Part 1: Using Decision Trees and Random Forest 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:

```
trees <- 1200
m_boosted_reg_untuned <- gbm(
formula = fuel_economy_combined ~ .,
data = train,
n.trees = trees,
distribution = "gaussian"
)
```

```
> summary(m_boosted_reg_untuned)
var rel.inf
eng_disp eng_disp 41.26273684
batt_capacity_ah batt_capacity_ah 24.53458898
transmission transmission 11.33253784
drive drive 8.59300859
regen_brake regen_brake 8.17877824
air_aspired_method air_aspired_method 2.11397865
num_gears num_gears 1.90999021
fuel_type fuel_type 1.65692562
num_cyl num_cyl 0.22260369
variable_valve variable_valve 0.11043532
cyl_deactivate cyl_deactivate 0.08441602
> boosted_stats_untuned
RMSE Rsquared MAE
2.4262643 0.8350367 1.7513331
```

The untuned GBM model performs better than the multiple linear regression model, but worse than the random forest.

I am going to tune the GBM by running a grid search:

```
#create hyperparameter grid
hyper_grid <- expand.grid(
shrinkage = seq(.07, .12, .01),
interaction.depth = 1:7,
optimal_trees = 0,
min_RMSE = 0
)
#grid search
for (i in 1:nrow(hyper_grid)) {
set.seed(123)
gbm.tune <- gbm(
formula = fuel_economy_combined ~ .,
data = train_random,
distribution = "gaussian",
n.trees = 5000,
interaction.depth = hyper_grid$interaction.depth[i],
shrinkage = hyper_grid$shrinkage[i],
)
hyper_grid$optimal_trees[i] <- which.min(gbm.tune$train.error)
hyper_grid$min_RMSE[i] <- sqrt(min(gbm.tune$train.error))
cat(i, "\n")
}
```

The hyper grid is 42 rows which is all combinations of shrinkage and interaction depths specified above.

```
> head(hyper_grid)
shrinkage interaction.depth optimal_trees min_RMSE
1 0.07 1 0 0
2 0.08 1 0 0
3 0.09 1 0 0
4 0.10 1 0 0
5 0.11 1 0 0
6 0.12 1 0 0
```

After running the grid search, it is apparent that there is overfitting. This is something to be very careful about. I am going to run a 5 fold cross validation to estimate out of bag error vs MSE. After running the 5 fold CV, this is the best model that does not overfit:

```
> m_boosted_reg <- gbm(
formula = fuel_economy_combined ~ .,
data = train,
n.trees = trees,
distribution = "gaussian",
shrinkage = .09,
cv.folds = 5,
interaction.depth = 5
)
best.iter <- gbm.perf(m_boosted_reg, method = "cv")
pred_boosted_reg_ <- predict(m_boosted_reg,n.trees=1183, newdata = test)
mse_boosted_reg_ <- RMSE(pred = pred_boosted_reg, obs = test$fuel_economy_combined) ^2
boosted_stats<-postResample(pred_boosted_reg,test$fuel_economy_combined)
```

The fitted black curve above is MSE and the fitted green curve is the out of bag estimated error. 1183 is the optimal amount of iterations.

```
> pred_boosted_reg <- predict(m_boosted_reg,n.trees=1183, newdata = test)
> mse_boosted_reg <- RMSE(pred = pred_boosted_reg, obs = test$fuel_economy_combined) ^2
> boosted_stats<-postResample(pred_boosted_reg,test$fuel_economy_combined)
> boosted_stats
RMSE Rsquared MAE
1.8018793 0.9092727 1.3334459
> mse_boosted_reg
3.246769
```

The tuned gradient boosted model performs better than the random forest with a MSE of 3.25 vs 3.67 for the random forest.

```
> summary(res)
Min. 1st Qu. Median Mean 3rd Qu. Max.
-5.40000 -0.90000 0.00000 0.07643 1.10000 9.10000
```

50% of the predictions are within 1 MPG of the EPA Government Estimate.

The largest residuals are exotics and a hybrid which are the more unique data points in the dataset.

```
> tmp[which(abs(res) > boosted_stats[1] * 3), ]
Division Carline fuel_economy_combined pred_boosted_reg
642 HYUNDAI MOTOR COMPANY Ioniq Blue 58 48.5
482 KIA MOTORS CORPORATION Forte FE 35 28.7
39 Lamborghini Aventador Coupe 11 17.2
40 Lamborghini Aventador Roadster 11 17.2
```