Step-by-Step Implementation for Polynomial Regression on Fuel Data.ipynb

Kernel: Python 3 (ipykernel)

#Import Required Libraries:
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import PolynomialFeatures
from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error
from sklearn.preprocessing import LabelEncoder

# Load your dataset
df = pd.read_csv('FuelConsumption.csv')

# Preview the dataset
df.head()

Handle Categorical Variables:

If the dataset contains categorical variables, you need to convert them to numerical values. One common way is to use LabelEncoder or one-hot encoding. Here's an example of using LabelEncoder for a column:

print("\nUnique values in VEHICLECLASS before encoding:", df['VEHICLECLASS'].unique())
label_encoder = LabelEncoder()
df['VEHICLECLASS_NUM'] = label_encoder.fit_transform(df['VEHICLECLASS'])
df = df.drop('VEHICLECLASS', axis=1)

Unique values in VEHICLECLASS before encoding: ['COMPACT' 'SUV - SMALL' 'MID-SIZE' 'MINICOMPACT' 'SUBCOMPACT'
 'TWO-SEATER' 'FULL-SIZE' 'STATION WAGON - SMALL' 'SUV - STANDARD'
 'VAN - CARGO' 'VAN - PASSENGER' 'PICKUP TRUCK - STANDARD' 'MINIVAN'
 'SPECIAL PURPOSE VEHICLE' 'STATION WAGON - MID-SIZE'
 'PICKUP TRUCK - SMALL']

df.head(10)

# 3. Drop unnecessary columns: MAKE and MODEL
df = df.drop(['MAKE', 'MODEL'], axis=1)

# 5. Select Features and Target
features = ['ENGINESIZE', 'CYLINDERS', 'FUELCONSUMPTION_CITY',
            'FUELCONSUMPTION_HWY', 'FUELCONSUMPTION_COMB',
            'FUELCONSUMPTION_COMB_MPG', 'VEHICLECLASS_NUM']
target = 'CO2EMISSIONS'

X = df[features]
y = df[target]

# 6. Split into Train and Test Sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

Y=mx+c Y=mx2+mx+1+c

# 7. Polynomial Feature Transformation
poly = PolynomialFeatures(degree=2, include_bias=False)
X_train_poly = poly.fit_transform(X_train)
X_test_poly = poly.transform(X_test)

# 8. Fit Polynomial Regression Model
model = LinearRegression()
model.fit(X_train_poly, y_train)

# 9. Predict on Test Set
from sklearn.metrics import r2_score
y_pred = model.predict(X_test_poly)

# 10. Evaluation Metrics
mse = mean_squared_error(y_test, y_pred)
r2 = r2_score(y_test, y_pred)

print(f"\nModel Performance Metrics:")
print(f"Mean Squared Error (MSE): {mse:.2f}")
print(f"R² Score: {r2:.4f}")

Model Performance Metrics:
Mean Squared Error (MSE): 219.32
R² Score: 0.9470

# 11. Visualize Regression Curve for ENGINESIZE
plt.scatter(X_test['ENGINESIZE'], y_test, color='red', label='Actual')
plt.scatter(X_test['ENGINESIZE'], y_pred, color='blue', alpha=0.5, label='Predicted')
plt.title("Polynomial Regression: Engine Size vs CO2 Emissions")
plt.xlabel("Engine Size")
plt.ylabel("CO2 Emissions")
plt.legend()
plt.grid(True)
plt.show()

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1. Model Performance Metrics

Mean Squared Error (MSE): 219.32

• What it means: On average, the squared difference between the predicted and actual CO2 emissions is 219.32.

• Interpretation: Lower MSE means better model accuracy. An MSE of 219 is reasonable depending on your CO2 emission scale (which in your case ranges roughly between 100–400 g/km).

📌 MSE is in squared units of the target variable (g/km²).

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R² Score: e.g., 0.8772 (if you got this earlier)

• What it means: Your model explains ~87.72% of the variability in CO2 emissions based on input features.

• Interpretation:

  • R² = 1 means perfect fit.

  • R² = 0 means the model performs no better than a horizontal line (mean of target).

  • R² ≈ 0.87 means it's a good fit, though there's still ~12% variance not captured — maybe due to noise or unmodeled factors like vehicle weight or fuel type.

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2. Graph – Regression Curve

You plotted Engine Size vs CO2 Emissions:

• Red points: Actual CO2 values from the test set.

• Blue points: Predicted CO2 values from your model.

If the blue dots closely follow the red, the model is generalizing well. If there’s a large scatter or pattern, the model may be underfitting or overfitting.

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• Interpretation: A vehicle with these specs is estimated to emit ~260 grams of CO2 per kilometer, based on the training data and polynomial regression.

• This prediction relies on patterns learned from the dataset — not real-world physics.

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4. What Could Improve the Model?

Issue	Recommendation
Slight underfit	Try degree=3 in PolynomialFeatures
Overfit	Try Ridge or Lasso regression
Features too correlated	Use PCA or remove redundant variables
Dataset limited	More rows (real data), include new features (e.g. vehicle weight, fuel type)