Quantitative Techniques
(Regression, Correlation and Gravity Model)
Correlation
(Let’s build from basics.)
👉 First imagine:
You notice that wherever rainfall is high, crop yield is also high.
You start wondering — Is there a relationship?
This “relationship” between two variables is studied using Correlation.
📖 Definition:
Correlation is a statistical technique that measures the strength and direction of the relationship between two variables.
- Strength = How strong is the relationship? (Are they tightly linked or loosely?)
- Direction = Is it positive (both move together) or negative (one goes up, other comes down)?
📊 Types of Correlation:
| Type | Meaning | Example |
|---|---|---|
| Positive Correlation | Both variables increase or decrease together | Rainfall ↑ → Crop Yield ↑ |
| Negative Correlation | One increases, other decreases | Altitude ↑ → Temperature ↓ |
| Zero Correlation | No relationship | Number of parks and literacy rate in a city |
📏 Correlation Coefficient (r):
- It is a number between -1 and +1.
- r = +1 ➔ Perfect positive correlation
- r = -1 ➔ Perfect negative correlation
- r = 0 ➔ No correlation
🧠 Simple Analogy:
Imagine two dancers on stage:
- If they move perfectly together ➔ r = +1 (positive correlation).
- If one moves forward and other backward ➔ r = -1 (negative correlation).
- If they dance randomly ➔ r = 0 (no correlation).
Regression
(Now a step deeper.)
👉 Suppose you now don’t just want to know there is a relationship between rainfall and crop yield, but you want to predict the crop yield if rainfall is 500mm!
Here Regression comes into play.
📖 Definition:
Regression is a statistical technique to predict the value of one variable based on the value of another.
It builds an equation (called a Regression Line) to mathematically express the relationship.
Simple Regression Equation:
Where:
- Y = Dependent Variable (Crop Yield)
- X = Independent Variable (Rainfall)
- a = Intercept (where the line cuts the Y-axis)
- b = Slope (rate of change)
🎯 Uses in Geography:
- Predicting population growth based on economic variables.
- Estimating soil erosion based on rainfall and slope.
- Studying urban sprawl in relation to transport infrastructure.
🔥 Quick Difference Between Correlation and Regression:
| Aspect | Correlation | Regression |
|---|---|---|
| Purpose | Measure relationship strength | Predict one variable from another |
| Directionality | Symmetrical (X ↔ Y) | One-way (X → Y) |
| Output | Correlation Coefficient (r) | Regression Equation (Y = a + bX) |
🧠 Real-world Analogy for Regression:
Imagine you are a tailor.
If you know a customer’s waist size, you can predict their trouser length based on past experience.
➔ You are subconsciously using a regression model!
✍️ Final Key Pointers for UPSC:
- Correlation tells whether and how strongly variables are related.
- Regression tells how to predict one variable based on another.
- Both are part of Quantitative Revolution tools making geography scientific, measurable, and predictive.
✅ Now you have a strong grip on Correlation and Regression!
Next we can go to Gravity Model, which is one of the most fascinating models linking geography with Newton’s Law! 🚀
Gravity Model in Geography
👉 Imagine two big cities, say Delhi and Mumbai.
- They have huge populations (size = mass in our example).
- Naturally, more people, goods, and services will flow between them compared to two small villages.
➔ The larger the cities and closer they are, the stronger the interaction (migration, trade, traffic, etc.).
➔ The smaller the cities or farther they are, the weaker the interaction.
This logic is what the Gravity Model captures!
Where does the idea come from?
👉 Borrowed from Newton’s Law of Gravitation:
“Force of attraction between two bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.”
Same idea applied to human geography!
Gravity Model Formula:
where:
- = Population of city 1
- = Population of city 2
- = Distance between them
- = Interaction (migration, trade, travel, etc.)
🎯 Key Understanding:
- More population → more interaction
- Less distance → more interaction
- More distance → less interaction (because distance acts as a friction or barrier)
🧠 Simple Analogy:
Think of two magnets:
- Bigger magnets attract more strongly.
- Closer magnets attract more strongly.
- Smaller and distant magnets hardly pull each other.
➔ Just like that, cities attract people, goods, services depending on their size and distance.
Applications of Gravity Model in Geography:
- Predicting migration patterns between cities.
- Estimating trade flows between countries.
- Understanding commuting patterns in urban areas.
- Planning transport networks.
✍️ Limitations of the Gravity Model:
- Assumes interaction only depends on size and distance, ignoring factors like:
- Cultural similarity
- Political relations
- Economic ties
- Real-world interactions can be non-symmetrical — city A influences B more than B influences A.
- Distance decay (the effect of distance) is not always uniform.
✨ Modern Improvements:
- Using transport cost or travel time instead of just physical distance.
- Adding other factors like economic opportunities, cultural links.
🔥 Final Crux for UPSC:
- Gravity Model shows that larger and closer places interact more.
- It is a quantitative tool making geography scientific, measurable, and predictive.
- Used mainly in migration, trade, traffic flow analysis.