Assignment 8 SVMs
Jordan Dever
2024-04-23
5. We have seen that we can ft an SVM with a non-linear kernel in order
to perform classifcation using a non-linear decision boundary. We will
now see that we can also obtain a non-linear decision boundary by
performing logistic regression using non-linear transformations of the
features.
5a) Generate a data set with n = 500 and p = 2, such that the observations belong
to two classes with a quadratic decision boundary
between them. For instance, you can do this as follows:
set.seed(1)
x1 <- runif(500) - 0.5
x2 <- runif(500) - 0.5
y <- 1 * (x1^2 - x2^2 > 0)
y = as.factor(y)
q5_df = data.frame(x1,x2,y)5b)Plot the observations, colored according to their class labels.
Your plot should display X1 on the x-axis, and X2 on the yaxis.
ggplot(q5_df, aes(x=x1, y =x2, col = y)) +
geom_point() +
theme_minimal()
5c)Fit a logistic regression model to the data, using X1 and X2 as predictors.
logit = glm(y~x1+x2, data = q5_df, family = 'binomial')
logit##
## Call: glm(formula = y ~ x1 + x2, family = "binomial", data = q5_df)
##
## Coefficients:
## (Intercept) x1 x2
## -0.087260 0.196199 -0.002854
##
## Degrees of Freedom: 499 Total (i.e. Null); 497 Residual
## Null Deviance: 692.2
## Residual Deviance: 691.8 AIC: 697.85d) Apply this model to the training data in order to obtain a predicted
class label for each training observation. Plot the observations, colored
according to the predicted class labels. The decision boundary should be linear.
logit_pred = predict(logit, data.frame(x1,x2))
plot(x1,x2,col = ifelse(logit_pred > 0,'red','blue')) 
q5_df$logit_lin = ifelse(logit_pred > 0,1,0)
sum(q5_df$y == q5_df$logit_lin) / nrow(q5_df)## [1] 0.575e) Now ft a logistic regression model to the data using non-linear
functions of X1 and X2 as predictors (e.g. X2 1 , X1×X2, log(X2),and so forth).
logit_non_linear = glm(y ~ log(x1) + log(x2), data = q5_df, family = 'binomial')## Warning in log(x1): NaNs produced## Warning in log(x2): NaNs produced## Warning: glm.fit: algorithm did not converge## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurredlogit_non_linear##
## Call: glm(formula = y ~ log(x1) + log(x2), family = "binomial", data = q5_df)
##
## Coefficients:
## (Intercept) log(x1) log(x2)
## -44.49 497.86 -528.98
##
## Degrees of Freedom: 120 Total (i.e. Null); 118 Residual
## (379 observations deleted due to missingness)
## Null Deviance: 167.7
## Residual Deviance: 1.895e-07 AIC: 65f) Apply this model to the training data in order to obtain a predicted
class label for each training observation. Plot the observations, colored
according to the predicted class labels. The decision boundary should be
obviously non-linear. If it is not, then repeat (a)-(e) until you come up with
an example in which the predicted class labels are obviously non-linear.
non_linear_pred = predict(logit_non_linear, data.frame(x1,x2))## Warning in log(x1): NaNs produced## Warning in log(x2): NaNs producedplot(x1,x2, col = ifelse(non_linear_pred>0,'red','blue'))
Looks like using log(x) did not work, going to try x^2
logit_non_linear = glm(y ~ I(x1**2) + I(x2**2), data = q5_df, family = 'binomial')## Warning: glm.fit: algorithm did not converge## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurrednon_linear_pred = predict(logit_non_linear, data.frame(x1,x2))
plot(x1,x2, col = ifelse(non_linear_pred>0,'red','blue'))
No longer has a linear boundary and was able to converge.
q5_df$glm_nonlin = ifelse(non_linear_pred>0,1,0)
sum(q5_df$y == q5_df$glm_nonlin) / nrow(q5_df)## [1] 15g) Fit a support vector classifer to the data with X1 and X2 as predictors.
Obtain a class prediction for each training observation. Plot the
observations, colored according to the predicted class labels.
set.seed(1)
linear_svm = svm(y~x1 + x2, data = q5_df, kernel = 'linear')
linear_pred = predict(linear_svm, q5_df)
plot(x1,x2,col = ifelse(linear_pred!=0,'red','blue')) 
linear_tune <- tune(svm, y~x1+x2, data = q5_df, kernel = "linear", ranges = list(
cost = c(0.1, 1, 10, 100, 1000),
gamma = c(0.5, 1, 2, 3, 4)))
linear_svm = linear_tune$best.model
linear_pred = predict(linear_svm, q5_df)
plot(x1,x2,col = ifelse(linear_pred!=0,'red','blue'))
q5_df$svm_lin = linear_pred
sum(q5_df$y == q5_df$svm_lin) / nrow(q5_df)## [1] 0.522After trying to tune this model, I was getting an error regarding reaching max iterations. When the model finally ran, it still gave the same previous graph where there is only predicted 0’s. This suggests the data may be class imbalance, noisy data, or the data may not be linearly separable.
5h) Fit a SVM using a non-linear kernel to the data. Obtain a class
prediction for each training observation. Plot the observations,
colored according to the predicted class labels.
set.seed(1)
#radial_svm = svm(y~I(x1**2) + I(x2**2), data = q5_df, kernel = 'radial')
radial_out <- tune(svm, y ~ x1 + x2, data = q5_df, kernel = "radial", ranges = list(
cost = c(0.1, 1, 10, 100, 1000), gamma = c(0.5, 1, 2, 3, 4)))
radial_svm = radial_out$best.model
radial_pred = predict(radial_svm, q5_df)
plot(x1,x2,col = ifelse(radial_pred!=0,'red','blue'))
q5_df$svm_nonlin = radial_pred
sum(q5_df$y == q5_df$svm_nonlin) / nrow(q5_df)## [1] 15i) Comment on your results.
After running the logistic regressions and SVMs, it seems that the best models produced were the Non-Linear SVM & Logistic Regression.This is based on the accuracy scores produced which both equal 1. The logistic regression took more effort to produce since I began with using log(x) but when I switched to x^2, it gave the best results. The linear models gave accuracy scores slightly better than chance, but were only able to predict 0’s. This means that our data was probably not linearly separable which would be true since it looks quadratic. It seems that doing an SVM is a more time efficient method to testing different non-linear models compared to logistic regression, especially because you could just make a function to run multiple SVMs, change out the kernels and some hyper-parameters, then use the model that produced the best results.
7. In this problem, you will use support vector approaches in order to
predict whether a given car gets high or low gas mileage based on the
Auto data set
7a) Create a binary variable that takes on a 1 for cars with gas
mileage above the median, and a 0 for cars with gas mileage
below the median.
auto = ISLR2::Auto
mpg_binary = rep(0, length(auto$mpg))
mpg_binary[auto$mpg > median(auto$mpg)] = 1
auto = data.frame(auto, mpg_binary)
auto$mpg_binary = as.factor(auto$mpg_binary)
auto = auto %>%
dplyr::select(-c(name,mpg))
summary(auto)## cylinders displacement horsepower weight acceleration
## Min. :3.000 Min. : 68.0 Min. : 46.0 Min. :1613 Min. : 8.00
## 1st Qu.:4.000 1st Qu.:105.0 1st Qu.: 75.0 1st Qu.:2225 1st Qu.:13.78
## Median :4.000 Median :151.0 Median : 93.5 Median :2804 Median :15.50
## Mean :5.472 Mean :194.4 Mean :104.5 Mean :2978 Mean :15.54
## 3rd Qu.:8.000 3rd Qu.:275.8 3rd Qu.:126.0 3rd Qu.:3615 3rd Qu.:17.02
## Max. :8.000 Max. :455.0 Max. :230.0 Max. :5140 Max. :24.80
## year origin mpg_binary
## Min. :70.00 Min. :1.000 0:196
## 1st Qu.:73.00 1st Qu.:1.000 1:196
## Median :76.00 Median :1.000
## Mean :75.98 Mean :1.577
## 3rd Qu.:79.00 3rd Qu.:2.000
## Max. :82.00 Max. :3.0007b) Fit a support vector classifer to the data with various values of cost,
in order to predict whether a car gets high or low gas mileage. Report the
cross-validation errors associated with different values of this parameter.
mileage variable to produce sensible results.
set.seed(1)
costs = seq(0.1,10,0.1)
linear_svm_tune = tune(svm, mpg_binary~., data = auto, kernel = 'linear',
scale = T, ranges = list(cost = costs))summary(linear_svm_tune)##
## Parameter tuning of 'svm':
##
## - sampling method: 10-fold cross validation
##
## - best parameters:
## cost
## 0.5
##
## - best performance: 0.08429487
##
## - Detailed performance results:
## cost error dispersion
## 1 0.1 0.09185897 0.04393409
## 2 0.2 0.08673077 0.04040897
## 3 0.3 0.08929487 0.03674971
## 4 0.4 0.08929487 0.03674971
## 5 0.5 0.08429487 0.04211652
## 6 0.6 0.08429487 0.03229996
## 7 0.7 0.08429487 0.03229996
## 8 0.8 0.08435897 0.03662670
## 9 0.9 0.08435897 0.03662670
## 10 1.0 0.08435897 0.03662670
## 11 1.1 0.08435897 0.03662670
## 12 1.2 0.08435897 0.03662670
## 13 1.3 0.08435897 0.03662670
## 14 1.4 0.08435897 0.03662670
## 15 1.5 0.08435897 0.03662670
## 16 1.6 0.08435897 0.03662670
## 17 1.7 0.08435897 0.03662670
## 18 1.8 0.08435897 0.03662670
## 19 1.9 0.08435897 0.03662670
## 20 2.0 0.08435897 0.03662670
## 21 2.1 0.08435897 0.03662670
## 22 2.2 0.08435897 0.03662670
## 23 2.3 0.08692308 0.03694444
## 24 2.4 0.08948718 0.03898410
## 25 2.5 0.08948718 0.03898410
## 26 2.6 0.08948718 0.03898410
## 27 2.7 0.08948718 0.03898410
## 28 2.8 0.08948718 0.03898410
## 29 2.9 0.08948718 0.03898410
## 30 3.0 0.08948718 0.03898410
## 31 3.1 0.08948718 0.03898410
## 32 3.2 0.08948718 0.03898410
## 33 3.3 0.08948718 0.03898410
## 34 3.4 0.08948718 0.03898410
## 35 3.5 0.08948718 0.03898410
## 36 3.6 0.08948718 0.03898410
## 37 3.7 0.08948718 0.03898410
## 38 3.8 0.08948718 0.03898410
## 39 3.9 0.08948718 0.03898410
## 40 4.0 0.08948718 0.03898410
## 41 4.1 0.08948718 0.03898410
## 42 4.2 0.08948718 0.03898410
## 43 4.3 0.08948718 0.03898410
## 44 4.4 0.08948718 0.03898410
## 45 4.5 0.08948718 0.03898410
## 46 4.6 0.08948718 0.03898410
## 47 4.7 0.08948718 0.03898410
## 48 4.8 0.08948718 0.03898410
## 49 4.9 0.08948718 0.03898410
## 50 5.0 0.08948718 0.03898410
## 51 5.1 0.08948718 0.03898410
## 52 5.2 0.08948718 0.03898410
## 53 5.3 0.08948718 0.03898410
## 54 5.4 0.08948718 0.03898410
## 55 5.5 0.08948718 0.03898410
## 56 5.6 0.08948718 0.03898410
## 57 5.7 0.08948718 0.03898410
## 58 5.8 0.08948718 0.03898410
## 59 5.9 0.08948718 0.03898410
## 60 6.0 0.08948718 0.03898410
## 61 6.1 0.08948718 0.03898410
## 62 6.2 0.08948718 0.03898410
## 63 6.3 0.08948718 0.03898410
## 64 6.4 0.08948718 0.03898410
## 65 6.5 0.08948718 0.03898410
## 66 6.6 0.08948718 0.03898410
## 67 6.7 0.08948718 0.03898410
## 68 6.8 0.08948718 0.03898410
## 69 6.9 0.08948718 0.03898410
## 70 7.0 0.08948718 0.03898410
## 71 7.1 0.08948718 0.03898410
## 72 7.2 0.08948718 0.03898410
## 73 7.3 0.08948718 0.03898410
## 74 7.4 0.08948718 0.03898410
## 75 7.5 0.08948718 0.03898410
## 76 7.6 0.08948718 0.03898410
## 77 7.7 0.08948718 0.03898410
## 78 7.8 0.08948718 0.03898410
## 79 7.9 0.08948718 0.03898410
## 80 8.0 0.08948718 0.03898410
## 81 8.1 0.08948718 0.03898410
## 82 8.2 0.08948718 0.03898410
## 83 8.3 0.08948718 0.03898410
## 84 8.4 0.08948718 0.03898410
## 85 8.5 0.08948718 0.03898410
## 86 8.6 0.08948718 0.03898410
## 87 8.7 0.08948718 0.03898410
## 88 8.8 0.08948718 0.03898410
## 89 8.9 0.08948718 0.03898410
## 90 9.0 0.08948718 0.03898410
## 91 9.1 0.08948718 0.03898410
## 92 9.2 0.08948718 0.03898410
## 93 9.3 0.08948718 0.03898410
## 94 9.4 0.08948718 0.03898410
## 95 9.5 0.08948718 0.03898410
## 96 9.6 0.08948718 0.03898410
## 97 9.7 0.08948718 0.03898410
## 98 9.8 0.08948718 0.03898410
## 99 9.9 0.08948718 0.03898410
## 100 10.0 0.08948718 0.03898410plot(linear_svm_tune$performances[,c(1,2)], type = 'l')
Best performance is 0.08429487 which occurs at costs 0.5 and 0.7. So at
a cost between (0.5,0.7) we would see the lowest error rate / highest
accuracy in this specific SVM model.
7c) Now repeat (b), this time using SVMs with radial and polynomial basis
kernels, with different values of gamma and degree and cost. Comment on your results.
cl <- makeCluster(detectCores())
registerDoParallel(cl)
set.seed(1)
gammas = seq(0.1,3,0.1)
costs = seq(0.1,3,0.1)
ctrl = tune.control(cross = 5)
#radial_svm_tune = tune(svm, mpg_binary~., data = auto, kernel = 'radial',
# scale = T, ranges = list(cost = costs, gamma = gammas))
radial_svm_tune <- tune(svm, mpg_binary ~ ., data = auto,
scale = TRUE,
ranges = list(cost = costs, gamma = gammas),
method = 'radial',
tunecontrol = ctrl)
summary(radial_svm_tune)##
## Parameter tuning of 'svm':
##
## - sampling method: 5-fold cross validation
##
## - best parameters:
## cost gamma
## 0.9 1.3
##
## - best performance: 0.06897111
##
## - Detailed performance results:
## cost gamma error dispersion
## 1 0.1 0.1 0.08935411 0.03862716
## 2 0.2 0.1 0.08935411 0.03862716
## 3 0.3 0.1 0.08935411 0.03862716
## 4 0.4 0.1 0.08935411 0.03862716
## 5 0.5 0.1 0.08679000 0.03333947
## 6 0.6 0.1 0.08679000 0.03333947
## 7 0.7 0.1 0.08935411 0.03410758
## 8 0.8 0.1 0.08935411 0.03410758
## 9 0.9 0.1 0.08935411 0.03410758
## 10 1.0 0.1 0.08935411 0.03410758
## 11 1.1 0.1 0.09188575 0.03332466
## 12 1.2 0.1 0.08935411 0.03410758
## 13 1.3 0.1 0.08935411 0.03410758
## 14 1.4 0.1 0.08935411 0.03410758
## 15 1.5 0.1 0.08935411 0.03410758
## 16 1.6 0.1 0.08935411 0.03410758
## 17 1.7 0.1 0.08935411 0.03410758
## 18 1.8 0.1 0.08935411 0.03410758
## 19 1.9 0.1 0.08935411 0.03410758
## 20 2.0 0.1 0.08935411 0.03410758
## 21 2.1 0.1 0.08682246 0.03578006
## 22 2.2 0.1 0.08682246 0.03578006
## 23 2.3 0.1 0.08938656 0.03294333
## 24 2.4 0.1 0.08682246 0.03215066
## 25 2.5 0.1 0.08682246 0.03215066
## 26 2.6 0.1 0.08682246 0.03215066
## 27 2.7 0.1 0.08682246 0.03215066
## 28 2.8 0.1 0.08682246 0.03215066
## 29 2.9 0.1 0.08682246 0.03215066
## 30 3.0 0.1 0.08682246 0.03215066
## 31 0.1 0.2 0.08935411 0.03862716
## 32 0.2 0.2 0.08935411 0.03862716
## 33 0.3 0.2 0.08935411 0.03862716
## 34 0.4 0.2 0.08935411 0.03862716
## 35 0.5 0.2 0.08679000 0.03333947
## 36 0.6 0.2 0.08679000 0.03333947
## 37 0.7 0.2 0.08682246 0.03578006
## 38 0.8 0.2 0.08682246 0.03578006
## 39 0.9 0.2 0.08682246 0.03578006
## 40 1.0 0.2 0.08938656 0.03294333
## 41 1.1 0.2 0.09191821 0.03085690
## 42 1.2 0.2 0.09191821 0.03085690
## 43 1.3 0.2 0.08938656 0.03294333
## 44 1.4 0.2 0.08682246 0.02805559
## 45 1.5 0.2 0.08425836 0.02681570
## 46 1.6 0.2 0.08682246 0.03215066
## 47 1.7 0.2 0.08679000 0.03205106
## 48 1.8 0.2 0.08679000 0.03205106
## 49 1.9 0.2 0.08935411 0.03024419
## 50 2.0 0.2 0.08935411 0.03024419
## 51 2.1 0.2 0.08682246 0.03084610
## 52 2.2 0.2 0.08682246 0.03084610
## 53 2.3 0.2 0.08682246 0.03084610
## 54 2.4 0.2 0.08682246 0.03084610
## 55 2.5 0.2 0.09195067 0.04216500
## 56 2.6 0.2 0.09195067 0.04216500
## 57 2.7 0.2 0.08938656 0.04367025
## 58 2.8 0.2 0.09191821 0.04211859
## 59 2.9 0.2 0.09191821 0.04211859
## 60 3.0 0.2 0.09191821 0.04211859
## 61 0.1 0.3 0.08679000 0.03901838
## 62 0.2 0.3 0.08935411 0.03862716
## 63 0.3 0.3 0.08935411 0.03862716
## 64 0.4 0.3 0.08679000 0.03333947
## 65 0.5 0.3 0.08935411 0.03410758
## 66 0.6 0.3 0.08938656 0.03294333
## 67 0.7 0.3 0.08938656 0.03294333
## 68 0.8 0.3 0.08425836 0.02681570
## 69 0.9 0.3 0.08425836 0.02681570
## 70 1.0 0.3 0.08682246 0.03215066
## 71 1.1 0.3 0.08425836 0.03236993
## 72 1.2 0.3 0.08679000 0.03205106
## 73 1.3 0.3 0.08429081 0.03365205
## 74 1.4 0.3 0.08172671 0.03482187
## 75 1.5 0.3 0.08429081 0.04031820
## 76 1.6 0.3 0.08685492 0.04587263
## 77 1.7 0.3 0.08938656 0.04367025
## 78 1.8 0.3 0.08938656 0.04367025
## 79 1.9 0.3 0.08938656 0.04367025
## 80 2.0 0.3 0.08682246 0.03800761
## 81 2.1 0.3 0.08682246 0.03800761
## 82 2.2 0.3 0.08682246 0.03800761
## 83 2.3 0.3 0.08682246 0.03800761
## 84 2.4 0.3 0.08172671 0.04031803
## 85 2.5 0.3 0.08172671 0.04031803
## 86 2.6 0.3 0.08425836 0.03925442
## 87 2.7 0.3 0.08425836 0.03925442
## 88 2.8 0.3 0.08425836 0.03925442
## 89 2.9 0.3 0.08422590 0.04023129
## 90 3.0 0.3 0.08422590 0.04023129
## 91 0.1 0.4 0.08679000 0.03901838
## 92 0.2 0.4 0.08679000 0.03901838
## 93 0.3 0.4 0.08679000 0.03333947
## 94 0.4 0.4 0.08169426 0.03478347
## 95 0.5 0.4 0.08425836 0.02681570
## 96 0.6 0.4 0.08425836 0.02681570
## 97 0.7 0.4 0.08682246 0.03215066
## 98 0.8 0.4 0.08425836 0.03236993
## 99 0.9 0.4 0.08425836 0.03236993
## 100 1.0 0.4 0.08169426 0.03358135
## 101 1.1 0.4 0.08425836 0.03925442
## 102 1.2 0.4 0.08172671 0.04129963
## 103 1.3 0.4 0.08172671 0.04031803
## 104 1.4 0.4 0.08429081 0.04605129
## 105 1.5 0.4 0.08429081 0.04605129
## 106 1.6 0.4 0.08172671 0.04031803
## 107 1.7 0.4 0.08172671 0.04031803
## 108 1.8 0.4 0.08172671 0.04031803
## 109 1.9 0.4 0.08425836 0.03925442
## 110 2.0 0.4 0.08169426 0.04126725
## 111 2.1 0.4 0.08169426 0.04126725
## 112 2.2 0.4 0.08169426 0.04126725
## 113 2.3 0.4 0.07656605 0.03015716
## 114 2.4 0.4 0.07909770 0.02928279
## 115 2.5 0.4 0.07909770 0.02928279
## 116 2.6 0.4 0.07909770 0.02928279
## 117 2.7 0.4 0.07653359 0.03265874
## 118 2.8 0.4 0.07653359 0.03265874
## 119 2.9 0.4 0.07143784 0.03465162
## 120 3.0 0.4 0.07143784 0.03465162
## 121 0.1 0.5 0.08679000 0.03901838
## 122 0.2 0.5 0.08679000 0.03901838
## 123 0.3 0.5 0.08169426 0.03478347
## 124 0.4 0.5 0.08425836 0.02681570
## 125 0.5 0.5 0.08425836 0.02681570
## 126 0.6 0.5 0.08682246 0.03215066
## 127 0.7 0.5 0.08169426 0.03358135
## 128 0.8 0.5 0.08422590 0.03351705
## 129 0.9 0.5 0.08172671 0.04031803
## 130 1.0 0.5 0.08172671 0.04031803
## 131 1.1 0.5 0.08425836 0.03925442
## 132 1.2 0.5 0.08425836 0.03925442
## 133 1.3 0.5 0.08682246 0.04494283
## 134 1.4 0.5 0.08425836 0.03925442
## 135 1.5 0.5 0.08169426 0.03358135
## 136 1.6 0.5 0.08422590 0.03229981
## 137 1.7 0.5 0.08166180 0.02668426
## 138 1.8 0.5 0.07913015 0.02793296
## 139 1.9 0.5 0.07913015 0.02793296
## 140 2.0 0.5 0.07400195 0.03197220
## 141 2.1 0.5 0.07400195 0.03197220
## 142 2.2 0.5 0.07147030 0.03227913
## 143 2.3 0.5 0.07400195 0.03197220
## 144 2.4 0.5 0.07400195 0.03197220
## 145 2.5 0.5 0.07400195 0.03197220
## 146 2.6 0.5 0.07400195 0.03197220
## 147 2.7 0.5 0.07400195 0.03197220
## 148 2.8 0.5 0.07400195 0.03197220
## 149 2.9 0.5 0.07400195 0.03197220
## 150 3.0 0.5 0.07656605 0.03015716
## 151 0.1 0.6 0.08679000 0.03901838
## 152 0.2 0.6 0.08935411 0.03862716
## 153 0.3 0.6 0.08169426 0.02968431
## 154 0.4 0.6 0.08425836 0.02681570
## 155 0.5 0.6 0.08425836 0.03236993
## 156 0.6 0.6 0.08169426 0.03358135
## 157 0.7 0.6 0.07916261 0.03458487
## 158 0.8 0.6 0.08172671 0.04031803
## 159 0.9 0.6 0.08172671 0.04031803
## 160 1.0 0.6 0.08425836 0.03925442
## 161 1.1 0.6 0.08425836 0.03925442
## 162 1.2 0.6 0.08682246 0.04494283
## 163 1.3 0.6 0.08429081 0.04691307
## 164 1.4 0.6 0.08172671 0.04129963
## 165 1.5 0.6 0.07913015 0.02793296
## 166 1.6 0.6 0.07913015 0.02793296
## 167 1.7 0.6 0.07403440 0.03074741
## 168 1.8 0.6 0.07403440 0.03074741
## 169 1.9 0.6 0.07403440 0.03074741
## 170 2.0 0.6 0.07656605 0.03015716
## 171 2.1 0.6 0.07400195 0.03197220
## 172 2.2 0.6 0.07400195 0.03197220
## 173 2.3 0.6 0.07400195 0.03197220
## 174 2.4 0.6 0.07400195 0.03197220
## 175 2.5 0.6 0.07400195 0.03197220
## 176 2.6 0.6 0.07400195 0.03197220
## 177 2.7 0.6 0.07656605 0.03015716
## 178 2.8 0.6 0.07656605 0.03015716
## 179 2.9 0.6 0.07656605 0.03015716
## 180 3.0 0.6 0.07656605 0.03015716
## 181 0.1 0.7 0.09188575 0.03793763
## 182 0.2 0.7 0.08679000 0.03333947
## 183 0.3 0.7 0.08425836 0.02681570
## 184 0.4 0.7 0.08425836 0.03236993
## 185 0.5 0.7 0.08169426 0.03358135
## 186 0.6 0.7 0.07916261 0.03458487
## 187 0.7 0.7 0.08172671 0.04031803
## 188 0.8 0.7 0.08172671 0.04031803
## 189 0.9 0.7 0.08172671 0.04031803
## 190 1.0 0.7 0.08172671 0.04129963
## 191 1.1 0.7 0.08172671 0.04129963
## 192 1.2 0.7 0.08172671 0.04129963
## 193 1.3 0.7 0.07916261 0.03572434
## 194 1.4 0.7 0.07150276 0.03233334
## 195 1.5 0.7 0.07403440 0.03074741
## 196 1.6 0.7 0.07403440 0.03074741
## 197 1.7 0.7 0.07403440 0.03074741
## 198 1.8 0.7 0.07656605 0.03015716
## 199 1.9 0.7 0.07656605 0.03015716
## 200 2.0 0.7 0.07656605 0.03015716
## 201 2.1 0.7 0.07656605 0.03015716
## 202 2.2 0.7 0.07656605 0.03015716
## 203 2.3 0.7 0.07656605 0.03015716
## 204 2.4 0.7 0.07656605 0.03015716
## 205 2.5 0.7 0.07656605 0.03015716
## 206 2.6 0.7 0.07913015 0.02936721
## 207 2.7 0.7 0.07913015 0.02936721
## 208 2.8 0.7 0.07913015 0.02936721
## 209 2.9 0.7 0.07913015 0.02936721
## 210 3.0 0.7 0.07656605 0.03015716
## 211 0.1 0.8 0.09441740 0.03701955
## 212 0.2 0.8 0.08932165 0.03278650
## 213 0.3 0.8 0.08425836 0.02681570
## 214 0.4 0.8 0.08425836 0.03236993
## 215 0.5 0.8 0.07916261 0.03458487
## 216 0.6 0.8 0.07916261 0.03458487
## 217 0.7 0.8 0.08172671 0.04031803
## 218 0.8 0.8 0.07919507 0.04212210
## 219 0.9 0.8 0.07919507 0.04212210
## 220 1.0 0.8 0.07916261 0.03572434
## 221 1.1 0.8 0.08172671 0.04129963
## 222 1.2 0.8 0.07406686 0.03797097
## 223 1.3 0.8 0.07150276 0.03233334
## 224 1.4 0.8 0.07150276 0.03233334
## 225 1.5 0.8 0.07403440 0.03202372
## 226 1.6 0.8 0.07656605 0.03015716
## 227 1.7 0.8 0.07656605 0.03015716
## 228 1.8 0.8 0.07656605 0.03015716
## 229 1.9 0.8 0.07656605 0.03015716
## 230 2.0 0.8 0.07656605 0.03015716
## 231 2.1 0.8 0.07656605 0.03015716
## 232 2.2 0.8 0.07656605 0.03015716
## 233 2.3 0.8 0.07656605 0.03015716
## 234 2.4 0.8 0.07656605 0.03015716
## 235 2.5 0.8 0.07913015 0.02936721
## 236 2.6 0.8 0.08166180 0.02818213
## 237 2.7 0.8 0.08166180 0.02818213
## 238 2.8 0.8 0.08166180 0.02818213
## 239 2.9 0.8 0.08166180 0.02818213
## 240 3.0 0.8 0.08166180 0.02818213
## 241 0.1 0.9 0.09444985 0.03481173
## 242 0.2 0.9 0.08675755 0.02786381
## 243 0.3 0.9 0.08169426 0.02677299
## 244 0.4 0.9 0.08172671 0.03365185
## 245 0.5 0.9 0.07916261 0.03458487
## 246 0.6 0.9 0.08172671 0.04031803
## 247 0.7 0.9 0.07919507 0.04212210
## 248 0.8 0.9 0.07663096 0.03645012
## 249 0.9 0.9 0.07663096 0.03645012
## 250 1.0 0.9 0.07916261 0.03572434
## 251 1.1 0.9 0.07663096 0.04363360
## 252 1.2 0.9 0.07150276 0.03233334
## 253 1.3 0.9 0.07403440 0.03202372
## 254 1.4 0.9 0.07403440 0.03202372
## 255 1.5 0.9 0.07403440 0.03202372
## 256 1.6 0.9 0.07403440 0.03202372
## 257 1.7 0.9 0.07403440 0.03202372
## 258 1.8 0.9 0.07403440 0.03202372
## 259 1.9 0.9 0.07403440 0.03202372
## 260 2.0 0.9 0.07403440 0.03202372
## 261 2.1 0.9 0.07656605 0.03015716
## 262 2.2 0.9 0.07656605 0.03015716
## 263 2.3 0.9 0.07656605 0.03015716
## 264 2.4 0.9 0.08166180 0.02818213
## 265 2.5 0.9 0.08166180 0.02818213
## 266 2.6 0.9 0.08166180 0.02818213
## 267 2.7 0.9 0.08166180 0.02818213
## 268 2.8 0.9 0.08166180 0.02818213
## 269 2.9 0.9 0.08166180 0.02818213
## 270 3.0 0.9 0.08166180 0.02818213
## 271 0.1 1.0 0.09698150 0.03356801
## 272 0.2 1.0 0.08675755 0.02786381
## 273 0.3 1.0 0.08679000 0.03205106
## 274 0.4 1.0 0.08172671 0.03365185
## 275 0.5 1.0 0.07916261 0.03458487
## 276 0.6 1.0 0.08172671 0.04031803
## 277 0.7 1.0 0.07663096 0.03645012
## 278 0.8 1.0 0.07409932 0.03801430
## 279 0.9 1.0 0.07663096 0.03645012
## 280 1.0 1.0 0.07406686 0.03797097
## 281 1.1 1.0 0.07659851 0.03749187
## 282 1.2 1.0 0.07403440 0.03202372
## 283 1.3 1.0 0.07403440 0.03202372
## 284 1.4 1.0 0.07403440 0.03202372
## 285 1.5 1.0 0.07403440 0.03202372
## 286 1.6 1.0 0.07403440 0.03202372
## 287 1.7 1.0 0.07656605 0.03015716
## 288 1.8 1.0 0.07656605 0.03015716
## 289 1.9 1.0 0.07656605 0.03015716
## 290 2.0 1.0 0.07656605 0.03015716
## 291 2.1 1.0 0.07656605 0.03015716
## 292 2.2 1.0 0.07656605 0.03015716
## 293 2.3 1.0 0.07913015 0.02936721
## 294 2.4 1.0 0.07913015 0.02936721
## 295 2.5 1.0 0.07913015 0.02936721
## 296 2.6 1.0 0.07913015 0.02936721
## 297 2.7 1.0 0.07913015 0.02936721
## 298 2.8 1.0 0.07913015 0.02936721
## 299 2.9 1.0 0.07913015 0.02936721
## 300 3.0 1.0 0.08166180 0.02818213
## 301 0.1 1.1 0.10204479 0.02864029
## 302 0.2 1.1 0.08675755 0.02786381
## 303 0.3 1.1 0.08425836 0.03236993
## 304 0.4 1.1 0.08172671 0.03482187
## 305 0.5 1.1 0.07663096 0.03645012
## 306 0.6 1.1 0.07666342 0.04366892
## 307 0.7 1.1 0.07409932 0.03801430
## 308 0.8 1.1 0.07663096 0.03645012
## 309 0.9 1.1 0.07153522 0.03926884
## 310 1.0 1.1 0.07403440 0.03202372
## 311 1.1 1.1 0.07659851 0.03749187
## 312 1.2 1.1 0.07403440 0.03202372
## 313 1.3 1.1 0.07403440 0.03202372
## 314 1.4 1.1 0.07403440 0.03202372
## 315 1.5 1.1 0.07656605 0.03015716
## 316 1.6 1.1 0.07656605 0.03015716
## 317 1.7 1.1 0.07656605 0.03015716
## 318 1.8 1.1 0.07656605 0.03015716
## 319 1.9 1.1 0.07656605 0.03015716
## 320 2.0 1.1 0.07656605 0.03015716
## 321 2.1 1.1 0.07656605 0.03015716
## 322 2.2 1.1 0.07913015 0.02936721
## 323 2.3 1.1 0.07913015 0.02936721
## 324 2.4 1.1 0.07913015 0.02936721
## 325 2.5 1.1 0.07913015 0.02936721
## 326 2.6 1.1 0.07913015 0.02936721
## 327 2.7 1.1 0.07913015 0.02936721
## 328 2.8 1.1 0.07913015 0.02936721
## 329 2.9 1.1 0.07913015 0.02936721
## 330 3.0 1.1 0.07913015 0.02936721
## 331 0.1 1.2 0.10963973 0.02455324
## 332 0.2 1.2 0.08932165 0.02412174
## 333 0.3 1.2 0.08172671 0.02972930
## 334 0.4 1.2 0.08172671 0.03482187
## 335 0.5 1.2 0.07663096 0.03645012
## 336 0.6 1.2 0.07666342 0.04366892
## 337 0.7 1.2 0.07663096 0.03645012
## 338 0.8 1.2 0.07409932 0.03801430
## 339 0.9 1.2 0.07153522 0.03926884
## 340 1.0 1.2 0.07406686 0.03797097
## 341 1.1 1.2 0.07659851 0.03749187
## 342 1.2 1.2 0.07659851 0.03749187
## 343 1.3 1.2 0.07656605 0.03015716
## 344 1.4 1.2 0.07656605 0.03015716
## 345 1.5 1.2 0.07656605 0.03015716
## 346 1.6 1.2 0.07656605 0.03015716
## 347 1.7 1.2 0.07656605 0.03015716
## 348 1.8 1.2 0.07913015 0.03568399
## 349 1.9 1.2 0.07913015 0.03568399
## 350 2.0 1.2 0.07656605 0.03015716
## 351 2.1 1.2 0.07913015 0.02936721
## 352 2.2 1.2 0.07913015 0.02936721
## 353 2.3 1.2 0.07913015 0.02936721
## 354 2.4 1.2 0.07659851 0.03024254
## 355 2.5 1.2 0.07659851 0.03024254
## 356 2.6 1.2 0.07659851 0.03024254
## 357 2.7 1.2 0.07659851 0.03024254
## 358 2.8 1.2 0.07659851 0.03024254
## 359 2.9 1.2 0.07659851 0.03024254
## 360 3.0 1.2 0.07659851 0.03024254
## 361 0.1 1.3 0.11476793 0.02537008
## 362 0.2 1.3 0.09185329 0.02300586
## 363 0.3 1.3 0.08425836 0.02681570
## 364 0.4 1.3 0.08172671 0.03482187
## 365 0.5 1.3 0.07916261 0.03572434
## 366 0.6 1.3 0.07663096 0.03645012
## 367 0.7 1.3 0.07409932 0.03801430
## 368 0.8 1.3 0.07153522 0.03926884
## 369 0.9 1.3 0.06897111 0.03360749
## 370 1.0 1.3 0.07406686 0.03797097
## 371 1.1 1.3 0.07659851 0.03640776
## 372 1.2 1.3 0.07659851 0.03640776
## 373 1.3 1.3 0.07659851 0.03640776
## 374 1.4 1.3 0.07659851 0.03640776
## 375 1.5 1.3 0.07403440 0.03074741
## 376 1.6 1.3 0.07659851 0.03640776
## 377 1.7 1.3 0.07659851 0.03640776
## 378 1.8 1.3 0.07659851 0.03640776
## 379 1.9 1.3 0.07659851 0.03640776
## 380 2.0 1.3 0.07916261 0.03575326
## 381 2.1 1.3 0.07659851 0.03024254
## 382 2.2 1.3 0.07659851 0.03024254
## 383 2.3 1.3 0.07659851 0.03024254
## 384 2.4 1.3 0.07659851 0.03024254
## 385 2.5 1.3 0.07659851 0.03024254
## 386 2.6 1.3 0.07659851 0.03024254
## 387 2.7 1.3 0.07659851 0.03024254
## 388 2.8 1.3 0.07659851 0.03024254
## 389 2.9 1.3 0.07656605 0.02409820
## 390 3.0 1.3 0.07656605 0.02409820
## 391 0.1 1.4 0.13012009 0.01892844
## 392 0.2 1.4 0.09188575 0.02128545
## 393 0.3 1.4 0.08425836 0.02681570
## 394 0.4 1.4 0.08169426 0.02677299
## 395 0.5 1.4 0.08172671 0.03365185
## 396 0.6 1.4 0.07666342 0.03760157
## 397 0.7 1.4 0.07409932 0.03801430
## 398 0.8 1.4 0.07153522 0.03926884
## 399 0.9 1.4 0.07150276 0.03233334
## 400 1.0 1.4 0.07659851 0.03640776
## 401 1.1 1.4 0.07659851 0.03640776
## 402 1.2 1.4 0.07659851 0.03640776
## 403 1.3 1.4 0.07659851 0.03640776
## 404 1.4 1.4 0.07659851 0.03640776
## 405 1.5 1.4 0.07659851 0.03640776
## 406 1.6 1.4 0.07659851 0.03640776
## 407 1.7 1.4 0.07659851 0.03640776
## 408 1.8 1.4 0.07659851 0.03640776
## 409 1.9 1.4 0.07916261 0.03575326
## 410 2.0 1.4 0.07916261 0.03575326
## 411 2.1 1.4 0.07659851 0.03024254
## 412 2.2 1.4 0.07659851 0.03024254
## 413 2.3 1.4 0.07659851 0.03024254
## 414 2.4 1.4 0.07659851 0.03024254
## 415 2.5 1.4 0.07659851 0.03024254
## 416 2.6 1.4 0.07403440 0.02483289
## 417 2.7 1.4 0.07656605 0.02409820
## 418 2.8 1.4 0.07656605 0.02409820
## 419 2.9 1.4 0.07656605 0.02409820
## 420 3.0 1.4 0.07656605 0.02409820
## 421 0.1 1.5 0.14037650 0.02426120
## 422 0.2 1.5 0.09694904 0.01948150
## 423 0.3 1.5 0.08679000 0.02486813
## 424 0.4 1.5 0.08675755 0.02473917
## 425 0.5 1.5 0.08425836 0.03236993
## 426 0.6 1.5 0.08172671 0.03482187
## 427 0.7 1.5 0.07409932 0.03801430
## 428 0.8 1.5 0.07409932 0.03801430
## 429 0.9 1.5 0.07403440 0.03074741
## 430 1.0 1.5 0.07659851 0.03640776
## 431 1.1 1.5 0.07659851 0.03640776
## 432 1.2 1.5 0.07659851 0.03640776
## 433 1.3 1.5 0.07659851 0.03640776
## 434 1.4 1.5 0.07659851 0.03640776
## 435 1.5 1.5 0.07659851 0.03640776
## 436 1.6 1.5 0.07659851 0.03640776
## 437 1.7 1.5 0.07659851 0.03640776
## 438 1.8 1.5 0.07916261 0.03575326
## 439 1.9 1.5 0.07916261 0.03575326
## 440 2.0 1.5 0.07916261 0.03575326
## 441 2.1 1.5 0.07916261 0.02802140
## 442 2.2 1.5 0.07916261 0.02802140
## 443 2.3 1.5 0.07659851 0.02244320
## 444 2.4 1.5 0.07913015 0.02124898
## 445 2.5 1.5 0.07913015 0.02124898
## 446 2.6 1.5 0.07913015 0.02124898
## 447 2.7 1.5 0.07913015 0.02124898
## 448 2.8 1.5 0.07913015 0.02124898
## 449 2.9 1.5 0.07913015 0.02124898
## 450 3.0 1.5 0.08169426 0.01969928
## 451 0.1 1.6 0.15316456 0.04064443
## 452 0.2 1.6 0.09698150 0.01746378
## 453 0.3 1.6 0.08932165 0.02412174
## 454 0.4 1.6 0.08675755 0.02473917
## 455 0.5 1.6 0.08169426 0.02677299
## 456 0.6 1.6 0.08679000 0.03077588
## 457 0.7 1.6 0.07663096 0.03645012
## 458 0.8 1.6 0.07406686 0.03080094
## 459 0.9 1.6 0.07659851 0.02885183
## 460 1.0 1.6 0.07916261 0.03458487
## 461 1.1 1.6 0.07916261 0.03458487
## 462 1.2 1.6 0.07916261 0.03458487
## 463 1.3 1.6 0.07916261 0.03458487
## 464 1.4 1.6 0.07916261 0.03458487
## 465 1.5 1.6 0.07916261 0.03458487
## 466 1.6 1.6 0.07916261 0.03458487
## 467 1.7 1.6 0.08172671 0.03365185
## 468 1.8 1.6 0.08172671 0.03365185
## 469 1.9 1.6 0.08172671 0.03365185
## 470 2.0 1.6 0.08172671 0.03365185
## 471 2.1 1.6 0.07916261 0.02802140
## 472 2.2 1.6 0.07659851 0.02244320
## 473 2.3 1.6 0.07913015 0.02124898
## 474 2.4 1.6 0.07913015 0.02124898
## 475 2.5 1.6 0.07913015 0.02124898
## 476 2.6 1.6 0.07913015 0.02124898
## 477 2.7 1.6 0.07913015 0.02124898
## 478 2.8 1.6 0.07913015 0.02124898
## 479 2.9 1.6 0.08169426 0.01969928
## 480 3.0 1.6 0.08169426 0.01969928
## 481 0.1 1.7 0.16079195 0.03240287
## 482 0.2 1.7 0.09698150 0.01746378
## 483 0.3 1.7 0.09188575 0.02128545
## 484 0.4 1.7 0.08932165 0.02235342
## 485 0.5 1.7 0.08169426 0.02677299
## 486 0.6 1.7 0.08679000 0.03077588
## 487 0.7 1.7 0.08169426 0.03358135
## 488 0.8 1.7 0.07406686 0.03080094
## 489 0.9 1.7 0.07659851 0.02885183
## 490 1.0 1.7 0.07916261 0.03458487
## 491 1.1 1.7 0.07916261 0.03458487
## 492 1.2 1.7 0.07916261 0.03458487
## 493 1.3 1.7 0.07916261 0.03458487
## 494 1.4 1.7 0.07916261 0.03458487
## 495 1.5 1.7 0.07916261 0.03458487
## 496 1.6 1.7 0.08172671 0.03365185
## 497 1.7 1.7 0.08172671 0.03365185
## 498 1.8 1.7 0.08172671 0.03365185
## 499 1.9 1.7 0.07916261 0.02802140
## 500 2.0 1.7 0.07916261 0.02802140
## 501 2.1 1.7 0.08169426 0.02677299
## 502 2.2 1.7 0.07913015 0.02124898
## 503 2.3 1.7 0.07913015 0.02124898
## 504 2.4 1.7 0.08169426 0.02677299
## 505 2.5 1.7 0.08169426 0.02677299
## 506 2.6 1.7 0.08675755 0.02778952
## 507 2.7 1.7 0.08675755 0.02778952
## 508 2.8 1.7 0.08932165 0.02568864
## 509 2.9 1.7 0.08932165 0.02568864
## 510 3.0 1.7 0.09444985 0.02514841
## 511 0.1 1.8 0.16588770 0.03036191
## 512 0.2 1.8 0.09951315 0.01913669
## 513 0.3 1.8 0.09441740 0.01960239
## 514 0.4 1.8 0.08932165 0.02235342
## 515 0.5 1.8 0.08169426 0.02677299
## 516 0.6 1.8 0.08169426 0.02677299
## 517 0.7 1.8 0.08675755 0.03198344
## 518 0.8 1.8 0.08166180 0.02668426
## 519 0.9 1.8 0.08675755 0.03198344
## 520 1.0 1.8 0.07916261 0.03458487
## 521 1.1 1.8 0.07916261 0.03458487
## 522 1.2 1.8 0.07916261 0.03458487
## 523 1.3 1.8 0.07916261 0.03458487
## 524 1.4 1.8 0.07916261 0.03458487
## 525 1.5 1.8 0.08172671 0.03365185
## 526 1.6 1.8 0.08172671 0.03365185
## 527 1.7 1.8 0.07916261 0.02802140
## 528 1.8 1.8 0.07916261 0.02802140
## 529 1.9 1.8 0.08169426 0.02677299
## 530 2.0 1.8 0.08675755 0.02778952
## 531 2.1 1.8 0.08675755 0.02778952
## 532 2.2 1.8 0.08675755 0.02778952
## 533 2.3 1.8 0.08675755 0.02778952
## 534 2.4 1.8 0.08675755 0.02778952
## 535 2.5 1.8 0.08675755 0.02778952
## 536 2.6 1.8 0.08675755 0.02778952
## 537 2.7 1.8 0.08932165 0.02568864
## 538 2.8 1.8 0.08932165 0.02568864
## 539 2.9 1.8 0.09188575 0.02476492
## 540 3.0 1.8 0.09444985 0.02514841
## 541 0.1 1.9 0.18883479 0.04675689
## 542 0.2 1.9 0.10710808 0.02115564
## 543 0.3 1.9 0.09698150 0.01746378
## 544 0.4 1.9 0.08679000 0.02315688
## 545 0.5 1.9 0.08425836 0.02523685
## 546 0.6 1.9 0.07913015 0.02793296
## 547 0.7 1.9 0.08675755 0.03198344
## 548 0.8 1.9 0.08416099 0.02132569
## 549 0.9 1.9 0.08675755 0.03198344
## 550 1.0 1.9 0.08675755 0.03198344
## 551 1.1 1.9 0.08675755 0.03198344
## 552 1.2 1.9 0.08675755 0.03198344
## 553 1.3 1.9 0.08675755 0.03198344
## 554 1.4 1.9 0.08932165 0.03017597
## 555 1.5 1.9 0.08932165 0.03017597
## 556 1.6 1.9 0.08675755 0.02473917
## 557 1.7 1.9 0.08675755 0.02473917
## 558 1.8 1.9 0.08675755 0.02473917
## 559 1.9 1.9 0.08928919 0.02560824
## 560 2.0 1.9 0.08928919 0.02560824
## 561 2.1 1.9 0.08928919 0.02560824
## 562 2.2 1.9 0.08928919 0.02560824
## 563 2.3 1.9 0.08928919 0.02560824
## 564 2.4 1.9 0.08928919 0.02560824
## 565 2.5 1.9 0.08928919 0.02560824
## 566 2.6 1.9 0.09185329 0.02296089
## 567 2.7 1.9 0.09185329 0.02296089
## 568 2.8 1.9 0.09185329 0.02296089
## 569 2.9 1.9 0.09694904 0.01948150
## 570 3.0 1.9 0.09698150 0.02161670
## 571 0.1 2.0 0.19905875 0.05511882
## 572 0.2 2.0 0.10967218 0.02124396
## 573 0.3 2.0 0.09441740 0.01960239
## 574 0.4 2.0 0.08935411 0.02249143
## 575 0.5 2.0 0.08425836 0.02523685
## 576 0.6 2.0 0.08166180 0.02668426
## 577 0.7 2.0 0.08419344 0.02660716
## 578 0.8 2.0 0.08416099 0.02132569
## 579 0.9 2.0 0.08672509 0.02622613
## 580 1.0 2.0 0.08675755 0.03198344
## 581 1.1 2.0 0.08675755 0.03198344
## 582 1.2 2.0 0.08675755 0.03198344
## 583 1.3 2.0 0.08675755 0.03198344
## 584 1.4 2.0 0.08932165 0.03017597
## 585 1.5 2.0 0.08675755 0.02473917
## 586 1.6 2.0 0.08675755 0.02473917
## 587 1.7 2.0 0.08675755 0.02473917
## 588 1.8 2.0 0.08928919 0.02560824
## 589 1.9 2.0 0.08928919 0.02560824
## 590 2.0 2.0 0.08928919 0.02560824
## 591 2.1 2.0 0.08928919 0.02560824
## 592 2.2 2.0 0.08928919 0.02560824
## 593 2.3 2.0 0.09182084 0.02456418
## 594 2.4 2.0 0.09182084 0.02456418
## 595 2.5 2.0 0.09438494 0.02141473
## 596 2.6 2.0 0.09438494 0.02141473
## 597 2.7 2.0 0.09438494 0.02141473
## 598 2.8 2.0 0.09441740 0.02154922
## 599 2.9 2.0 0.09698150 0.02161670
## 600 3.0 2.0 0.09698150 0.02161670
## 601 0.1 2.1 0.21181435 0.05804602
## 602 0.2 2.1 0.11480039 0.01276472
## 603 0.3 2.1 0.09698150 0.01746378
## 604 0.4 2.1 0.09188575 0.02128545
## 605 0.5 2.1 0.08425836 0.02523685
## 606 0.6 2.1 0.08422590 0.02514684
## 607 0.7 2.1 0.08162934 0.02141701
## 608 0.8 2.1 0.08416099 0.02132569
## 609 0.9 2.1 0.08672509 0.02622613
## 610 1.0 2.1 0.08672509 0.02622613
## 611 1.1 2.1 0.08928919 0.03140988
## 612 1.2 2.1 0.08928919 0.03140988
## 613 1.3 2.1 0.09185329 0.02929165
## 614 1.4 2.1 0.08928919 0.02399305
## 615 1.5 2.1 0.08928919 0.02399305
## 616 1.6 2.1 0.08928919 0.02399305
## 617 1.7 2.1 0.09182084 0.02456418
## 618 1.8 2.1 0.09182084 0.02456418
## 619 1.9 2.1 0.09182084 0.02456418
## 620 2.0 2.1 0.09182084 0.02456418
## 621 2.1 2.1 0.09182084 0.02456418
## 622 2.2 2.1 0.09182084 0.02456418
## 623 2.3 2.1 0.09182084 0.02456418
## 624 2.4 2.1 0.09182084 0.02456418
## 625 2.5 2.1 0.09438494 0.02141473
## 626 2.6 2.1 0.09185329 0.02296089
## 627 2.7 2.1 0.09441740 0.02154922
## 628 2.8 2.1 0.09441740 0.02154922
## 629 2.9 2.1 0.09698150 0.02161670
## 630 3.0 2.1 0.09441740 0.02507458
## 631 0.1 2.2 0.23982473 0.07284439
## 632 0.2 2.2 0.12499189 0.02267882
## 633 0.3 2.2 0.09441740 0.01960239
## 634 0.4 2.2 0.09188575 0.02128545
## 635 0.5 2.2 0.08425836 0.02523685
## 636 0.6 2.2 0.08422590 0.02514684
## 637 0.7 2.2 0.08162934 0.02141701
## 638 0.8 2.2 0.08159688 0.01695602
## 639 0.9 2.2 0.08672509 0.02622613
## 640 1.0 2.2 0.08672509 0.02622613
## 641 1.1 2.2 0.08672509 0.02622613
## 642 1.2 2.2 0.09185329 0.02929165
## 643 1.3 2.2 0.08928919 0.02399305
## 644 1.4 2.2 0.08928919 0.02399305
## 645 1.5 2.2 0.08928919 0.02399305
## 646 1.6 2.2 0.09182084 0.02456418
## 647 1.7 2.2 0.09182084 0.02456418
## 648 1.8 2.2 0.09182084 0.02456418
## 649 1.9 2.2 0.09182084 0.02456418
## 650 2.0 2.2 0.09182084 0.02456418
## 651 2.1 2.2 0.09182084 0.02456418
## 652 2.2 2.2 0.09182084 0.02456418
## 653 2.3 2.2 0.09182084 0.02456418
## 654 2.4 2.2 0.09185329 0.02296089
## 655 2.5 2.2 0.09185329 0.02296089
## 656 2.6 2.2 0.09185329 0.02296089
## 657 2.7 2.2 0.09441740 0.02154922
## 658 2.8 2.2 0.09441740 0.02507458
## 659 2.9 2.2 0.09441740 0.02507458
## 660 3.0 2.2 0.09441740 0.02507458
## 661 0.1 2.3 0.27559234 0.08655256
## 662 0.2 2.3 0.12755599 0.02549476
## 663 0.3 2.3 0.09951315 0.02107750
## 664 0.4 2.3 0.08935411 0.02249143
## 665 0.5 2.3 0.08682246 0.02495498
## 666 0.6 2.3 0.08422590 0.02514684
## 667 0.7 2.3 0.08419344 0.01947332
## 668 0.8 2.3 0.08159688 0.01695602
## 669 0.9 2.3 0.08672509 0.02622613
## 670 1.0 2.3 0.08672509 0.02622613
## 671 1.1 2.3 0.08672509 0.02622613
## 672 1.2 2.3 0.08928919 0.02399305
## 673 1.3 2.3 0.08928919 0.02399305
## 674 1.4 2.3 0.08928919 0.02399305
## 675 1.5 2.3 0.09182084 0.02456418
## 676 1.6 2.3 0.09182084 0.02456418
## 677 1.7 2.3 0.09182084 0.02456418
## 678 1.8 2.3 0.09182084 0.02456418
## 679 1.9 2.3 0.09182084 0.02456418
## 680 2.0 2.3 0.09182084 0.02456418
## 681 2.1 2.3 0.09182084 0.02456418
## 682 2.2 2.3 0.09182084 0.02456418
## 683 2.3 2.3 0.08928919 0.02560824
## 684 2.4 2.3 0.09185329 0.02296089
## 685 2.5 2.3 0.09185329 0.02296089
## 686 2.6 2.3 0.09441740 0.02154922
## 687 2.7 2.3 0.09185329 0.02468573
## 688 2.8 2.3 0.09441740 0.02507458
## 689 2.9 2.3 0.09441740 0.02507458
## 690 3.0 2.3 0.09698150 0.02963436
## 691 0.1 2.4 0.29604025 0.07971079
## 692 0.2 2.4 0.14031159 0.02549801
## 693 0.3 2.4 0.10207725 0.02035949
## 694 0.4 2.4 0.08935411 0.02249143
## 695 0.5 2.4 0.09188575 0.02128545
## 696 0.6 2.4 0.08422590 0.02514684
## 697 0.7 2.4 0.08419344 0.01947332
## 698 0.8 2.4 0.08159688 0.01695602
## 699 0.9 2.4 0.08672509 0.02622613
## 700 1.0 2.4 0.08672509 0.02622613
## 701 1.1 2.4 0.08928919 0.02399305
## 702 1.2 2.4 0.08928919 0.02399305
## 703 1.3 2.4 0.08928919 0.02399305
## 704 1.4 2.4 0.08928919 0.02399305
## 705 1.5 2.4 0.09182084 0.02456418
## 706 1.6 2.4 0.09182084 0.02456418
## 707 1.7 2.4 0.09182084 0.02456418
## 708 1.8 2.4 0.09182084 0.02456418
## 709 1.9 2.4 0.09182084 0.02456418
## 710 2.0 2.4 0.09182084 0.02456418
## 711 2.1 2.4 0.08928919 0.02560824
## 712 2.2 2.4 0.08928919 0.02560824
## 713 2.3 2.4 0.09185329 0.02296089
## 714 2.4 2.4 0.09185329 0.02296089
## 715 2.5 2.4 0.09441740 0.02154922
## 716 2.6 2.4 0.09185329 0.02468573
## 717 2.7 2.4 0.09441740 0.02507458
## 718 2.8 2.4 0.09441740 0.02507458
## 719 2.9 2.4 0.09698150 0.02963436
## 720 3.0 2.4 0.09698150 0.02963436
## 721 0.1 2.5 0.35215839 0.09407715
## 722 0.2 2.5 0.15306719 0.02009433
## 723 0.3 2.5 0.10207725 0.02035949
## 724 0.4 2.5 0.09191821 0.02142549
## 725 0.5 2.5 0.08932165 0.02412174
## 726 0.6 2.5 0.08679000 0.02486813
## 727 0.7 2.5 0.08419344 0.01947332
## 728 0.8 2.5 0.08416099 0.01443041
## 729 0.9 2.5 0.08416099 0.02132569
## 730 1.0 2.5 0.08672509 0.02622613
## 731 1.1 2.5 0.08928919 0.02399305
## 732 1.2 2.5 0.08928919 0.02399305
## 733 1.3 2.5 0.08928919 0.02399305
## 734 1.4 2.5 0.09182084 0.02456418
## 735 1.5 2.5 0.09182084 0.02456418
## 736 1.6 2.5 0.09182084 0.02456418
## 737 1.7 2.5 0.09182084 0.02456418
## 738 1.8 2.5 0.09182084 0.02456418
## 739 1.9 2.5 0.09182084 0.02456418
## 740 2.0 2.5 0.08928919 0.02560824
## 741 2.1 2.5 0.08928919 0.02560824
## 742 2.2 2.5 0.08928919 0.02560824
## 743 2.3 2.5 0.09185329 0.02296089
## 744 2.4 2.5 0.09441740 0.02154922
## 745 2.5 2.5 0.09185329 0.02468573
## 746 2.6 2.5 0.09185329 0.02468573
## 747 2.7 2.5 0.09441740 0.02507458
## 748 2.8 2.5 0.09698150 0.02963436
## 749 2.9 2.5 0.09698150 0.02963436
## 750 3.0 2.5 0.09698150 0.02963436
## 751 0.1 2.6 0.37007465 0.10483795
## 752 0.2 2.6 0.15306719 0.02383585
## 753 0.3 2.6 0.10464135 0.01919166
## 754 0.4 2.6 0.09191821 0.02142549
## 755 0.5 2.6 0.09188575 0.02484826
## 756 0.6 2.6 0.08935411 0.02588880
## 757 0.7 2.6 0.08675755 0.01911749
## 758 0.8 2.6 0.08672509 0.01395396
## 759 0.9 2.6 0.08416099 0.02132569
## 760 1.0 2.6 0.08928919 0.02399305
## 761 1.1 2.6 0.08928919 0.02399305
## 762 1.2 2.6 0.08928919 0.02399305
## 763 1.3 2.6 0.08928919 0.02399305
## 764 1.4 2.6 0.09182084 0.02456418
## 765 1.5 2.6 0.09182084 0.02456418
## 766 1.6 2.6 0.09182084 0.02456418
## 767 1.7 2.6 0.09182084 0.02456418
## 768 1.8 2.6 0.09182084 0.02456418
## 769 1.9 2.6 0.08928919 0.02560824
## 770 2.0 2.6 0.08928919 0.02560824
## 771 2.1 2.6 0.08928919 0.02560824
## 772 2.2 2.6 0.08928919 0.02560824
## 773 2.3 2.6 0.09441740 0.02154922
## 774 2.4 2.6 0.09185329 0.02468573
## 775 2.5 2.6 0.09185329 0.02468573
## 776 2.6 2.6 0.09441740 0.02507458
## 777 2.7 2.6 0.09441740 0.02507458
## 778 2.8 2.6 0.09698150 0.02963436
## 779 2.9 2.6 0.09698150 0.02963436
## 780 3.0 2.6 0.09954560 0.03454566
## 781 0.1 2.7 0.40334307 0.10396513
## 782 0.2 2.7 0.15303473 0.01986185
## 783 0.3 2.7 0.10720545 0.01969460
## 784 0.4 2.7 0.10207725 0.02035949
## 785 0.5 2.7 0.08932165 0.02412174
## 786 0.6 2.7 0.08935411 0.02588880
## 787 0.7 2.7 0.08928919 0.01814162
## 788 0.8 2.7 0.08672509 0.01395396
## 789 0.9 2.7 0.08928919 0.01814162
## 790 1.0 2.7 0.08928919 0.02399305
## 791 1.1 2.7 0.08928919 0.02399305
## 792 1.2 2.7 0.08928919 0.02399305
## 793 1.3 2.7 0.09182084 0.02456418
## 794 1.4 2.7 0.09182084 0.02456418
## 795 1.5 2.7 0.09182084 0.02456418
## 796 1.6 2.7 0.09182084 0.02456418
## 797 1.7 2.7 0.09182084 0.02456418
## 798 1.8 2.7 0.08928919 0.02560824
## 799 1.9 2.7 0.08928919 0.02560824
## 800 2.0 2.7 0.08928919 0.02560824
## 801 2.1 2.7 0.08928919 0.02560824
## 802 2.2 2.7 0.08928919 0.02560824
## 803 2.3 2.7 0.09185329 0.02468573
## 804 2.4 2.7 0.09185329 0.02468573
## 805 2.5 2.7 0.09185329 0.02468573
## 806 2.6 2.7 0.09441740 0.02507458
## 807 2.7 2.7 0.09698150 0.02963436
## 808 2.8 2.7 0.09698150 0.02963436
## 809 2.9 2.7 0.09954560 0.03454566
## 810 3.0 2.7 0.09954560 0.03454566
## 811 0.1 2.8 0.43644920 0.09333641
## 812 0.2 2.8 0.15813048 0.02452399
## 813 0.3 2.8 0.11230120 0.02305475
## 814 0.4 2.8 0.10207725 0.02035949
## 815 0.5 2.8 0.09444985 0.01974915
## 816 0.6 2.8 0.08935411 0.02588880
## 817 0.7 2.8 0.08932165 0.02043264
## 818 0.8 2.8 0.08672509 0.01395396
## 819 0.9 2.8 0.08928919 0.01814162
## 820 1.0 2.8 0.09185329 0.02300586
## 821 1.1 2.8 0.09185329 0.02300586
## 822 1.2 2.8 0.08928919 0.02399305
## 823 1.3 2.8 0.09182084 0.02456418
## 824 1.4 2.8 0.09182084 0.02456418
## 825 1.5 2.8 0.09182084 0.02456418
## 826 1.6 2.8 0.09182084 0.02456418
## 827 1.7 2.8 0.08928919 0.02560824
## 828 1.8 2.8 0.08928919 0.02560824
## 829 1.9 2.8 0.08928919 0.02560824
## 830 2.0 2.8 0.08928919 0.02560824
## 831 2.1 2.8 0.08928919 0.02560824
## 832 2.2 2.8 0.09441740 0.02154922
## 833 2.3 2.8 0.09185329 0.02468573
## 834 2.4 2.8 0.09185329 0.02468573
## 835 2.5 2.8 0.09185329 0.02468573
## 836 2.6 2.8 0.09698150 0.02963436
## 837 2.7 2.8 0.09698150 0.02963436
## 838 2.8 2.8 0.09954560 0.03454566
## 839 2.9 2.8 0.09698150 0.02963436
## 840 3.0 2.8 0.09698150 0.02963436
## 841 0.1 2.9 0.45173645 0.08651772
## 842 0.2 2.9 0.16069458 0.02624916
## 843 0.3 2.9 0.11483285 0.02557253
## 844 0.4 2.9 0.10207725 0.02035949
## 845 0.5 2.9 0.09444985 0.01974915
## 846 0.6 2.9 0.09444985 0.02173044
## 847 0.7 2.9 0.08932165 0.02043264
## 848 0.8 2.9 0.08672509 0.01395396
## 849 0.9 2.9 0.08928919 0.01814162
## 850 1.0 2.9 0.09185329 0.02300586
## 851 1.1 2.9 0.09185329 0.02300586
## 852 1.2 2.9 0.09438494 0.02325454
## 853 1.3 2.9 0.09438494 0.02325454
## 854 1.4 2.9 0.09438494 0.02325454
## 855 1.5 2.9 0.09182084 0.02456418
## 856 1.6 2.9 0.09182084 0.02456418
## 857 1.7 2.9 0.08928919 0.02560824
## 858 1.8 2.9 0.08928919 0.02560824
## 859 1.9 2.9 0.08928919 0.02560824
## 860 2.0 2.9 0.08928919 0.02560824
## 861 2.1 2.9 0.09185329 0.02296089
## 862 2.2 2.9 0.09185329 0.02468573
## 863 2.3 2.9 0.09185329 0.02468573
## 864 2.4 2.9 0.09185329 0.02468573
## 865 2.5 2.9 0.09441740 0.02507458
## 866 2.6 2.9 0.09698150 0.02963436
## 867 2.7 2.9 0.09698150 0.02963436
## 868 2.8 2.9 0.09698150 0.02963436
## 869 2.9 2.9 0.09698150 0.02963436
## 870 3.0 2.9 0.09698150 0.02963436
## 871 0.1 3.0 0.46449205 0.07859356
## 872 0.2 3.0 0.16832197 0.02871720
## 873 0.3 3.0 0.11992859 0.02328662
## 874 0.4 3.0 0.10464135 0.01919166
## 875 0.5 3.0 0.09444985 0.01974915
## 876 0.6 3.0 0.08932165 0.01590997
## 877 0.7 3.0 0.08932165 0.02043264
## 878 0.8 3.0 0.08672509 0.01395396
## 879 0.9 3.0 0.08928919 0.01814162
## 880 1.0 3.0 0.09185329 0.02300586
## 881 1.1 3.0 0.09185329 0.02300586
## 882 1.2 3.0 0.09438494 0.02325454
## 883 1.3 3.0 0.09438494 0.02325454
## 884 1.4 3.0 0.09182084 0.01889049
## 885 1.5 3.0 0.09438494 0.02325454
## 886 1.6 3.0 0.09185329 0.02468573
## 887 1.7 3.0 0.09185329 0.02468573
## 888 1.8 3.0 0.09185329 0.02468573
## 889 1.9 3.0 0.09185329 0.02468573
## 890 2.0 3.0 0.09185329 0.02296089
## 891 2.1 3.0 0.08928919 0.02560824
## 892 2.2 3.0 0.09185329 0.02468573
## 893 2.3 3.0 0.09185329 0.02468573
## 894 2.4 3.0 0.09185329 0.02468573
## 895 2.5 3.0 0.09441740 0.02507458
## 896 2.6 3.0 0.09698150 0.02963436
## 897 2.7 3.0 0.09698150 0.02963436
## 898 2.8 3.0 0.09698150 0.02963436
## 899 2.9 3.0 0.09698150 0.02963436
## 900 3.0 3.0 0.09698150 0.02963436stopCluster(cl)The model with the best performance uses a cost of 0.9 and a gamma of 1.3. This gives us an error rate of 0.06897111.
cl <- makeCluster(detectCores())
registerDoParallel(cl)
gammas = seq(0.1,1.5,0.1)
costs = seq(0.1,1.5,0.1)
degrees = 2 #seq(1,3,1) --- Changing because it is taking to long to run
ctrl = tune.control(cross = 5)
poly_svm_tune = tune(svm, mpg_binary~., data = auto, method = 'polynomial',
scale = T, ranges = list(cost = costs, gamma = gammas,
degree = degrees))
summary(poly_svm_tune)##
## Parameter tuning of 'svm':
##
## - sampling method: 10-fold cross validation
##
## - best parameters:
## cost gamma degree
## 1.1 1 2
##
## - best performance: 0.07115385
##
## - Detailed performance results:
## cost gamma degree error dispersion
## 1 0.1 0.1 2 0.09160256 0.05496767
## 2 0.2 0.1 2 0.09160256 0.05496767
## 3 0.3 0.1 2 0.09160256 0.05496767
## 4 0.4 0.1 2 0.09160256 0.05496767
## 5 0.5 0.1 2 0.09160256 0.05496767
## 6 0.6 0.1 2 0.09160256 0.05496767
## 7 0.7 0.1 2 0.09160256 0.05496767
## 8 0.8 0.1 2 0.09160256 0.05496767
## 9 0.9 0.1 2 0.09160256 0.05496767
## 10 1.0 0.1 2 0.09160256 0.05496767
## 11 1.1 0.1 2 0.08903846 0.05759286
## 12 1.2 0.1 2 0.08903846 0.05759286
## 13 1.3 0.1 2 0.08903846 0.05759286
## 14 1.4 0.1 2 0.09160256 0.06004878
## 15 1.5 0.1 2 0.08903846 0.05759286
## 16 0.1 0.2 2 0.09160256 0.05496767
## 17 0.2 0.2 2 0.09160256 0.05496767
## 18 0.3 0.2 2 0.09160256 0.05496767
## 19 0.4 0.2 2 0.09160256 0.05496767
## 20 0.5 0.2 2 0.09160256 0.05496767
## 21 0.6 0.2 2 0.09160256 0.05496767
## 22 0.7 0.2 2 0.08903846 0.05759286
## 23 0.8 0.2 2 0.08903846 0.05759286
## 24 0.9 0.2 2 0.08647436 0.05489453
## 25 1.0 0.2 2 0.08903846 0.05759286
## 26 1.1 0.2 2 0.08647436 0.05749448
## 27 1.2 0.2 2 0.08647436 0.05749448
## 28 1.3 0.2 2 0.08647436 0.05749448
## 29 1.4 0.2 2 0.08647436 0.05620954
## 30 1.5 0.2 2 0.08647436 0.05216516
## 31 0.1 0.3 2 0.08903846 0.05759286
## 32 0.2 0.3 2 0.08903846 0.05759286
## 33 0.3 0.3 2 0.09160256 0.05496767
## 34 0.4 0.3 2 0.09160256 0.05496767
## 35 0.5 0.3 2 0.08903846 0.05759286
## 36 0.6 0.3 2 0.08903846 0.05759286
## 37 0.7 0.3 2 0.08391026 0.05465781
## 38 0.8 0.3 2 0.08391026 0.05465781
## 39 0.9 0.3 2 0.08134615 0.05691343
## 40 1.0 0.3 2 0.08134615 0.05818282
## 41 1.1 0.3 2 0.08391026 0.05465781
## 42 1.2 0.3 2 0.08391026 0.05465781
## 43 1.3 0.3 2 0.08647436 0.05875132
## 44 1.4 0.3 2 0.08647436 0.05875132
## 45 1.5 0.3 2 0.08647436 0.05875132
## 46 0.1 0.4 2 0.08647436 0.05749448
## 47 0.2 0.4 2 0.08903846 0.05759286
## 48 0.3 0.4 2 0.08903846 0.05759286
## 49 0.4 0.4 2 0.08903846 0.05759286
## 50 0.5 0.4 2 0.08391026 0.05465781
## 51 0.6 0.4 2 0.08641026 0.05725603
## 52 0.7 0.4 2 0.08391026 0.05976527
## 53 0.8 0.4 2 0.08134615 0.05818282
## 54 0.9 0.4 2 0.08647436 0.05620954
## 55 1.0 0.4 2 0.08641026 0.05725603
## 56 1.1 0.4 2 0.08641026 0.05725603
## 57 1.2 0.4 2 0.08128205 0.05536192
## 58 1.3 0.4 2 0.08128205 0.05536192
## 59 1.4 0.4 2 0.07871795 0.05745980
## 60 1.5 0.4 2 0.07871795 0.05745980
## 61 0.1 0.5 2 0.08647436 0.05749448
## 62 0.2 0.5 2 0.08647436 0.05749448
## 63 0.3 0.5 2 0.08647436 0.05749448
## 64 0.4 0.5 2 0.08134615 0.05561507
## 65 0.5 0.5 2 0.08128205 0.06160727
## 66 0.6 0.5 2 0.08134615 0.05818282
## 67 0.7 0.5 2 0.08134615 0.05818282
## 68 0.8 0.5 2 0.08384615 0.05573017
## 69 0.9 0.5 2 0.08384615 0.05573017
## 70 1.0 0.5 2 0.08128205 0.05536192
## 71 1.1 0.5 2 0.07871795 0.05745980
## 72 1.2 0.5 2 0.07871795 0.05745980
## 73 1.3 0.5 2 0.07871795 0.05745980
## 74 1.4 0.5 2 0.08128205 0.05402629
## 75 1.5 0.5 2 0.08128205 0.05402629
## 76 0.1 0.6 2 0.08647436 0.05749448
## 77 0.2 0.6 2 0.08647436 0.05749448
## 78 0.3 0.6 2 0.08391026 0.05853020
## 79 0.4 0.6 2 0.08384615 0.06425395
## 80 0.5 0.6 2 0.08134615 0.05818282
## 81 0.6 0.6 2 0.07621795 0.05580520
## 82 0.7 0.6 2 0.07871795 0.05871739
## 83 0.8 0.6 2 0.08128205 0.05536192
## 84 0.9 0.6 2 0.08128205 0.05536192
## 85 1.0 0.6 2 0.07871795 0.05745980
## 86 1.1 0.6 2 0.07871795 0.05745980
## 87 1.2 0.6 2 0.08128205 0.05402629
## 88 1.3 0.6 2 0.08128205 0.05402629
## 89 1.4 0.6 2 0.08128205 0.05402629
## 90 1.5 0.6 2 0.08384615 0.05164827
## 91 0.1 0.7 2 0.08903846 0.05631017
## 92 0.2 0.7 2 0.08647436 0.05749448
## 93 0.3 0.7 2 0.08134615 0.06183485
## 94 0.4 0.7 2 0.08384615 0.06425395
## 95 0.5 0.7 2 0.07621795 0.05580520
## 96 0.6 0.7 2 0.07871795 0.05871739
## 97 0.7 0.7 2 0.08128205 0.05536192
## 98 0.8 0.7 2 0.08128205 0.05536192
## 99 0.9 0.7 2 0.07871795 0.05745980
## 100 1.0 0.7 2 0.07871795 0.05745980
## 101 1.1 0.7 2 0.08128205 0.05402629
## 102 1.2 0.7 2 0.08384615 0.05304381
## 103 1.3 0.7 2 0.08128205 0.04980494
## 104 1.4 0.7 2 0.07871795 0.04924442
## 105 1.5 0.7 2 0.07621795 0.04573294
## 106 0.1 0.8 2 0.08910256 0.05901538
## 107 0.2 0.8 2 0.08647436 0.05749448
## 108 0.3 0.8 2 0.08134615 0.06183485
## 109 0.4 0.8 2 0.07615385 0.06057894
## 110 0.5 0.8 2 0.08128205 0.05794090
## 111 0.6 0.8 2 0.08384615 0.05440357
## 112 0.7 0.8 2 0.08128205 0.05402629
## 113 0.8 0.8 2 0.07871795 0.05617407
## 114 0.9 0.8 2 0.08128205 0.05666609
## 115 1.0 0.8 2 0.08384615 0.05304381
## 116 1.1 0.8 2 0.08384615 0.05304381
## 117 1.2 0.8 2 0.07365385 0.04795136
## 118 1.3 0.8 2 0.07365385 0.04795136
## 119 1.4 0.8 2 0.07621795 0.04573294
## 120 1.5 0.8 2 0.07878205 0.04489056
## 121 0.1 0.9 2 0.09166667 0.05898442
## 122 0.2 0.9 2 0.08141026 0.05709648
## 123 0.3 0.9 2 0.07878205 0.06018548
## 124 0.4 0.9 2 0.07871795 0.05871739
## 125 0.5 0.9 2 0.08128205 0.05794090
## 126 0.6 0.9 2 0.08384615 0.05440357
## 127 0.7 0.9 2 0.08128205 0.05402629
## 128 0.8 0.9 2 0.07871795 0.05617407
## 129 0.9 0.9 2 0.08384615 0.05304381
## 130 1.0 0.9 2 0.07621795 0.04730332
## 131 1.1 0.9 2 0.07365385 0.04795136
## 132 1.2 0.9 2 0.07365385 0.04795136
## 133 1.3 0.9 2 0.07371795 0.04504545
## 134 1.4 0.9 2 0.07371795 0.04504545
## 135 1.5 0.9 2 0.07628205 0.04596849
## 136 0.1 1.0 2 0.08653846 0.06135196
## 137 0.2 1.0 2 0.08141026 0.05709648
## 138 0.3 1.0 2 0.07365385 0.05763724
## 139 0.4 1.0 2 0.08128205 0.05794090
## 140 0.5 1.0 2 0.08384615 0.05440357
## 141 0.6 1.0 2 0.08384615 0.05440357
## 142 0.7 1.0 2 0.08384615 0.05440357
## 143 0.8 1.0 2 0.08128205 0.05402629
## 144 0.9 1.0 2 0.07621795 0.04730332
## 145 1.0 1.0 2 0.07365385 0.04795136
## 146 1.1 1.0 2 0.07115385 0.04556946
## 147 1.2 1.0 2 0.07371795 0.04504545
## 148 1.3 1.0 2 0.07371795 0.04504545
## 149 1.4 1.0 2 0.07628205 0.04596849
## 150 1.5 1.0 2 0.07628205 0.04596849
## 151 0.1 1.1 2 0.08653846 0.06135196
## 152 0.2 1.1 2 0.08910256 0.06377480
## 153 0.3 1.1 2 0.07371795 0.05524320
## 154 0.4 1.1 2 0.08128205 0.05794090
## 155 0.5 1.1 2 0.08384615 0.05440357
## 156 0.6 1.1 2 0.08384615 0.05440357
## 157 0.7 1.1 2 0.08384615 0.05440357
## 158 0.8 1.1 2 0.07878205 0.04803507
## 159 0.9 1.1 2 0.07365385 0.04640291
## 160 1.0 1.1 2 0.07115385 0.04556946
## 161 1.1 1.1 2 0.07371795 0.04504545
## 162 1.2 1.1 2 0.07371795 0.04504545
## 163 1.3 1.1 2 0.07628205 0.04596849
## 164 1.4 1.1 2 0.07628205 0.04596849
## 165 1.5 1.1 2 0.07628205 0.04596849
## 166 0.1 1.2 2 0.08653846 0.06135196
## 167 0.2 1.2 2 0.08910256 0.06377480
## 168 0.3 1.2 2 0.07371795 0.05524320
## 169 0.4 1.2 2 0.08134615 0.05428566
## 170 0.5 1.2 2 0.08384615 0.05440357
## 171 0.6 1.2 2 0.08384615 0.05440357
## 172 0.7 1.2 2 0.07878205 0.05239920
## 173 0.8 1.2 2 0.07621795 0.04410667
## 174 0.9 1.2 2 0.07115385 0.04224181
## 175 1.0 1.2 2 0.07115385 0.04556946
## 176 1.1 1.2 2 0.07371795 0.04504545
## 177 1.2 1.2 2 0.07371795 0.04504545
## 178 1.3 1.2 2 0.07628205 0.04596849
## 179 1.4 1.2 2 0.07628205 0.04596849
## 180 1.5 1.2 2 0.07628205 0.04596849
## 181 0.1 1.3 2 0.08653846 0.06135196
## 182 0.2 1.3 2 0.08397436 0.05993656
## 183 0.3 1.3 2 0.08141026 0.05311968
## 184 0.4 1.3 2 0.08391026 0.05465781
## 185 0.5 1.3 2 0.08134615 0.05152405
## 186 0.6 1.3 2 0.08128205 0.05536192
## 187 0.7 1.3 2 0.07621795 0.04882322
## 188 0.8 1.3 2 0.07371795 0.04167598
## 189 0.9 1.3 2 0.07115385 0.04224181
## 190 1.0 1.3 2 0.07371795 0.04167598
## 191 1.1 1.3 2 0.07628205 0.04267196
## 192 1.2 1.3 2 0.07628205 0.04596849
## 193 1.3 1.3 2 0.07628205 0.04596849
## 194 1.4 1.3 2 0.07628205 0.04596849
## 195 1.5 1.3 2 0.08141026 0.04065561
## 196 0.1 1.4 2 0.08653846 0.06135196
## 197 0.2 1.4 2 0.08397436 0.05993656
## 198 0.3 1.4 2 0.08141026 0.05311968
## 199 0.4 1.4 2 0.08897436 0.05468566
## 200 0.5 1.4 2 0.08897436 0.05468566
## 201 0.6 1.4 2 0.07628205 0.05051148
## 202 0.7 1.4 2 0.07621795 0.04882322
## 203 0.8 1.4 2 0.07371795 0.04167598
## 204 0.9 1.4 2 0.07371795 0.04167598
## 205 1.0 1.4 2 0.07371795 0.04167598
## 206 1.1 1.4 2 0.07628205 0.04267196
## 207 1.2 1.4 2 0.07884615 0.04347752
## 208 1.3 1.4 2 0.08141026 0.04065561
## 209 1.4 1.4 2 0.08141026 0.04065561
## 210 1.5 1.4 2 0.08141026 0.04065561
## 211 0.1 1.5 2 0.09166667 0.06374616
## 212 0.2 1.5 2 0.08653846 0.05766935
## 213 0.3 1.5 2 0.08397436 0.05484506
## 214 0.4 1.5 2 0.08897436 0.05468566
## 215 0.5 1.5 2 0.08641026 0.05590113
## 216 0.6 1.5 2 0.08141026 0.05029408
## 217 0.7 1.5 2 0.07628205 0.04267196
## 218 0.8 1.5 2 0.07371795 0.04167598
## 219 0.9 1.5 2 0.07371795 0.04167598
## 220 1.0 1.5 2 0.07371795 0.04167598
## 221 1.1 1.5 2 0.07371795 0.04167598
## 222 1.2 1.5 2 0.08141026 0.04065561
## 223 1.3 1.5 2 0.08141026 0.04065561
## 224 1.4 1.5 2 0.08141026 0.04065561
## 225 1.5 1.5 2 0.08141026 0.04065561stopCluster(cl)The polynomial best parameters are a cost of 1.1, gamma of 0.9, and a degree of 2, but this is also with my extremely reduced ranges due to the hours spent trying to run this code with seq(0.1,10,0.1) on all three parameters.
With the radial SVM we get an error rate of 0.0690 and with the polynomial SVM we get an error rate of 0.0637. This suggests that the polynomial model is slightly better
7d) Make some plots to back up your assertions in (b) and (c).
svm_best_rad = svm(mpg_binary~., data = auto, kernel = 'radial', scale = T,
cost = 0.9 , gamma = 1.3)
plot(svm_best_rad, auto, weight ~ horsepower)
plot(svm_best_rad, auto, year ~ acceleration)
plot(svm_best_rad, auto, weight ~ displacement)
plot(svm_best_rad, auto, weight ~ acceleration)
svm_best_poly = svm(mpg_binary~., data = auto, kernel = 'polynomial', scale = T,
cost = 1.1 , gamma = 0.9, degree = 2)
plot(svm_best_poly, auto, weight ~ horsepower)
plot(svm_best_poly, auto, year ~ acceleration)
plot(svm_best_poly, auto, weight ~ displacement)
plot(svm_best_poly, auto, weight ~ acceleration)
8. This problem involves the OJ data set which is part of the ISLR2 package.
8a) Create a training set containing a random sample of 800 observations,
and a test set containing the remaining observations.
OJ = ISLR2::OJ
set.seed(1)
index = sample(1:nrow(OJ), 800)
OJ_train = OJ[index,]
OJ_test = OJ[-index,]8b) Fit a support vector classifer to the training data using cost = 0.01,
with Purchase as the response and the other variables as predictors. Use the
summary() function to produce summary statistics, and describe the results obtained.
oj_linear = svm(Purchase ~., data = OJ_train, kernel = 'linear', cost = 0.01, scale = T)
summary(oj_linear)##
## Call:
## svm(formula = Purchase ~ ., data = OJ_train, kernel = "linear", cost = 0.01,
## scale = T)
##
##
## Parameters:
## SVM-Type: C-classification
## SVM-Kernel: linear
## cost: 0.01
##
## Number of Support Vectors: 435
##
## ( 219 216 )
##
##
## Number of Classes: 2
##
## Levels:
## CH MMOf our 800 observations, we have 435 support vectors to help classify if people will purchase Citrus Hill or Minute Maid with 219 Vectors for Citrus Hill and 216 for Minute Maid.
8c) What are the training and test error rates?
train_err = mean(predict(oj_linear, OJ_train) != OJ_train$Purchase)
test_err = mean(predict(oj_linear, OJ_test) != OJ_test$Purchase)
paste('Train Error: ' , train_err)## [1] "Train Error: 0.175"paste('Test Error: ', test_err)## [1] "Test Error: 0.177777777777778"We get a Train Error of 0.175 and a Test Error of 0.177.
8d) Use the tune() function to select an optimal cost. Consider values in the
range 0.01 to 10.
set.seed(1)
costs = seq(0.01, 10, 0.1)
ctrl = tune.control(cross = 5)
#oj_tune = tune(svm, Purchase~., data=OJ_train,
# ranges = list(cost = costs,tunecontrol = ctrl), method = 'linear')
library(doParallel)
# Set up parallel processing
cl <- makeCluster(detectCores())
registerDoParallel(cl)
# Perform hyperparameter tuning
oj_tune <- tune(svm, Purchase ~ ., data = OJ_train,
ranges = list(cost = costs),
tunecontrol = ctrl, method = 'linear')
# Stop cluster
stopCluster(cl)
summary(oj_tune)##
## Parameter tuning of 'svm':
##
## - sampling method: 5-fold cross validation
##
## - best parameters:
## cost
## 0.61
##
## - best performance: 0.165
##
## - Detailed performance results:
## cost error dispersion
## 1 0.01 0.39375 0.021194781
## 2 0.11 0.19000 0.009478594
## 3 0.21 0.17750 0.018540496
## 4 0.31 0.17625 0.022707378
## 5 0.41 0.17500 0.015934436
## 6 0.51 0.17125 0.018006075
## 7 0.61 0.16500 0.016886570
## 8 0.71 0.16625 0.016298006
## 9 0.81 0.16625 0.018006075
## 10 0.91 0.16500 0.016886570
## 11 1.01 0.16625 0.014388581
## 12 1.11 0.16625 0.016298006
## 13 1.21 0.16625 0.018540496
## 14 1.31 0.16875 0.015934436
## 15 1.41 0.17000 0.018957189
## 16 1.51 0.17125 0.018540496
## 17 1.61 0.17250 0.020539596
## 18 1.71 0.17125 0.020058508
## 19 1.81 0.17125 0.020058508
## 20 1.91 0.17250 0.018540496
## 21 2.01 0.17375 0.019465514
## 22 2.11 0.17375 0.019465514
## 23 2.21 0.17375 0.019465514
## 24 2.31 0.17250 0.018006075
## 25 2.41 0.17375 0.019465514
## 26 2.51 0.17625 0.016770510
## 27 2.61 0.17625 0.016770510
## 28 2.71 0.17750 0.014388581
## 29 2.81 0.17750 0.014388581
## 30 2.91 0.17625 0.013549677
## 31 3.01 0.17625 0.013549677
## 32 3.11 0.17625 0.013549677
## 33 3.21 0.17750 0.013693064
## 34 3.31 0.17875 0.013693064
## 35 3.41 0.17875 0.013693064
## 36 3.51 0.17875 0.013693064
## 37 3.61 0.17875 0.013693064
## 38 3.71 0.17875 0.013693064
## 39 3.81 0.17875 0.013693064
## 40 3.91 0.17875 0.013693064
## 41 4.01 0.17875 0.013693064
## 42 4.11 0.17875 0.013693064
## 43 4.21 0.18000 0.014252193
## 44 4.31 0.18125 0.011692679
## 45 4.41 0.18125 0.011692679
## 46 4.51 0.18000 0.012022115
## 47 4.61 0.18000 0.012022115
## 48 4.71 0.17875 0.010458250
## 49 4.81 0.17875 0.010458250
## 50 4.91 0.17875 0.010458250
## 51 5.01 0.18000 0.012022115
## 52 5.11 0.18000 0.012022115
## 53 5.21 0.17875 0.011353689
## 54 5.31 0.17875 0.011353689
## 55 5.41 0.17875 0.011353689
## 56 5.51 0.17875 0.011353689
## 57 5.61 0.17875 0.011353689
## 58 5.71 0.17875 0.011353689
## 59 5.81 0.17875 0.011353689
## 60 5.91 0.17875 0.011353689
## 61 6.01 0.17875 0.011353689
## 62 6.11 0.17875 0.011353689
## 63 6.21 0.17875 0.011353689
## 64 6.31 0.18125 0.012500000
## 65 6.41 0.18125 0.012500000
## 66 6.51 0.18125 0.012500000
## 67 6.61 0.18250 0.012022115
## 68 6.71 0.18250 0.012022115
## 69 6.81 0.18250 0.012022115
## 70 6.91 0.18250 0.012022115
## 71 7.01 0.18375 0.012960276
## 72 7.11 0.18375 0.012960276
## 73 7.21 0.18625 0.014921670
## 74 7.31 0.18625 0.014921670
## 75 7.41 0.18625 0.014921670
## 76 7.51 0.18625 0.014921670
## 77 7.61 0.18625 0.014921670
## 78 7.71 0.18625 0.014921670
## 79 7.81 0.18500 0.015687375
## 80 7.91 0.18500 0.015687375
## 81 8.01 0.18500 0.015687375
## 82 8.11 0.18500 0.015687375
## 83 8.21 0.18375 0.014388581
## 84 8.31 0.18375 0.014388581
## 85 8.41 0.18375 0.014388581
## 86 8.51 0.18375 0.014388581
## 87 8.61 0.18375 0.014388581
## 88 8.71 0.18375 0.014388581
## 89 8.81 0.18375 0.014388581
## 90 8.91 0.18375 0.014388581
## 91 9.01 0.18375 0.014388581
## 92 9.11 0.18250 0.013549677
## 93 9.21 0.18375 0.015051993
## 94 9.31 0.18375 0.015051993
## 95 9.41 0.18375 0.015051993
## 96 9.51 0.18375 0.015051993
## 97 9.61 0.18375 0.015051993
## 98 9.71 0.18375 0.015051993
## 99 9.81 0.18375 0.015051993
## 100 9.91 0.18375 0.015051993We get an optimal cost of 0.61 with an error rate of 0.165. I did adjust the limits on cost because I have had the SVM running for a lot longer than expected.
8e) Compute the training and test error rates using this new value for cost.
train_err = mean(predict(oj_tune$best.model, OJ_train) != OJ_train$Purchase)
test_err = mean(predict(oj_tune$best.model, OJ_test) != OJ_test$Purchase)
paste('Train Error: ', train_err)## [1] "Train Error: 0.14875"paste('Test Error: ', test_err)## [1] "Test Error: 0.181481481481481"We get a train error of 0.149 which is lower than our prior linear model, but the test error is 0.181 which is higher.
8f) Repeat parts (b) through (e) using a support vector machine with a radial
kernel. Use the default value for gamma.
oj_radial = svm(Purchase ~., data = OJ_train, kernel = 'radial', cost = 0.01, scale = T)
summary(oj_radial)##
## Call:
## svm(formula = Purchase ~ ., data = OJ_train, kernel = "radial", cost = 0.01,
## scale = T)
##
##
## Parameters:
## SVM-Type: C-classification
## SVM-Kernel: radial
## cost: 0.01
##
## Number of Support Vectors: 634
##
## ( 319 315 )
##
##
## Number of Classes: 2
##
## Levels:
## CH MMWith our set cost of 0.01, we get a total of 634 support vectors out of 800 observations with 319 for Citrus Hill and 315 for Minute Maid.
train_err = mean(predict(oj_radial, OJ_train) != OJ_train$Purchase)
test_err = mean(predict(oj_radial, OJ_test) != OJ_test$Purchase)
paste('Train Error: ', train_err)## [1] "Train Error: 0.39375"paste('Test Error: ', test_err)## [1] "Test Error: 0.377777777777778"We get the error rates of 0.393 for training and 0.377 for test, which are worse than the linear models we have used.
cl <- makeCluster(detectCores())
registerDoParallel(cl)
set.seed(1)
costs = seq(0.01, 2, 0.1) #lowering because it will not finish running
ctrl = tune.control(cross = 5)
oj_tune_rad = tune(svm, Purchase~., data=OJ_train,
ranges = list(cost = costs,tunecontrol = ctrl), method = 'radial')
summary(oj_tune_rad)##
## Parameter tuning of 'svm':
##
## - sampling method: 10-fold cross validation
##
## - best parameters:
## cost tunecontrol
## 0.51 FALSE
##
## - best performance: 0.16625
##
## - Detailed performance results:
## cost
## 1 0.01
## 2 0.11
## 3 0.21
## 4 0.31
## 5 0.41
## 6 0.51
## 7 0.61
## 8 0.71
## 9 0.81
## 10 0.91
## 11 1.01
## 12 1.11
## 13 1.21
## 14 1.31
## 15 1.41
## 16 1.51
## 17 1.61
## 18 1.71
## 19 1.81
## 20 1.91
## 21 0.01
## 22 0.11
## 23 0.21
## 24 0.31
## 25 0.41
## 26 0.51
## 27 0.61
## 28 0.71
## 29 0.81
## 30 0.91
## 31 1.01
## 32 1.11
## 33 1.21
## 34 1.31
## 35 1.41
## 36 1.51
## 37 1.61
## 38 1.71
## 39 1.81
## 40 1.91
## 41 0.01
## 42 0.11
## 43 0.21
## 44 0.31
## 45 0.41
## 46 0.51
## 47 0.61
## 48 0.71
## 49 0.81
## 50 0.91
## 51 1.01
## 52 1.11
## 53 1.21
## 54 1.31
## 55 1.41
## 56 1.51
## 57 1.61
## 58 1.71
## 59 1.81
## 60 1.91
## 61 0.01
## 62 0.11
## 63 0.21
## 64 0.31
## 65 0.41
## 66 0.51
## 67 0.61
## 68 0.71
## 69 0.81
## 70 0.91
## 71 1.01
## 72 1.11
## 73 1.21
## 74 1.31
## 75 1.41
## 76 1.51
## 77 1.61
## 78 1.71
## 79 1.81
## 80 1.91
## 81 0.01
## 82 0.11
## 83 0.21
## 84 0.31
## 85 0.41
## 86 0.51
## 87 0.61
## 88 0.71
## 89 0.81
## 90 0.91
## 91 1.01
## 92 1.11
## 93 1.21
## 94 1.31
## 95 1.41
## 96 1.51
## 97 1.61
## 98 1.71
## 99 1.81
## 100 1.91
## 101 0.01
## 102 0.11
## 103 0.21
## 104 0.31
## 105 0.41
## 106 0.51
## 107 0.61
## 108 0.71
## 109 0.81
## 110 0.91
## 111 1.01
## 112 1.11
## 113 1.21
## 114 1.31
## 115 1.41
## 116 1.51
## 117 1.61
## 118 1.71
## 119 1.81
## 120 1.91
## 121 0.01
## 122 0.11
## 123 0.21
## 124 0.31
## 125 0.41
## 126 0.51
## 127 0.61
## 128 0.71
## 129 0.81
## 130 0.91
## 131 1.01
## 132 1.11
## 133 1.21
## 134 1.31
## 135 1.41
## 136 1.51
## 137 1.61
## 138 1.71
## 139 1.81
## 140 1.91
## 141 0.01
## 142 0.11
## 143 0.21
## 144 0.31
## 145 0.41
## 146 0.51
## 147 0.61
## 148 0.71
## 149 0.81
## 150 0.91
## 151 1.01
## 152 1.11
## 153 1.21
## 154 1.31
## 155 1.41
## 156 1.51
## 157 1.61
## 158 1.71
## 159 1.81
## 160 1.91
## 161 0.01
## 162 0.11
## 163 0.21
## 164 0.31
## 165 0.41
## 166 0.51
## 167 0.61
## 168 0.71
## 169 0.81
## 170 0.91
## 171 1.01
## 172 1.11
## 173 1.21
## 174 1.31
## 175 1.41
## 176 1.51
## 177 1.61
## 178 1.71
## 179 1.81
## 180 1.91
## 181 0.01
## 182 0.11
## 183 0.21
## 184 0.31
## 185 0.41
## 186 0.51
## 187 0.61
## 188 0.71
## 189 0.81
## 190 0.91
## 191 1.01
## 192 1.11
## 193 1.21
## 194 1.31
## 195 1.41
## 196 1.51
## 197 1.61
## 198 1.71
## 199 1.81
## 200 1.91
## 201 0.01
## 202 0.11
## 203 0.21
## 204 0.31
## 205 0.41
## 206 0.51
## 207 0.61
## 208 0.71
## 209 0.81
## 210 0.91
## 211 1.01
## 212 1.11
## 213 1.21
## 214 1.31
## 215 1.41
## 216 1.51
## 217 1.61
## 218 1.71
## 219 1.81
## 220 1.91
## 221 0.01
## 222 0.11
## 223 0.21
## 224 0.31
## 225 0.41
## 226 0.51
## 227 0.61
## 228 0.71
## 229 0.81
## 230 0.91
## 231 1.01
## 232 1.11
## 233 1.21
## 234 1.31
## 235 1.41
## 236 1.51
## 237 1.61
## 238 1.71
## 239 1.81
## 240 1.91
## 241 0.01
## 242 0.11
## 243 0.21
## 244 0.31
## 245 0.41
## 246 0.51
## 247 0.61
## 248 0.71
## 249 0.81
## 250 0.91
## 251 1.01
## 252 1.11
## 253 1.21
## 254 1.31
## 255 1.41
## 256 1.51
## 257 1.61
## 258 1.71
## 259 1.81
## 260 1.91
## tunecontrol
## 1 FALSE
## 2 FALSE
## 3 FALSE
## 4 FALSE
## 5 FALSE
## 6 FALSE
## 7 FALSE
## 8 FALSE
## 9 FALSE
## 10 FALSE
## 11 FALSE
## 12 FALSE
## 13 FALSE
## 14 FALSE
## 15 FALSE
## 16 FALSE
## 17 FALSE
## 18 FALSE
## 19 FALSE
## 20 FALSE
## 21 1
## 22 1
## 23 1
## 24 1
## 25 1
## 26 1
## 27 1
## 28 1
## 29 1
## 30 1
## 31 1
## 32 1
## 33 1
## 34 1
## 35 1
## 36 1
## 37 1
## 38 1
## 39 1
## 40 1
## 41 function (x, ...) , UseMethod("mean")
## 42 function (x, ...) , UseMethod("mean")
## 43 function (x, ...) , UseMethod("mean")
## 44 function (x, ...) , UseMethod("mean")
## 45 function (x, ...) , UseMethod("mean")
## 46 function (x, ...) , UseMethod("mean")
## 47 function (x, ...) , UseMethod("mean")
## 48 function (x, ...) , UseMethod("mean")
## 49 function (x, ...) , UseMethod("mean")
## 50 function (x, ...) , UseMethod("mean")
## 51 function (x, ...) , UseMethod("mean")
## 52 function (x, ...) , UseMethod("mean")
## 53 function (x, ...) , UseMethod("mean")
## 54 function (x, ...) , UseMethod("mean")
## 55 function (x, ...) , UseMethod("mean")
## 56 function (x, ...) , UseMethod("mean")
## 57 function (x, ...) , UseMethod("mean")
## 58 function (x, ...) , UseMethod("mean")
## 59 function (x, ...) , UseMethod("mean")
## 60 function (x, ...) , UseMethod("mean")
## 61 cross
## 62 cross
## 63 cross
## 64 cross
## 65 cross
## 66 cross
## 67 cross
## 68 cross
## 69 cross
## 70 cross
## 71 cross
## 72 cross
## 73 cross
## 74 cross
## 75 cross
## 76 cross
## 77 cross
## 78 cross
## 79 cross
## 80 cross
## 81 function (x, ...) , UseMethod("mean")
## 82 function (x, ...) , UseMethod("mean")
## 83 function (x, ...) , UseMethod("mean")
## 84 function (x, ...) , UseMethod("mean")
## 85 function (x, ...) , UseMethod("mean")
## 86 function (x, ...) , UseMethod("mean")
## 87 function (x, ...) , UseMethod("mean")
## 88 function (x, ...) , UseMethod("mean")
## 89 function (x, ...) , UseMethod("mean")
## 90 function (x, ...) , UseMethod("mean")
## 91 function (x, ...) , UseMethod("mean")
## 92 function (x, ...) , UseMethod("mean")
## 93 function (x, ...) , UseMethod("mean")
## 94 function (x, ...) , UseMethod("mean")
## 95 function (x, ...) , UseMethod("mean")
## 96 function (x, ...) , UseMethod("mean")
## 97 function (x, ...) , UseMethod("mean")
## 98 function (x, ...) , UseMethod("mean")
## 99 function (x, ...) , UseMethod("mean")
## 100 function (x, ...) , UseMethod("mean")
## 101 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 102 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 103 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 104 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 105 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 106 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 107 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 108 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 109 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 110 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 111 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 112 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 113 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 114 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 115 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 116 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 117 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 118 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 119 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 120 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 121 5
## 122 5
## 123 5
## 124 5
## 125 5
## 126 5
## 127 5
## 128 5
## 129 5
## 130 5
## 131 5
## 132 5
## 133 5
## 134 5
## 135 5
## 136 5
## 137 5
## 138 5
## 139 5
## 140 5
## 141 0.6666667
## 142 0.6666667
## 143 0.6666667
## 144 0.6666667
## 145 0.6666667
## 146 0.6666667
## 147 0.6666667
## 148 0.6666667
## 149 0.6666667
## 150 0.6666667
## 151 0.6666667
## 152 0.6666667
## 153 0.6666667
## 154 0.6666667
## 155 0.6666667
## 156 0.6666667
## 157 0.6666667
## 158 0.6666667
## 159 0.6666667
## 160 0.6666667
## 161 10
## 162 10
## 163 10
## 164 10
## 165 10
## 166 10
## 167 10
## 168 10
## 169 10
## 170 10
## 171 10
## 172 10
## 173 10
## 174 10
## 175 10
## 176 10
## 177 10
## 178 10
## 179 10
## 180 10
## 181 0.9
## 182 0.9
## 183 0.9
## 184 0.9
## 185 0.9
## 186 0.9
## 187 0.9
## 188 0.9
## 189 0.9
## 190 0.9
## 191 0.9
## 192 0.9
## 193 0.9
## 194 0.9
## 195 0.9
## 196 0.9
## 197 0.9
## 198 0.9
## 199 0.9
## 200 0.9
## 201 TRUE
## 202 TRUE
## 203 TRUE
## 204 TRUE
## 205 TRUE
## 206 TRUE
## 207 TRUE
## 208 TRUE
## 209 TRUE
## 210 TRUE
## 211 TRUE
## 212 TRUE
## 213 TRUE
## 214 TRUE
## 215 TRUE
## 216 TRUE
## 217 TRUE
## 218 TRUE
## 219 TRUE
## 220 TRUE
## 221 TRUE
## 222 TRUE
## 223 TRUE
## 224 TRUE
## 225 TRUE
## 226 TRUE
## 227 TRUE
## 228 TRUE
## 229 TRUE
## 230 TRUE
## 231 TRUE
## 232 TRUE
## 233 TRUE
## 234 TRUE
## 235 TRUE
## 236 TRUE
## 237 TRUE
## 238 TRUE
## 239 TRUE
## 240 TRUE
## 241 NULL
## 242 NULL
## 243 NULL
## 244 NULL
## 245 NULL
## 246 NULL
## 247 NULL
## 248 NULL
## 249 NULL
## 250 NULL
## 251 NULL
## 252 NULL
## 253 NULL
## 254 NULL
## 255 NULL
## 256 NULL
## 257 NULL
## 258 NULL
## 259 NULL
## 260 NULL
## error dispersion
## 1 0.39375 0.04007372
## 2 0.18625 0.02853482
## 3 0.18250 0.03238227
## 4 0.17875 0.03230175
## 5 0.17625 0.02531057
## 6 0.16625 0.02433134
## 7 0.16875 0.02301117
## 8 0.16750 0.02776389
## 9 0.17000 0.02513851
## 10 0.16750 0.02220485
## 11 0.17125 0.02128673
## 12 0.17125 0.01958777
## 13 0.17250 0.02108185
## 14 0.17375 0.02161050
## 15 0.17375 0.02389938
## 16 0.17625 0.02161050
## 17 0.17625 0.02161050
## 18 0.17750 0.02188988
## 19 0.17625 0.02079162
## 20 0.17625 0.02079162
## 21 0.39375 0.04007372
## 22 0.18625 0.02853482
## 23 0.18250 0.03238227
## 24 0.17875 0.03230175
## 25 0.17625 0.02531057
## 26 0.16625 0.02433134
## 27 0.16875 0.02301117
## 28 0.16750 0.02776389
## 29 0.17000 0.02513851
## 30 0.16750 0.02220485
## 31 0.17125 0.02128673
## 32 0.17125 0.01958777
## 33 0.17250 0.02108185
## 34 0.17375 0.02161050
## 35 0.17375 0.02389938
## 36 0.17625 0.02161050
## 37 0.17625 0.02161050
## 38 0.17750 0.02188988
## 39 0.17625 0.02079162
## 40 0.17625 0.02079162
## 41 0.39375 0.04007372
## 42 0.18625 0.02853482
## 43 0.18250 0.03238227
## 44 0.17875 0.03230175
## 45 0.17625 0.02531057
## 46 0.16625 0.02433134
## 47 0.16875 0.02301117
## 48 0.16750 0.02776389
## 49 0.17000 0.02513851
## 50 0.16750 0.02220485
## 51 0.17125 0.02128673
## 52 0.17125 0.01958777
## 53 0.17250 0.02108185
## 54 0.17375 0.02161050
## 55 0.17375 0.02389938
## 56 0.17625 0.02161050
## 57 0.17625 0.02161050
## 58 0.17750 0.02188988
## 59 0.17625 0.02079162
## 60 0.17625 0.02079162
## 61 0.39375 0.04007372
## 62 0.18625 0.02853482
## 63 0.18250 0.03238227
## 64 0.17875 0.03230175
## 65 0.17625 0.02531057
## 66 0.16625 0.02433134
## 67 0.16875 0.02301117
## 68 0.16750 0.02776389
## 69 0.17000 0.02513851
## 70 0.16750 0.02220485
## 71 0.17125 0.02128673
## 72 0.17125 0.01958777
## 73 0.17250 0.02108185
## 74 0.17375 0.02161050
## 75 0.17375 0.02389938
## 76 0.17625 0.02161050
## 77 0.17625 0.02161050
## 78 0.17750 0.02188988
## 79 0.17625 0.02079162
## 80 0.17625 0.02079162
## 81 0.39375 0.04007372
## 82 0.18625 0.02853482
## 83 0.18250 0.03238227
## 84 0.17875 0.03230175
## 85 0.17625 0.02531057
## 86 0.16625 0.02433134
## 87 0.16875 0.02301117
## 88 0.16750 0.02776389
## 89 0.17000 0.02513851
## 90 0.16750 0.02220485
## 91 0.17125 0.02128673
## 92 0.17125 0.01958777
## 93 0.17250 0.02108185
## 94 0.17375 0.02161050
## 95 0.17375 0.02389938
## 96 0.17625 0.02161050
## 97 0.17625 0.02161050
## 98 0.17750 0.02188988
## 99 0.17625 0.02079162
## 100 0.17625 0.02079162
## 101 0.39375 0.04007372
## 102 0.18625 0.02853482
## 103 0.18250 0.03238227
## 104 0.17875 0.03230175
## 105 0.17625 0.02531057
## 106 0.16625 0.02433134
## 107 0.16875 0.02301117
## 108 0.16750 0.02776389
## 109 0.17000 0.02513851
## 110 0.16750 0.02220485
## 111 0.17125 0.02128673
## 112 0.17125 0.01958777
## 113 0.17250 0.02108185
## 114 0.17375 0.02161050
## 115 0.17375 0.02389938
## 116 0.17625 0.02161050
## 117 0.17625 0.02161050
## 118 0.17750 0.02188988
## 119 0.17625 0.02079162
## 120 0.17625 0.02079162
## 121 0.39375 0.04007372
## 122 0.18625 0.02853482
## 123 0.18250 0.03238227
## 124 0.17875 0.03230175
## 125 0.17625 0.02531057
## 126 0.16625 0.02433134
## 127 0.16875 0.02301117
## 128 0.16750 0.02776389
## 129 0.17000 0.02513851
## 130 0.16750 0.02220485
## 131 0.17125 0.02128673
## 132 0.17125 0.01958777
## 133 0.17250 0.02108185
## 134 0.17375 0.02161050
## 135 0.17375 0.02389938
## 136 0.17625 0.02161050
## 137 0.17625 0.02161050
## 138 0.17750 0.02188988
## 139 0.17625 0.02079162
## 140 0.17625 0.02079162
## 141 0.39375 0.04007372
## 142 0.18625 0.02853482
## 143 0.18250 0.03238227
## 144 0.17875 0.03230175
## 145 0.17625 0.02531057
## 146 0.16625 0.02433134
## 147 0.16875 0.02301117
## 148 0.16750 0.02776389
## 149 0.17000 0.02513851
## 150 0.16750 0.02220485
## 151 0.17125 0.02128673
## 152 0.17125 0.01958777
## 153 0.17250 0.02108185
## 154 0.17375 0.02161050
## 155 0.17375 0.02389938
## 156 0.17625 0.02161050
## 157 0.17625 0.02161050
## 158 0.17750 0.02188988
## 159 0.17625 0.02079162
## 160 0.17625 0.02079162
## 161 0.39375 0.04007372
## 162 0.18625 0.02853482
## 163 0.18250 0.03238227
## 164 0.17875 0.03230175
## 165 0.17625 0.02531057
## 166 0.16625 0.02433134
## 167 0.16875 0.02301117
## 168 0.16750 0.02776389
## 169 0.17000 0.02513851
## 170 0.16750 0.02220485
## 171 0.17125 0.02128673
## 172 0.17125 0.01958777
## 173 0.17250 0.02108185
## 174 0.17375 0.02161050
## 175 0.17375 0.02389938
## 176 0.17625 0.02161050
## 177 0.17625 0.02161050
## 178 0.17750 0.02188988
## 179 0.17625 0.02079162
## 180 0.17625 0.02079162
## 181 0.39375 0.04007372
## 182 0.18625 0.02853482
## 183 0.18250 0.03238227
## 184 0.17875 0.03230175
## 185 0.17625 0.02531057
## 186 0.16625 0.02433134
## 187 0.16875 0.02301117
## 188 0.16750 0.02776389
## 189 0.17000 0.02513851
## 190 0.16750 0.02220485
## 191 0.17125 0.02128673
## 192 0.17125 0.01958777
## 193 0.17250 0.02108185
## 194 0.17375 0.02161050
## 195 0.17375 0.02389938
## 196 0.17625 0.02161050
## 197 0.17625 0.02161050
## 198 0.17750 0.02188988
## 199 0.17625 0.02079162
## 200 0.17625 0.02079162
## 201 0.39375 0.04007372
## 202 0.18625 0.02853482
## 203 0.18250 0.03238227
## 204 0.17875 0.03230175
## 205 0.17625 0.02531057
## 206 0.16625 0.02433134
## 207 0.16875 0.02301117
## 208 0.16750 0.02776389
## 209 0.17000 0.02513851
## 210 0.16750 0.02220485
## 211 0.17125 0.02128673
## 212 0.17125 0.01958777
## 213 0.17250 0.02108185
## 214 0.17375 0.02161050
## 215 0.17375 0.02389938
## 216 0.17625 0.02161050
## 217 0.17625 0.02161050
## 218 0.17750 0.02188988
## 219 0.17625 0.02079162
## 220 0.17625 0.02079162
## 221 0.39375 0.04007372
## 222 0.18625 0.02853482
## 223 0.18250 0.03238227
## 224 0.17875 0.03230175
## 225 0.17625 0.02531057
## 226 0.16625 0.02433134
## 227 0.16875 0.02301117
## 228 0.16750 0.02776389
## 229 0.17000 0.02513851
## 230 0.16750 0.02220485
## 231 0.17125 0.02128673
## 232 0.17125 0.01958777
## 233 0.17250 0.02108185
## 234 0.17375 0.02161050
## 235 0.17375 0.02389938
## 236 0.17625 0.02161050
## 237 0.17625 0.02161050
## 238 0.17750 0.02188988
## 239 0.17625 0.02079162
## 240 0.17625 0.02079162
## 241 0.39375 0.04007372
## 242 0.18625 0.02853482
## 243 0.18250 0.03238227
## 244 0.17875 0.03230175
## 245 0.17625 0.02531057
## 246 0.16625 0.02433134
## 247 0.16875 0.02301117
## 248 0.16750 0.02776389
## 249 0.17000 0.02513851
## 250 0.16750 0.02220485
## 251 0.17125 0.02128673
## 252 0.17125 0.01958777
## 253 0.17250 0.02108185
## 254 0.17375 0.02161050
## 255 0.17375 0.02389938
## 256 0.17625 0.02161050
## 257 0.17625 0.02161050
## 258 0.17750 0.02188988
## 259 0.17625 0.02079162
## 260 0.17625 0.02079162stopCluster(cl)We get an error rate of 0.166 with the best cost of 0.51.
train_err = mean(predict(oj_tune_rad$best.model, OJ_train) != OJ_train$Purchase)
test_err = mean(predict(oj_tune_rad$best.model, OJ_test) != OJ_test$Purchase)
paste('Train Error: ', train_err)## [1] "Train Error: 0.14875"paste('Test Error: ', test_err)## [1] "Test Error: 0.177777777777778"When we use tuned hyper-parameters for radial, we get better results. Our train error went down to 0.149 and a test error of 0.177 which is the same as our current best linear model.
8g) Repeat parts (b) through (e) using a support vector machine
with a polynomial kernel. Set degree = 2.
oj_poly = svm(Purchase ~., data = OJ_train, kernel = 'polynomial',
cost = 0.01, scale = T, degree = 2)
summary(oj_poly)##
## Call:
## svm(formula = Purchase ~ ., data = OJ_train, kernel = "polynomial",
## cost = 0.01, degree = 2, scale = T)
##
##
## Parameters:
## SVM-Type: C-classification
## SVM-Kernel: polynomial
## cost: 0.01
## degree: 2
## coef.0: 0
##
## Number of Support Vectors: 636
##
## ( 321 315 )
##
##
## Number of Classes: 2
##
## Levels:
## CH MMWith our cost of 0.01 on a polynomial of 2, we get 636 support vectors with 321 belonging to Citrus Hill and 315 belonging to Minute Maid.
train_err = mean(predict(oj_poly, OJ_train) != OJ_train$Purchase)
test_err = mean(predict(oj_poly, OJ_test) != OJ_test$Purchase)
paste('Train Error: ', train_err)## [1] "Train Error: 0.3725"paste('Test Error: ', test_err)## [1] "Test Error: 0.366666666666667"We get the error rates of 0.372 for training and 0.366 which are not as good as our prior models.
set.seed(1)
cl <- makeCluster(detectCores())
registerDoParallel(cl)
costs = seq(0.01, 2, 0.1) #changing because it taking too long to run
ctrl = tune.control(cross = 5)
oj_tune_poly = tune(svm, Purchase~., data=OJ_train,
ranges = list(cost = costs,tunecontrol = ctrl), method = 'polynomial',
degree = 2)
summary(oj_tune_poly)##
## Parameter tuning of 'svm':
##
## - sampling method: 10-fold cross validation
##
## - best parameters:
## cost tunecontrol
## 0.51 FALSE
##
## - best performance: 0.16625
##
## - Detailed performance results:
## cost
## 1 0.01
## 2 0.11
## 3 0.21
## 4 0.31
## 5 0.41
## 6 0.51
## 7 0.61
## 8 0.71
## 9 0.81
## 10 0.91
## 11 1.01
## 12 1.11
## 13 1.21
## 14 1.31
## 15 1.41
## 16 1.51
## 17 1.61
## 18 1.71
## 19 1.81
## 20 1.91
## 21 0.01
## 22 0.11
## 23 0.21
## 24 0.31
## 25 0.41
## 26 0.51
## 27 0.61
## 28 0.71
## 29 0.81
## 30 0.91
## 31 1.01
## 32 1.11
## 33 1.21
## 34 1.31
## 35 1.41
## 36 1.51
## 37 1.61
## 38 1.71
## 39 1.81
## 40 1.91
## 41 0.01
## 42 0.11
## 43 0.21
## 44 0.31
## 45 0.41
## 46 0.51
## 47 0.61
## 48 0.71
## 49 0.81
## 50 0.91
## 51 1.01
## 52 1.11
## 53 1.21
## 54 1.31
## 55 1.41
## 56 1.51
## 57 1.61
## 58 1.71
## 59 1.81
## 60 1.91
## 61 0.01
## 62 0.11
## 63 0.21
## 64 0.31
## 65 0.41
## 66 0.51
## 67 0.61
## 68 0.71
## 69 0.81
## 70 0.91
## 71 1.01
## 72 1.11
## 73 1.21
## 74 1.31
## 75 1.41
## 76 1.51
## 77 1.61
## 78 1.71
## 79 1.81
## 80 1.91
## 81 0.01
## 82 0.11
## 83 0.21
## 84 0.31
## 85 0.41
## 86 0.51
## 87 0.61
## 88 0.71
## 89 0.81
## 90 0.91
## 91 1.01
## 92 1.11
## 93 1.21
## 94 1.31
## 95 1.41
## 96 1.51
## 97 1.61
## 98 1.71
## 99 1.81
## 100 1.91
## 101 0.01
## 102 0.11
## 103 0.21
## 104 0.31
## 105 0.41
## 106 0.51
## 107 0.61
## 108 0.71
## 109 0.81
## 110 0.91
## 111 1.01
## 112 1.11
## 113 1.21
## 114 1.31
## 115 1.41
## 116 1.51
## 117 1.61
## 118 1.71
## 119 1.81
## 120 1.91
## 121 0.01
## 122 0.11
## 123 0.21
## 124 0.31
## 125 0.41
## 126 0.51
## 127 0.61
## 128 0.71
## 129 0.81
## 130 0.91
## 131 1.01
## 132 1.11
## 133 1.21
## 134 1.31
## 135 1.41
## 136 1.51
## 137 1.61
## 138 1.71
## 139 1.81
## 140 1.91
## 141 0.01
## 142 0.11
## 143 0.21
## 144 0.31
## 145 0.41
## 146 0.51
## 147 0.61
## 148 0.71
## 149 0.81
## 150 0.91
## 151 1.01
## 152 1.11
## 153 1.21
## 154 1.31
## 155 1.41
## 156 1.51
## 157 1.61
## 158 1.71
## 159 1.81
## 160 1.91
## 161 0.01
## 162 0.11
## 163 0.21
## 164 0.31
## 165 0.41
## 166 0.51
## 167 0.61
## 168 0.71
## 169 0.81
## 170 0.91
## 171 1.01
## 172 1.11
## 173 1.21
## 174 1.31
## 175 1.41
## 176 1.51
## 177 1.61
## 178 1.71
## 179 1.81
## 180 1.91
## 181 0.01
## 182 0.11
## 183 0.21
## 184 0.31
## 185 0.41
## 186 0.51
## 187 0.61
## 188 0.71
## 189 0.81
## 190 0.91
## 191 1.01
## 192 1.11
## 193 1.21
## 194 1.31
## 195 1.41
## 196 1.51
## 197 1.61
## 198 1.71
## 199 1.81
## 200 1.91
## 201 0.01
## 202 0.11
## 203 0.21
## 204 0.31
## 205 0.41
## 206 0.51
## 207 0.61
## 208 0.71
## 209 0.81
## 210 0.91
## 211 1.01
## 212 1.11
## 213 1.21
## 214 1.31
## 215 1.41
## 216 1.51
## 217 1.61
## 218 1.71
## 219 1.81
## 220 1.91
## 221 0.01
## 222 0.11
## 223 0.21
## 224 0.31
## 225 0.41
## 226 0.51
## 227 0.61
## 228 0.71
## 229 0.81
## 230 0.91
## 231 1.01
## 232 1.11
## 233 1.21
## 234 1.31
## 235 1.41
## 236 1.51
## 237 1.61
## 238 1.71
## 239 1.81
## 240 1.91
## 241 0.01
## 242 0.11
## 243 0.21
## 244 0.31
## 245 0.41
## 246 0.51
## 247 0.61
## 248 0.71
## 249 0.81
## 250 0.91
## 251 1.01
## 252 1.11
## 253 1.21
## 254 1.31
## 255 1.41
## 256 1.51
## 257 1.61
## 258 1.71
## 259 1.81
## 260 1.91
## tunecontrol
## 1 FALSE
## 2 FALSE
## 3 FALSE
## 4 FALSE
## 5 FALSE
## 6 FALSE
## 7 FALSE
## 8 FALSE
## 9 FALSE
## 10 FALSE
## 11 FALSE
## 12 FALSE
## 13 FALSE
## 14 FALSE
## 15 FALSE
## 16 FALSE
## 17 FALSE
## 18 FALSE
## 19 FALSE
## 20 FALSE
## 21 1
## 22 1
## 23 1
## 24 1
## 25 1
## 26 1
## 27 1
## 28 1
## 29 1
## 30 1
## 31 1
## 32 1
## 33 1
## 34 1
## 35 1
## 36 1
## 37 1
## 38 1
## 39 1
## 40 1
## 41 function (x, ...) , UseMethod("mean")
## 42 function (x, ...) , UseMethod("mean")
## 43 function (x, ...) , UseMethod("mean")
## 44 function (x, ...) , UseMethod("mean")
## 45 function (x, ...) , UseMethod("mean")
## 46 function (x, ...) , UseMethod("mean")
## 47 function (x, ...) , UseMethod("mean")
## 48 function (x, ...) , UseMethod("mean")
## 49 function (x, ...) , UseMethod("mean")
## 50 function (x, ...) , UseMethod("mean")
## 51 function (x, ...) , UseMethod("mean")
## 52 function (x, ...) , UseMethod("mean")
## 53 function (x, ...) , UseMethod("mean")
## 54 function (x, ...) , UseMethod("mean")
## 55 function (x, ...) , UseMethod("mean")
## 56 function (x, ...) , UseMethod("mean")
## 57 function (x, ...) , UseMethod("mean")
## 58 function (x, ...) , UseMethod("mean")
## 59 function (x, ...) , UseMethod("mean")
## 60 function (x, ...) , UseMethod("mean")
## 61 cross
## 62 cross
## 63 cross
## 64 cross
## 65 cross
## 66 cross
## 67 cross
## 68 cross
## 69 cross
## 70 cross
## 71 cross
## 72 cross
## 73 cross
## 74 cross
## 75 cross
## 76 cross
## 77 cross
## 78 cross
## 79 cross
## 80 cross
## 81 function (x, ...) , UseMethod("mean")
## 82 function (x, ...) , UseMethod("mean")
## 83 function (x, ...) , UseMethod("mean")
## 84 function (x, ...) , UseMethod("mean")
## 85 function (x, ...) , UseMethod("mean")
## 86 function (x, ...) , UseMethod("mean")
## 87 function (x, ...) , UseMethod("mean")
## 88 function (x, ...) , UseMethod("mean")
## 89 function (x, ...) , UseMethod("mean")
## 90 function (x, ...) , UseMethod("mean")
## 91 function (x, ...) , UseMethod("mean")
## 92 function (x, ...) , UseMethod("mean")
## 93 function (x, ...) , UseMethod("mean")
## 94 function (x, ...) , UseMethod("mean")
## 95 function (x, ...) , UseMethod("mean")
## 96 function (x, ...) , UseMethod("mean")
## 97 function (x, ...) , UseMethod("mean")
## 98 function (x, ...) , UseMethod("mean")
## 99 function (x, ...) , UseMethod("mean")
## 100 function (x, ...) , UseMethod("mean")
## 101 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 102 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 103 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 104 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 105 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 106 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 107 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 108 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 109 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 110 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 111 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 112 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 113 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 114 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 115 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 116 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 117 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 118 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 119 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 120 function (x, na.rm = FALSE) , sqrt(var(if (is.vector(x) || is.factor(x)) x else as.double(x), , na.rm = na.rm))
## 121 5
## 122 5
## 123 5
## 124 5
## 125 5
## 126 5
## 127 5
## 128 5
## 129 5
## 130 5
## 131 5
## 132 5
## 133 5
## 134 5
## 135 5
## 136 5
## 137 5
## 138 5
## 139 5
## 140 5
## 141 0.6666667
## 142 0.6666667
## 143 0.6666667
## 144 0.6666667
## 145 0.6666667
## 146 0.6666667
## 147 0.6666667
## 148 0.6666667
## 149 0.6666667
## 150 0.6666667
## 151 0.6666667
## 152 0.6666667
## 153 0.6666667
## 154 0.6666667
## 155 0.6666667
## 156 0.6666667
## 157 0.6666667
## 158 0.6666667
## 159 0.6666667
## 160 0.6666667
## 161 10
## 162 10
## 163 10
## 164 10
## 165 10
## 166 10
## 167 10
## 168 10
## 169 10
## 170 10
## 171 10
## 172 10
## 173 10
## 174 10
## 175 10
## 176 10
## 177 10
## 178 10
## 179 10
## 180 10
## 181 0.9
## 182 0.9
## 183 0.9
## 184 0.9
## 185 0.9
## 186 0.9
## 187 0.9
## 188 0.9
## 189 0.9
## 190 0.9
## 191 0.9
## 192 0.9
## 193 0.9
## 194 0.9
## 195 0.9
## 196 0.9
## 197 0.9
## 198 0.9
## 199 0.9
## 200 0.9
## 201 TRUE
## 202 TRUE
## 203 TRUE
## 204 TRUE
## 205 TRUE
## 206 TRUE
## 207 TRUE
## 208 TRUE
## 209 TRUE
## 210 TRUE
## 211 TRUE
## 212 TRUE
## 213 TRUE
## 214 TRUE
## 215 TRUE
## 216 TRUE
## 217 TRUE
## 218 TRUE
## 219 TRUE
## 220 TRUE
## 221 TRUE
## 222 TRUE
## 223 TRUE
## 224 TRUE
## 225 TRUE
## 226 TRUE
## 227 TRUE
## 228 TRUE
## 229 TRUE
## 230 TRUE
## 231 TRUE
## 232 TRUE
## 233 TRUE
## 234 TRUE
## 235 TRUE
## 236 TRUE
## 237 TRUE
## 238 TRUE
## 239 TRUE
## 240 TRUE
## 241 NULL
## 242 NULL
## 243 NULL
## 244 NULL
## 245 NULL
## 246 NULL
## 247 NULL
## 248 NULL
## 249 NULL
## 250 NULL
## 251 NULL
## 252 NULL
## 253 NULL
## 254 NULL
## 255 NULL
## 256 NULL
## 257 NULL
## 258 NULL
## 259 NULL
## 260 NULL
## error dispersion
## 1 0.39375 0.04007372
## 2 0.18625 0.02853482
## 3 0.18250 0.03238227
## 4 0.17875 0.03230175
## 5 0.17625 0.02531057
## 6 0.16625 0.02433134
## 7 0.16875 0.02301117
## 8 0.16750 0.02776389
## 9 0.17000 0.02513851
## 10 0.16750 0.02220485
## 11 0.17125 0.02128673
## 12 0.17125 0.01958777
## 13 0.17250 0.02108185
## 14 0.17375 0.02161050
## 15 0.17375 0.02389938
## 16 0.17625 0.02161050
## 17 0.17625 0.02161050
## 18 0.17750 0.02188988
## 19 0.17625 0.02079162
## 20 0.17625 0.02079162
## 21 0.39375 0.04007372
## 22 0.18625 0.02853482
## 23 0.18250 0.03238227
## 24 0.17875 0.03230175
## 25 0.17625 0.02531057
## 26 0.16625 0.02433134
## 27 0.16875 0.02301117
## 28 0.16750 0.02776389
## 29 0.17000 0.02513851
## 30 0.16750 0.02220485
## 31 0.17125 0.02128673
## 32 0.17125 0.01958777
## 33 0.17250 0.02108185
## 34 0.17375 0.02161050
## 35 0.17375 0.02389938
## 36 0.17625 0.02161050
## 37 0.17625 0.02161050
## 38 0.17750 0.02188988
## 39 0.17625 0.02079162
## 40 0.17625 0.02079162
## 41 0.39375 0.04007372
## 42 0.18625 0.02853482
## 43 0.18250 0.03238227
## 44 0.17875 0.03230175
## 45 0.17625 0.02531057
## 46 0.16625 0.02433134
## 47 0.16875 0.02301117
## 48 0.16750 0.02776389
## 49 0.17000 0.02513851
## 50 0.16750 0.02220485
## 51 0.17125 0.02128673
## 52 0.17125 0.01958777
## 53 0.17250 0.02108185
## 54 0.17375 0.02161050
## 55 0.17375 0.02389938
## 56 0.17625 0.02161050
## 57 0.17625 0.02161050
## 58 0.17750 0.02188988
## 59 0.17625 0.02079162
## 60 0.17625 0.02079162
## 61 0.39375 0.04007372
## 62 0.18625 0.02853482
## 63 0.18250 0.03238227
## 64 0.17875 0.03230175
## 65 0.17625 0.02531057
## 66 0.16625 0.02433134
## 67 0.16875 0.02301117
## 68 0.16750 0.02776389
## 69 0.17000 0.02513851
## 70 0.16750 0.02220485
## 71 0.17125 0.02128673
## 72 0.17125 0.01958777
## 73 0.17250 0.02108185
## 74 0.17375 0.02161050
## 75 0.17375 0.02389938
## 76 0.17625 0.02161050
## 77 0.17625 0.02161050
## 78 0.17750 0.02188988
## 79 0.17625 0.02079162
## 80 0.17625 0.02079162
## 81 0.39375 0.04007372
## 82 0.18625 0.02853482
## 83 0.18250 0.03238227
## 84 0.17875 0.03230175
## 85 0.17625 0.02531057
## 86 0.16625 0.02433134
## 87 0.16875 0.02301117
## 88 0.16750 0.02776389
## 89 0.17000 0.02513851
## 90 0.16750 0.02220485
## 91 0.17125 0.02128673
## 92 0.17125 0.01958777
## 93 0.17250 0.02108185
## 94 0.17375 0.02161050
## 95 0.17375 0.02389938
## 96 0.17625 0.02161050
## 97 0.17625 0.02161050
## 98 0.17750 0.02188988
## 99 0.17625 0.02079162
## 100 0.17625 0.02079162
## 101 0.39375 0.04007372
## 102 0.18625 0.02853482
## 103 0.18250 0.03238227
## 104 0.17875 0.03230175
## 105 0.17625 0.02531057
## 106 0.16625 0.02433134
## 107 0.16875 0.02301117
## 108 0.16750 0.02776389
## 109 0.17000 0.02513851
## 110 0.16750 0.02220485
## 111 0.17125 0.02128673
## 112 0.17125 0.01958777
## 113 0.17250 0.02108185
## 114 0.17375 0.02161050
## 115 0.17375 0.02389938
## 116 0.17625 0.02161050
## 117 0.17625 0.02161050
## 118 0.17750 0.02188988
## 119 0.17625 0.02079162
## 120 0.17625 0.02079162
## 121 0.39375 0.04007372
## 122 0.18625 0.02853482
## 123 0.18250 0.03238227
## 124 0.17875 0.03230175
## 125 0.17625 0.02531057
## 126 0.16625 0.02433134
## 127 0.16875 0.02301117
## 128 0.16750 0.02776389
## 129 0.17000 0.02513851
## 130 0.16750 0.02220485
## 131 0.17125 0.02128673
## 132 0.17125 0.01958777
## 133 0.17250 0.02108185
## 134 0.17375 0.02161050
## 135 0.17375 0.02389938
## 136 0.17625 0.02161050
## 137 0.17625 0.02161050
## 138 0.17750 0.02188988
## 139 0.17625 0.02079162
## 140 0.17625 0.02079162
## 141 0.39375 0.04007372
## 142 0.18625 0.02853482
## 143 0.18250 0.03238227
## 144 0.17875 0.03230175
## 145 0.17625 0.02531057
## 146 0.16625 0.02433134
## 147 0.16875 0.02301117
## 148 0.16750 0.02776389
## 149 0.17000 0.02513851
## 150 0.16750 0.02220485
## 151 0.17125 0.02128673
## 152 0.17125 0.01958777
## 153 0.17250 0.02108185
## 154 0.17375 0.02161050
## 155 0.17375 0.02389938
## 156 0.17625 0.02161050
## 157 0.17625 0.02161050
## 158 0.17750 0.02188988
## 159 0.17625 0.02079162
## 160 0.17625 0.02079162
## 161 0.39375 0.04007372
## 162 0.18625 0.02853482
## 163 0.18250 0.03238227
## 164 0.17875 0.03230175
## 165 0.17625 0.02531057
## 166 0.16625 0.02433134
## 167 0.16875 0.02301117
## 168 0.16750 0.02776389
## 169 0.17000 0.02513851
## 170 0.16750 0.02220485
## 171 0.17125 0.02128673
## 172 0.17125 0.01958777
## 173 0.17250 0.02108185
## 174 0.17375 0.02161050
## 175 0.17375 0.02389938
## 176 0.17625 0.02161050
## 177 0.17625 0.02161050
## 178 0.17750 0.02188988
## 179 0.17625 0.02079162
## 180 0.17625 0.02079162
## 181 0.39375 0.04007372
## 182 0.18625 0.02853482
## 183 0.18250 0.03238227
## 184 0.17875 0.03230175
## 185 0.17625 0.02531057
## 186 0.16625 0.02433134
## 187 0.16875 0.02301117
## 188 0.16750 0.02776389
## 189 0.17000 0.02513851
## 190 0.16750 0.02220485
## 191 0.17125 0.02128673
## 192 0.17125 0.01958777
## 193 0.17250 0.02108185
## 194 0.17375 0.02161050
## 195 0.17375 0.02389938
## 196 0.17625 0.02161050
## 197 0.17625 0.02161050
## 198 0.17750 0.02188988
## 199 0.17625 0.02079162
## 200 0.17625 0.02079162
## 201 0.39375 0.04007372
## 202 0.18625 0.02853482
## 203 0.18250 0.03238227
## 204 0.17875 0.03230175
## 205 0.17625 0.02531057
## 206 0.16625 0.02433134
## 207 0.16875 0.02301117
## 208 0.16750 0.02776389
## 209 0.17000 0.02513851
## 210 0.16750 0.02220485
## 211 0.17125 0.02128673
## 212 0.17125 0.01958777
## 213 0.17250 0.02108185
## 214 0.17375 0.02161050
## 215 0.17375 0.02389938
## 216 0.17625 0.02161050
## 217 0.17625 0.02161050
## 218 0.17750 0.02188988
## 219 0.17625 0.02079162
## 220 0.17625 0.02079162
## 221 0.39375 0.04007372
## 222 0.18625 0.02853482
## 223 0.18250 0.03238227
## 224 0.17875 0.03230175
## 225 0.17625 0.02531057
## 226 0.16625 0.02433134
## 227 0.16875 0.02301117
## 228 0.16750 0.02776389
## 229 0.17000 0.02513851
## 230 0.16750 0.02220485
## 231 0.17125 0.02128673
## 232 0.17125 0.01958777
## 233 0.17250 0.02108185
## 234 0.17375 0.02161050
## 235 0.17375 0.02389938
## 236 0.17625 0.02161050
## 237 0.17625 0.02161050
## 238 0.17750 0.02188988
## 239 0.17625 0.02079162
## 240 0.17625 0.02079162
## 241 0.39375 0.04007372
## 242 0.18625 0.02853482
## 243 0.18250 0.03238227
## 244 0.17875 0.03230175
## 245 0.17625 0.02531057
## 246 0.16625 0.02433134
## 247 0.16875 0.02301117
## 248 0.16750 0.02776389
## 249 0.17000 0.02513851
## 250 0.16750 0.02220485
## 251 0.17125 0.02128673
## 252 0.17125 0.01958777
## 253 0.17250 0.02108185
## 254 0.17375 0.02161050
## 255 0.17375 0.02389938
## 256 0.17625 0.02161050
## 257 0.17625 0.02161050
## 258 0.17750 0.02188988
## 259 0.17625 0.02079162
## 260 0.17625 0.02079162stopCluster(cl)We get our best performance of 0.16625 with a cost of 0.51. The range was reduced due to how long it was taking to run the SVM.
train_err = mean(predict(oj_tune_poly$best.model, OJ_train) != OJ_train$Purchase)
test_err = mean(predict(oj_tune_poly$best.model, OJ_test) != OJ_test$Purchase)
paste('Train Error: ', train_err)## [1] "Train Error: 0.14875"paste('Test Error: ', test_err)## [1] "Test Error: 0.177777777777778"We get a train error of 0.149 and a test error of 0.177 which is exactly the same as our hyper-parameter version of radial.
8h) Overall, which approach seems to give the best results on this data?
Overall, the best approach to getting the lowest Test Error was doing hyper-parameter tuning which lead to the best results except for the linear model, but the original linear model gave similar results. I believe if I adjusted my range (I won’t because they took hours to run) then I would of gotten at least a test error of 0.177 for the hyper-parameter version of linear.
Comment on your results. Note you will need to fit the classifier without the gas