# Using SVM to Predict MPG for 2019 Vehicles

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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

fuel_type

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

variable_valve

N: 38

Y:1215

Starting with an untuned base model:

`set.seed(123)`

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)

`svm_stats_untuned`

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)){

set.seed(123)

m_svm_untuned <- svm(

formula = fuel_economy_combined ~ .,

data = train,

gamma = hyper_grid$gamma[j],

cost = hyper_grid$cost[j]

)

pred_svm_untuned <-predict(

m_svm_untuned,

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:

`set.seed(123)`

m_svm_tuned <- svm(

formula = fuel_economy_combined ~ .,

data = test,

gamma = .25,

cost = 32,

scale=TRUE

)

pred_svm_tuned <- predict(m_svm_tuned,test)

yhat<-pred_svm_tuned

y<-test$fuel_economy_combined

svm_stats<-postResample(yhat,y)

`svm_stats`

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.

`summary(m_svm_tuned)`

Call:

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

Parameters:

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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