📈 Linear Regression Project — Car MPG & Diamond Price

This repository demonstrates an end-to-end, beginner-friendly but thorough workflow for linear regression using two classic datasets:

• Auto MPG — predict miles-per-gallon (MPG) from vehicle attributes
• Diamonds — predict price from diamond characteristics

The notebook walks through data loading → exploratory plots → feature selection → model training → evaluation → prediction.
All exploratory scatter plots are pre-exported and stored in the assets/ folder for use in reports or slides.

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🎯 Problem Statement

• Build simple linear regression models for tabular prediction tasks
• Practice feature selection and interpret exploratory plots
• Evaluate models with R² score and make point predictions
• Reuse plots (already exported to assets/)

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🗂 Data Sources

Loaded directly from IBM Skills Network public buckets (as used in the notebook):

• Auto MPG
  https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBM-BD0231EN-SkillsNetwork/datasets/mpg.csv

• Diamonds
  https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBM-BD0231EN-SkillsNetwork/datasets/diamonds.csv

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🔍 Exploratory Data Analysis (EDA)

A) Auto MPG — Relationships to MPG

The notebook visualizes how engine/vehicle attributes relate to MPG:

• Horsepower vs MPG
  

• Cylinders vs MPG
  

• Engine Displacement vs MPG
  

• Weight vs MPG
  

Intuition from plots (typical patterns):

• Higher horsepower, cylinders, displacement, and weight generally correlate with lower MPG.

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B) Diamonds — Relationships to Price

The notebook explores how physical characteristics relate to price:

• Carat vs Price
  

• “s” vs Price (as used in the notebook’s column selection)
  

• Depth vs Price
  

• Table vs Price
  

Intuition from plots (typical patterns):

• Carat vs price - strong positive correlation but also high variance (heteroscedasticity)
• Depth and table often show weaker or more nuanced relationships.

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🧠 Feature Sets & Targets

Auto MPG

• Target: MPG
• Features: Horsepower, Weight

Diamonds

• Target: price
• Features: carat, depth (as per the model in the notebook)

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🧪 Modeling & Evaluation

Both tasks use sklearn.linear_model.LinearRegression trained on the full dataset (no split in the lab).
Evaluation uses the R² score (model.score(X, y)), where higher is better.

Results

1) Auto MPG — Linear Regression

• Model: MPG ~ Horsepower + Weight
• R² (on full data): 0.7063752737298348
• Example prediction:
  Input Horsepower = 100, Weight = 2000 ⇒ MPG ≈ 29.3216

Interpretation:
A simple two-feature linear model captures a substantial share of variance in MPG (≈70%). Plots indicate the expected negative relationships between power/weight and fuel economy.

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2) Diamonds — Linear Regression

• Model: price ~ carat + depth
• R² (on full data): 0.8506754571636563
• Example prediction:
  Input carat = 0.3, depth = 60 ⇒ price ≈ 244.956

Interpretation:
With just carat and depth, the model explains ~85% of price variance—carat is highly predictive; depth adds a smaller adjustment.

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🧭 Step-by-Step (Notebook Flow)

1. Load data via pandas.read_csv from the given URLs
2. Visual EDA with DataFrame.plot.scatter to inspect relationships
3. Select features/target per task
4. Instantiate & fit LinearRegression()
5. Evaluate with model.score(X, y) (R²)
6. Predict sample values to sanity-check the model

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🛠️ Tech Stack

• Python 3.10+, Jupyter Notebook/Lab
• Libraries: pandas, numpy, matplotlib, scikit-learn

Quick install

pip install pandas numpy matplotlib scikit-learn jupyterlab

▶️ How to Run

# 1) Clone
git clone https://github.com/ShyamSundarVijayakumar/linear_regression_project.git
cd linear_regression_project

# 2) (Optional) Create & activate a venv
python -m venv venv
# Windows: .\venv\Scripts\activate
# macOS/Linux:
source venv/bin/activate

# 3) Install deps
pip install -r requirements.txt

# 4) Launch
jupyter lab
# Open "Building_and_training_a_model_using_Linear_Regression.ipynb" and run cells

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✅ Key Takeaways

• Simple linear models can be strong baselines:
  • Auto MPG with only Horsepower and Weight already achieves R² ≈ 0.71.
  • Diamonds with just carat and depth achieves R² ≈ 0.85.
• EDA guides feature choices: Visual trends in scatter plots help prioritize variables.
• Predictions are interpretable: The model outputs make intuitive sense when cross-checked with domain intuition.

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💡 Suggestions / Next Steps

• Train/Test Split or Cross-Validation:

  • Evaluate generalization (e.g., train_test_split or KFold) and report test R².

• Residual Diagnostics

  • Plot residuals vs fitted, check normality of residuals, and look for heteroscedasticity.

• Add/Compare Models

• Try Ridge/Lasso/ElasticNet (regularization), PolynomialFeatures, and tree-based models; compare metrics.

• Scaling

  • Standardize features if you expand to models sensitive to scale.

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👨‍💻 Author

Shyam Sundar Vijayakumar
Data Scientist | Optimization Specialist

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📜 License

This project is licensed under the MIT License. Shared for educational and portfolio purposes. Attribution is appreciated.