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📊 Study on Crime Rates in India using Regression Analysis

📌 Overview

This repository contains an end-to-end statistical analysis of crime rates in India, focusing on IPC and SLL crimes and their relationship with key socio-economic indicators across Indian states and union territories.

The project applies multiple linear regression, diagnostic testing, and model refinement to examine whether commonly cited economic variables meaningfully explain variations in crime rates.

This work was carried out as part of an academic dissertation and emphasizes statistical rigor over black-box modeling.

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🎯 Objectives

The primary goals of this study are:

1. Quantify the relationship between crime rates and socio-economic indicators such as:

   • Unemployment (rural & urban)
   • GDP and NSDP
   • Inflation (general & food)

2. Compare IPC vs SLL crime behavior under identical predictors

3. Diagnose and correct regression issues, including:

   • Influential observations
   • Multicollinearity
   • Heteroscedasticity

4. Identify statistically significant predictors of crime rates

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📂 Dataset Description

• Observations: 33 Indian states & union territories (2021)

• Response Variables:

  • Rate_IPC: IPC crimes per lakh population
  • Rate_SLL: SLL crimes per lakh population

• Predictor Variables:

  • Rural unemployment rate
  • Urban unemployment rate
  • Log(GDP)
  • Log(NSDP)
  • General CPI inflation
  • Food CPI inflation
  • Population-based dummy variables

Data Sources:

• National Crime Records Bureau (NCRB)
• Reserve Bank of India (RBI)

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🧪 Methodology

The analysis follows a classical regression pipeline, not shortcuts.

1️⃣ Exploratory Data Analysis

• Scatter plots of each predictor vs response
• Initial visual assessment of linearity and spread

2️⃣ Regression Modeling

Two primary models were fitted:

• Case 1: IPC crime rate as response
• Case 2: SLL crime rate as response

Each model initially included all predictors jointly.

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3️⃣ Regression Diagnostics

To ensure validity of inference, the following diagnostics were performed:

• Influential Point Detection

  • Standardized residuals
  • Cook’s Distance

• Multicollinearity

  • Correlation heatmaps
  • Variance Inflation Factors (VIF)

• Heteroscedasticity

  • Residual vs fitted plots
  • Glejser test
  • Goldfeld–Quandt test

Only statistically justified corrections were applied.

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4️⃣ Model Refinement

After removing influential observations and redundant predictors:

• Final models reduced to GDP as the sole significant predictor
• Separate final regressions for IPC and SLL crimes

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📈 Key Findings

• GDP is the only statistically significant predictor (at 10% level) for both IPC and SLL crime rates

• Most commonly assumed predictors (unemployment, inflation) do not show significance

• Overall explanatory power of the models remains limited

  • Indicates missing socio-structural variables
  • Highlights limits of purely economic explanations

👉 This is an important negative result, not a failure.

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🧠 Interpretation

This study demonstrates that:

• Crime is not adequately explained by macro-economic indicators alone

• Statistical diagnostics matter — naïve regression would lead to misleading conclusions

• There is strong scope for:

  • Micro-level data
  • Policy, policing, education, and demographic variables
  • Panel or time-series extensions

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🛠 Tools & Technologies

• Language: R

• Libraries:

  • car
  • ggplot2
  • reshape2

• Statistical Methods:

  • OLS regression
  • Diagnostic testing
  • Correlation analysis

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📁 Repository Structure

├── data/
│   └── regression_data.csv
├── report/
|   ├── Study_on_crime_rate_in_India.docx
│   └── Study_on_crime_rate_in_India.pdf
├── scripts/
│   ├── scatterplot.R
│   ├── regression.R
│   ├── regression_diagnostics.R
│   └── dummy.R
├── LICENSE
└── README.md

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📚 References

• Goon, Gupta & Dasgupta — Fundamentals of Statistics (Vol I & II)
• NCRB — Crimes in India 2021
• RBI — Handbook of Statistics on Indian States

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📜 License

This project is licensed under the MIT License — see the
LICENSE file for details.

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🙏 Acknowledgement

This project was completed under the guidance of Prof. Mausumi Bose, with sincere thanks to her and college for giving me such an opportunity.

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