R: MLR, Decision Trees and Random Forest to Predict MPG for 2019 Vehicles

I am going to use regression, decision trees, and the random forest algorithm to predict combined miles per gallon for all 2019 motor vehicles.  The raw data is located on the EPA government site

After preliminary diagnostics, exploration and cleaning I am going to start with a multiple linear regression model.

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        

Call:
lm(formula = fuel_economy_combined ~ eng_disp + transmission + 
    num_gears + air_aspired_method + regen_brake + batt_capacity_ah + 
    drive + fuel_type + cyl_deactivate + variable_valve, data = cars_19)

Residuals:
     Min       1Q   Median       3Q      Max 
-12.7880  -1.6012   0.1102   1.6116  17.3181 

Coefficients:
                                                   Estimate Std. Error t value Pr(>|t|)    
(Intercept)                                        36.05642    0.82585  43.660  < 2e-16 ***
eng_disp                                           -2.79257    0.08579 -32.550  < 2e-16 ***
transmissionAM                                      2.74053    0.44727   6.127 1.20e-09 ***
transmissionAMS                                     0.73943    0.34554   2.140 0.032560 *  
transmissionCVT                                     6.83932    0.62652  10.916  < 2e-16 ***
transmissionM                                       1.08359    0.31706   3.418 0.000652 ***
transmissionSA                                      0.63231    0.22435   2.818 0.004903 ** 
transmissionSCV                                     2.73768    0.40176   6.814 1.48e-11 ***
num_gears                                           0.21496    0.07389   2.909 0.003691 ** 
air_aspired_methodOther                            -2.70781    1.99491  -1.357 0.174916    
air_aspired_methodSupercharged                     -1.62171    0.42210  -3.842 0.000128 ***
air_aspired_methodTurbocharged                     -1.79047    0.22084  -8.107 1.24e-15 ***
air_aspired_methodTurbocharged+Supercharged        -1.68028    1.04031  -1.615 0.106532    
regen_brakeElectrical Regen Brake                  12.59523    0.90030  13.990  < 2e-16 ***
regen_brakeHydraulic Regen Brake                    6.69040    1.94379   3.442 0.000597 ***
batt_capacity_ah                                   -0.47689    0.11838  -4.028 5.96e-05 ***
drive2-Wheel Drive, Rear                           -2.54806    0.24756 -10.293  < 2e-16 ***
drive4-Wheel Drive                                 -3.14862    0.29649 -10.620  < 2e-16 ***
driveAll Wheel Drive                               -3.12875    0.22300 -14.030  < 2e-16 ***
drivePart-time 4-Wheel Drive                       -3.94765    0.46909  -8.415  < 2e-16 ***
fuel_typeGasoline (Mid Grade Unleaded Recommended) -5.54594    0.97450  -5.691 1.58e-08 ***
fuel_typeGasoline (Premium Unleaded Recommended)   -5.44412    0.70009  -7.776 1.57e-14 ***
fuel_typeGasoline (Premium Unleaded Required)      -6.01955    0.70542  -8.533  < 2e-16 ***
fuel_typeGasoline (Regular Unleaded Recommended)   -6.43743    0.68767  -9.361  < 2e-16 ***
cyl_deactivateY                                     0.52100    0.27109   1.922 0.054851 .  
variable_valveY                                     2.00533    0.59508   3.370 0.000775 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

  standard error: 2.608 on 1227 degrees of freedom
Multiple R-squared:  0.8104,    Adjusted R-squared:  0.8066 
F-statistic: 209.8 on 25 and 1227 DF,  p-value: < 2.2e-16 

The fitted MSE is 6.8 and predicted MSE of 6.83.  Some of the below residuals are too large.  The extreme large residual is a Hyundai Ioniq which none of the models predict very well as it is unique vehicle (versus the other data points).
Let's try a decision tree regression model.

#regression tree full
m_reg_tree_full <- rpart(formula = fuel_economy_combined ~ .,
                         data    = train,
                         method  = "anova",)
#regression tree tuned
m_reg_tree_trimmed <- rpart(
  formula = fuel_economy_combined ~ .,
  data    = train,
  method  = "anova",
  control = list(minsplit = 10, cp = .0005)
)

#rpart.plot(m_reg_tree_full)
plotcp(m_reg_tree_full)

pred_decision_tree_full <- predict(m_reg_tree_full, newdata = test)
mse_tree_full <- RMSE(pred = pred_decision_tree_full, obs = test$fuel_economy_combined) ^2

pred_decision_tree_trimmed <- predict(m_reg_tree_trimmed, newdata = test)
mse_tree_trimmed <- RMSE(pred = pred_decision_tree_trimmed, obs = test$fuel_economy_combined) ^2
plotcp(m_reg_tree_trimmed)


After tuning the decision tree the predicted MSE is 6.20 which is better than the regression model.

Finally let's try a random forest model.  The random forest should produce the best model as it will attempt to remove some of the correlation within the decision tree structure.

#random forest
m_random_forest_full <-randomForest(formula = fuel_economy_combined ~ ., data = train)
predict_random_forest_full <- predict(m_random_forest_full, newdata = test)
mse_random_forest_full <- RMSE(pred = predict_random_forest_full, obs = test$fuel_economy_combined) ^ 2

which.min(m_random_forest_full$mse)

#random forest tuned
m_random_forest <- randomForest(formula = fuel_economy_combined ~ ., data = train, ntree = 250)
plot(m_random_forest)
predict_random_forest <- predict(m_random_forest, newdata = test)
mse_random_forest <- RMSE(pred = predict_random_forest, obs = test$fuel_economy_combined) ^ 2

plot(tmp$test.fuel_economy_combined - tmp$r.predict_random_forrest., ylab = "residuals",main = "Random Forest")

varImpPlot(m_random_forest)



The error stabilizes at 250 trees.  randomForest() by default uses 500 trees which is unnecessary.


After tuning the random forest the model has the lowest fitted and predicted MSE of 3.67 which is substantially better than the MSE of the decision tree 6.2

The random forest also has an r-squared of .9

Engine size, number of cylinders, and transmission type are the largest contributors to accuracy.


No comments:

Post a Comment