.9300 0.6673 0.1992 0.2907
## 56 57 58 59 60 61 62 63 64 65 66
## 0.0804 0.7348 0.3549 0.5075 0.3440 0.8328 0.2714 0.0933 0.2907 0.8057 0.5657
## 67 68 69 70 71 72 73 74 75 76 77
## 0.1510 0.8584 0.7468 0.9242 0.8678 0.8667 0.8029 0.1414 0.8346 0.8033 0.9061
## 78 79 80 81 82 83 84 85 86 87 88
## 0.4456 0.9162 0.9261 0.8126 0.9539 0.3969 0.0330 0.9039 0.8059 0.7043 0.3414
## 89 90 91 92 93 94 95 96 97 98 99
## 0.2414 0.4340 0.2725 0.8701 0.8886 0.8142 0.4822 0.7402 0.8864 0.8486 0.7611
## 100 101 102 103 104 105 106 107 108 109 110
## 0.2776 0.4095 0.8767 0.4247 0.8020 0.1441 0.8094 0.7210 0.8126 0.8813 0.6530
## 111 112 113 114 115 116 117 118 119 120 121
## 0.6744 0.7970 0.3888 0.6924 0.8766 0.1135 0.8759 0.7699 0.9139 0.2554 0.6652
## 122 123 124 125 126 127 128 129 130 131 132
## 0.1952 0.3399 0.2291 0.7200 0.4864 0.3971 0.6423 0.0870 0.4113 0.8931 0.8904
## 133 134 135 136 137 138 139 140 141 142 143
## 0.2935 0.4284 0.6583 0.1793 0.1500 0.9271 0.2004 0.9089 0.0932 0.1417 0.8551
## 144 145 146 147 148 149 150 151 152 153 154
## 0.7116 0.0830 0.1484 0.6467 0.2990 0.0382 0.4455 0.9063 0.2760 0.9107 0.7776
## 155 156 157 158 159 160 161 162 163 164 165
## 0.2423 0.7145 0.3409 0.6079 0.7595 0.7909 0.0636 0.9049 0.8940 0.4650 0.8186
## 166 167 168 169 170 171 172 173 174 175 176
## 0.8301 0.0994 0.5327 0.8150 0.9132 0.2476 0.3204 0.8631 0.1410 0.8393 0.8113
## 177 178 179 180 181 182 183 184 185 186 187
## 0.5625 0.9578 0.5897 0.2454 0.1316 0.0726 0.3256 0.8671 0.8899 0.2611 0.8752
## 188 189 190 191 192 193 194 195 196 197 198
## 0.4288 0.1484 0.8900 0.8627 0.8389 0.1933 0.7467 0.9138 0.9347 0.2353 0.5786
## 199 200 201 202 203 204 205 206 207 208 209
## 0.8247 0.4330 0.2009 0.3392 0.0578 0.7702 0.1923 0.8304 0.8750 0.4471 0.7154
## 210 211 212 213 214 215 216 217 218 219 220
## 0.0953 0.2174 0.2955 0.4478 0.8032 0.2619 0.3312 0.1967 0.6748 0.1988 0.9110
## 221 222 223 224 225 226 227 228 229 230 231
## 0.8978 0.1409 0.3176 0.8670 0.6522 0.8533 0.8074 0.4876 0.4309 0.7486 0.5732
## 232 233 234 235 236 237 238 239 240 241 242
## 0.9048 0.0906 0.5690 0.8904 0.9149 0.1491 0.3967 0.0940 0.0822 0.9039 0.3450
## 243 244 245 246 247 248 249 250 251 252 253
## 0.0982 0.1563 0.9074 0.8448 0.3535 0.3645 0.8428 0.3102 0.8890 0.3322 0.6900
## 254 255 256 257 258 259 260 261 262 263 264
## 0.1892 0.1955 0.7133 0.5022 0.5246 0.4857 0.2719 0.1288 0.9398 0.2717 0.4782
## 265 266 267 268 269 270 271 272 273 274 275
## 0.6427 0.8989 0.8962 0.1539 0.4124 0.6116 0.3792 0.2616 0.9599 0.3722 0.9371
## 276 277 278 279 280 281 282 283 284 285 286
## 0.7878 0.7750 0.2400 0.1786 0.3923 0.8867 0.1252 0.2719 0.1270 0.6997 0.3036
## 287 288 289 290 291 292 293 294 295 296 297
## 0.0552 0.8911 0.0837 0.3418 0.9198 0.8645 0.1354 0.2081 0.2016 0.8569 0.3309
## 298 299 300 301 302 303
## 0.8053 0.1289 0.8420 0.2140 0.9001 0.8610##AUC
## [1] "Area Under the Curve (AUC)"## [1] TRUE## [1] 0.8007## Area under the curve: 0.8007##Confusion Matrix
## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 106 36
## 1 32 129
##
## Accuracy : 0.7756
## 95% CI : (0.7244, 0.8213)
## No Information Rate : 0.5446
## P-Value [Acc > NIR] : <2e-16
##
## Kappa : 0.5486
##
## Mcnemar's Test P-Value : 0.716
##
## Sensitivity : 0.7818
## Specificity : 0.7681
## Pos Pred Value : 0.8012
## Neg Pred Value : 0.7465
## Prevalence : 0.5446
## Detection Rate : 0.4257
## Detection Prevalence : 0.5314
## Balanced Accuracy : 0.7750
##
## 'Positive' Class : 1
## 'What is the probability of an individual having heart disease who is 50 years old,
has a resting blood pressure of 115, does not experience chest pain, and has maximum heart rate of 133? '
log_model5 <- glm(target ~ age + trestbps + cp + thalach, data = heart_data, family = "binomial")
new_data <- data.frame(age = 50, trestbps = 115, cp = factor(0, levels = levels(heart_data$cp)), thalach = 133)##Predicted Probs
predicted_probability2 <- predict(log_model5, newdata = new_data, type = "response")
predicted_odds2 <- predicted_probability2 / (1 - predicted_probability2)
##Results
## Probability of having Heart Disease: 0.2756## Odds of Having Heart Disease: 0.3805'What is the probability of an an individual having heart disease who
is 50 years old, has a resting blood pressure of 125, experiences typical angina, and has maximum heart rate of 155? '
log_model6 <- glm(target ~ age + trestbps + cp + thalach, data = heart_data, family = "binomial")
new_data <- data.frame(age = 50, trestbps = 125, cp = factor(1, levels = levels(heart_data$cp)), thalach = 155)##Predicted Probs
predicted_probability3 <- predict(log_model6, newdata = new_data, type = "response")
predicted_odds3 <- predicted_probability3 / (1 - predicted_probability3)##Results
## Probability of having Heart Disease: 0.8218## Odds of Having Heart Disease: 4.611#5. Random Forest Classification Model
Partition the data set into training and testing data
Training set
## [1] "Number of rows for the training set"## Training Data Rows: 257## Training Data Columns: 15Testing set
## [1] "Number of rows for the test set"## Test Set Rows: 46## Test Set Columns: 15## [1] "Graph the training and testing error against the number of trees using a classification random forest model for the \npresence of heart disease (target) using variables age (age), sex (sex), \nchest pain type (cp), resting blood pressure (trestbps), cholesterol measurement (chol), \nresting electrocardiographic measurement (restecg), exercise-induced angina (exang), \nand number of major vessels (ca). Use a maximum of 150 trees. Use set.seed(6522048).\nWhat is the optimal number of trees for the random forest model? \n"set.seed(6522048)
tree_model1 <- randomForest(target ~ age + trestbps + sex + cp + chol + restecg +
exang + ca, data=training.data, ntree = 150,
importance = TRUE)##
## Call:
## randomForest(formula = target ~ age + trestbps + sex + cp + chol + restecg + exang + ca, data = training.data, ntree = 150, importance = TRUE)
## Type of random forest: classification
## Number of trees: 150
## No. of variables tried at each split: 2
##
## OOB estimate of error rate: 18.29%
## Confusion matrix:
## 0 1 class.error
## 0 95 24 0.2016807
## 1 23 115 0.1666667
## Optimal Number of Trees: 103##Predict on the Training set
## [1] "Training Data Confusion Matrix and Statistics:"## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 119 0
## 1 0 138
##
## Accuracy : 1
## 95% CI : (0.9857, 1)
## No Information Rate : 0.537
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 1
##
## Mcnemar's Test P-Value : NA
##
## Sensitivity : 1.000
## Specificity : 1.000
## Pos Pred Value : 1.000
## Neg Pred Value : 1.000
## Prevalence : 0.463
## Detection Rate : 0.463
## Detection Prevalence : 0.463
## Balanced Accuracy : 1.000
##
## 'Positive' Class : 0
## #Predict on the Testing set
## [1] "Testing Data Confusion Matrix and Statistics:"## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 15 5
## 1 4 22
##
## Accuracy : 0.8043
## 95% CI : (0.6609, 0.9064)
## No Information Rate : 0.587
## P-Value [Acc > NIR] : 0.00155
##
## Kappa : 0.5996
##
## Mcnemar's Test P-Value : 1.00000
##
## Sensitivity : 0.7895
## Specificity : 0.8148
## Pos Pred Value : 0.7500
## Neg Pred Value : 0.8462
## Prevalence : 0.4130
## Detection Rate : 0.3261
## Detection Prevalence : 0.4348
## Balanced Accuracy : 0.8021
##
## 'Positive' Class : 0
## ##Plot Variable Importance Plot in Random Forest
##RMSE
Loop through different numbers of trees to calculate RMSE
##Calculate RMSE for Test Set
## RMSE for Training Set: 0.0624## RMSE for Test Set: 0.4423Plot RMSE for Training and Testing sets
'Using the appropriate number of trees found, create a classification random
forest model for the presence of heart disease (target) using variables age (age),
sex (sex), chest pain type (cp), resting blood pressure (trestbps), cholesterol
measurement (chol), resting electrocardiographic measurement (restecg),
exercise-induced angina (exang), and number of major vessels (ca). '
set.seed(6522048)
tree_model2 <- randomForest(target ~ age + trestbps + sex + cp + chol + restecg +
exang + ca, data=training.data, ntree = 38,
importance = TRUE)
print(tree_model2)#Predict on the Training set
## [1] "Training Data Confusion Matrix and Statistics:"## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 119 0
## 1 0 138
##
## Accuracy : 1
## 95% CI : (0.9857, 1)
## No Information Rate : 0.537
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 1
##
## Mcnemar's Test P-Value : NA
##
## Sensitivity : 1.000
## Specificity : 1.000
## Pos Pred Value : 1.000
## Neg Pred Value : 1.000
## Prevalence : 0.463
## Detection Rate : 0.463
## Detection Prevalence : 0.463
## Balanced Accuracy : 1.000
##
## 'Positive' Class : 0
## #Predict on the Testing set
## [1] "Testing Data Confusion Matrix and Statistics:"## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 14 4
## 1 5 23
##
## Accuracy : 0.8043
## 95% CI : (0.6609, 0.9064)
## No Information Rate : 0.587
## P-Value [Acc > NIR] : 0.00155
##
## Kappa : 0.5933
##
## Mcnemar's Test P-Value : 1.00000
##
## Sensitivity : 0.7368
## Specificity : 0.8519
## Pos Pred Value : 0.7778
## Neg Pred Value : 0.8214
## Prevalence : 0.4130
## Detection Rate : 0.3043
## Detection Prevalence : 0.3913
## Balanced Accuracy : 0.7943
##
## 'Positive' Class : 0
## #6. Random Forest Regression Model
## Training Data Rows: 242## Training Data Columns: 15## [1] "Number of rows for the test set"## Test Set Rows: 61## Test Set Columns: 15Graph the mean squared error against the number of trees for a random forest regression model for maximum heart rate achieved using age (age), sex (sex), chest pain type (cp), resting blood pressure (trestbps), cholesterol measurement (chol), resting electrocardiographic measurement (restecg), exercise-induced angina (exang), and number of major vessels (ca). Use a maximum of 80 trees.
set.seed(6522048)
tree_model3 <- randomForest(thalach ~ age + trestbps + sex + cp + chol + restecg +
exang + ca, data=training.data, ntree = 80,
importance = TRUE)##
## Call:
## randomForest(formula = thalach ~ age + trestbps + sex + cp + chol + restecg + exang + ca, data = training.data, ntree = 80, importance = TRUE)
## Type of random forest: regression
## Number of trees: 80
## No. of variables tried at each split: 2
##
## Mean of squared residuals: 444.0429
## % Var explained: 18.95## Length Class Mode
## call 5 -none- call
## type 1 -none- character
## predicted 242 -none- numeric
## mse 80 -none- numeric
## rsq 80 -none- numeric
## oob.times 242 -none- numeric
## importance 16 -none- numeric
## importanceSD 8 -none- numeric
## localImportance 0 -none- NULL
## proximity 0 -none- NULL
## ntree 1 -none- numeric
## mtry 1 -none- numeric
## forest 11 -none- list
## coefs 0 -none- NULL
## y 242 -none- numeric
## test 0 -none- NULL
## inbag 0 -none- NULL
## terms 3 terms call
## Optimal Number of Trees: 54##RMSE
RMSE <- function(pred, obs) {
return(sqrt(mean((as.numeric(pred) - as.numeric(obs))^2)))
}set.seed(6522048)
tree_model4 <- randomForest(thalach ~ age + trestbps + sex + cp + chol + restecg +
exang + ca, data=training.data, ntree = 54,
importance = TRUE)##Calculate RMSE for Training Set
train_predictions1 <- predict(tree_model4, newdata = training.data)
train_rmse1 <- RMSE(train_predictions, training.data$target)##Calculate RMSE for Test Set
test_predictions <- predict(tree_model4, newdata = testing.data)
test_rmse1 <- RMSE(test_predictions, testing.data$target)## RMSE for Training Set: 0.1871## RMSE for Test Set: 147.2516Plot RMSE for Training and Testing sets
