R: SVM to Predict MPG for 2019 Vehicles

August 11, 2019

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Continuing on the below post, I am going to use a support vector machine (SVM) to predict combined miles per gallon for all 2019 motor vehicles.

Part 1: Using Decision Trees and Random Forest to Predict MPG for 2019 Vehicles

Part 2: Using Gradient Boosted Machine to Predict MPG for 2019 Vehicles

The raw data is located on the EPA government site

The variables/features I am using for the models are: Engine displacement (size), number of cylinders, transmission type, number of gears, air inspired method, regenerative braking type, battery capacity Ah, drivetrain, fuel type, cylinder deactivate, and variable valve. 

There are 1253 vehicles in the dataset (does not include pure electric vehicles) summarized below.

fuel_economy_combined    eng_disp        num_cyl       transmission
Min. :11.00 Min. :1.000 Min. : 3.000 A :301
1st Qu.:19.00 1st Qu.:2.000 1st Qu.: 4.000 AM : 46
Median :23.00 Median :3.000 Median : 6.000 AMS: 87
Mean :23.32 Mean :3.063 Mean : 5.533 CVT: 50
3rd Qu.:26.00 3rd Qu.:3.600 3rd Qu.: 6.000 M :148
Max. :58.00 Max. :8.000 Max. :16.000 SA :555
SCV: 66
num_gears air_aspired_method
Min. : 1.000 Naturally Aspirated :523
1st Qu.: 6.000 Other : 5
Median : 7.000 Supercharged : 55
Mean : 7.111 Turbocharged :663
3rd Qu.: 8.000 Turbocharged+Supercharged: 7
Max. :10.000

regen_brake batt_capacity_ah
No :1194 Min. : 0.0000
Electrical Regen Brake: 57 1st Qu.: 0.0000
Hydraulic Regen Brake : 2 Median : 0.0000
Mean : 0.3618
3rd Qu.: 0.0000
Max. :20.0000

drive cyl_deactivate
2-Wheel Drive, Front :345 Y: 172
2-Wheel Drive, Rear :345 N:1081
4-Wheel Drive :174
All Wheel Drive :349
Part-time 4-Wheel Drive: 40

Diesel, ultra low sulfur (15 ppm, maximum): 28
Gasoline (Mid Grade Unleaded Recommended) : 16
Gasoline (Premium Unleaded Recommended) :298
Gasoline (Premium Unleaded Required) :320
Gasoline (Regular Unleaded Recommended) :591

N: 38

Starting with an untuned base model:

m_svm_untuned <- svm(formula = fuel_economy_combined ~ .,
data = test)

pred_svm_untuned <- predict(m_svm_untuned, test)

yhat <- pred_svm_untuned
y <- test$fuel_economy_combined
svm_stats_untuned <- postResample(yhat, y)

RMSE Rsquared MAE
2.3296249 0.8324886 1.4964907

Similar to the results for the untuned boosted model.  I am going to run a grid search and tune the support vector machine.

hyper_grid <- expand.grid(
cost = 2^seq(-5,5,1),
gamma= 2^seq(-5,5,1)
e <- NULL

for(j in 1:nrow(hyper_grid)){
m_svm_untuned <- svm(
formula = fuel_economy_combined ~ .,
data = train,
gamma = hyper_grid$gamma[j],
cost = hyper_grid$cost[j]

pred_svm_untuned <-predict(
newdata = test

yhat <- pred_svm_untuned
y <- test$fuel_economy_combined
e[j] <- postResample(yhat, y)[1]
cat(j, "\n")

which.min(e) #minimum MSE

The best tuned support vector machine has a cost of 32 and a gamma of .25.

I am going to run this combination:

m_svm_tuned <- svm(
formula = fuel_economy_combined ~ .,
data = test,
gamma = .25,
cost = 32,

pred_svm_tuned <- predict(m_svm_tuned,test)


RMSE Rsquared MAE
0.9331948 0.9712492 0.7133039

The tuned support vector machine outperforms the gradient boosted model substantially with a MSE of .87 vs a MSE of 3.25 for the gradient boosted model and a MSE of 3.67 for the random forest.


svm(formula = fuel_economy_combined ~ ., data = test, gamma = 0.25, cost = 32, scale = TRUE)

SVM-Type: eps-regression
SVM-Kernel: radial
cost: 32
gamma: 0.25
epsilon: 0.1

Number of Support Vectors: 232

sum(abs(res)<=1) / 314
[1] 0.8503185 

The model is able to predict 85% of vehicles within 1 MPG of EPA estimate. Considering I am not rounding this is a great result.

The model also does a much better job with outliers as none of the models predicted the Hyundai Ioniq well.

tmp[which(abs(res) > svm_stats[1] * 3), ] #what cars are 3 se residuals
Division Carline fuel_economy_combined pred_svm_tuned
641 HYUNDAI MOTOR COMPANY Ioniq 55 49.01012
568 TOYOTA CAMRY XSE 26 22.53976
692 Volkswagen Arteon 4Motion 23 26.45806
984 Volkswagen Atlas 19 22.23552

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