Table of Contents
Introduction: Correlation क्या है?
Topic is What is Correlation? Let’s Start.
Definition:
Correlation दो या अधिक variables के बीच संबंध (relationship) का अध्ययन है। यह measure करता है कि एक variable बदलने पर दूसरा variable किस दिशा और कितनी मात्रा में बदलता है।
👉 Important Note: Correlation ≠ Causation
केवल संबंध होना यह नहीं बताता कि एक variable दूसरे का कारण है।
Also Link for Correlation
✍️ Examples:
- Study Hours ↑ → Marks ↑ ⇒ Positive correlation
- Temperature ↑ → Blanket Usage ↓ ⇒ Negative correlation
- Shoe Size ↔ Exam Marks ⇒ Zero correlation
Types of Correlation
Correlation को तीन आधारों पर classify किया जाता है:
(A) Direction के आधार पर
- Positive Correlation (सकारात्मक सहसंबंध)
- जब एक variable बढ़ता है और दूसरा भी बढ़ता है
- Formula:
- Example: Income ↑ → Expenditure ↑
- Negative Correlation (नकारात्मक सहसंबंध)
- जब एक variable बढ़ता है और दूसरा घटता है
- Formula:
- Example: Temperature ↑ → Blanket Usage ↓
- Zero Correlation (शून्य सहसंबंध)
- Variables के बीच कोई संबंध नहीं
- Formula:
- Example: Shoe Size ↔ Exam Marks
(B) Form/Shape के आधार पर
- Linear Correlation (रेखीय सहसंबंध)
- Relation straight line equation से explain हो
- Equation:
- Example: Distance ↔ Time (constant speed)
- Non-linear Correlation (वक्र-रेखीय सहसंबंध)
- Relation curve में हो
- Equation:
- Example: Age ↔ Physical Fitness
(C) Degree of Correlation के आधार पर
- Perfect Correlation:
या 
- High Degree:
- Moderate:
- Low:
या 
Your are reading Topic is What is Correlation,
Comparison Table: Types of Correlation
| Basis | Type | Formula/Value | Example |
|---|---|---|---|
| Direction | Positive |  | Study Time ↑ → Marks ↑ |
| Direction | Negative |  | Temp ↑ → Blanket Usage ↓ |
| Direction | Zero |  | Shoe Size ↔ Marks |
| Form/Shape | Linear |  | Distance ↔ Time |
| Form/Shape | Non-linear |  | Age ↔ Fitness |
| Degree | Perfect |  | Physics Laws |
| Degree | High |  | Height ↔ Weight |
| Degree | Moderate |  | Practice ↔ Performance |
| Degree | Low |  | Rainfall ↔ Car Sales |
Shortcut Formula:
![r = \frac{n\sum xy - (\sum x)(\sum y)}{\sqrt{[n\sum x^2-(\sum x)^2][n\sum y^2-(\sum y)^2]}}](https://rajrank.com/wp-content/ql-cache/quicklatex.com-76a96ab3018648b88d5bbefa2a681a07_l3.png "Rendered by QuickLaTeX.com")
Properties:
- ⇒ Perfect Positive
- ⇒ Perfect Negative
- ⇒ No correlation
- Unit-free measure
⇒ No correlationSolved Example (Karl Pearson’s r)
Data:
| x | y |
|---|---|
| 1 | 2 |
| 2 | 4 |
| 3 | 3 |
| 4 | 5 |
| 5 | 7 |
Solution:
Interpretation: Strong Positive Correlation
Spearman’s Rank Correlation (ρ)
Formula:
Where:
- d = Rank difference
- n = Number of observations
Solved Example:
| Student | Maths Rank | Stats Rank |
|---|---|---|
| A | 1 | 2 |
| B | 2 | 1 |
| C | 3 | 3 |
| D | 4 | 5 |
| E | 5 | 4 |
Solution:
Interpretation: High Positive Correlation
Practice MCQs (Correlation)
Q1. Income ↑ और Saving ↑ ⇒ कौन सा correlation है?
A) Negative
B) Positive
C) Zero
D) Perfect
Q2. Shoe Size और Exam Marks ⇒ कौन सा correlation है?
A) Positive
B) Negative
C) Perfect
D) Zero
Q3. Karl Pearson’s correlation coefficient (r) की value किस range में रहती है?
A) [0, 1]
B) (−∞, +∞)
C) [−1, +1]
D) (0, 100)
Q4. Spearman’s Rank correlation formula में “d” क्या दर्शाता है?
A) Deviation from mean
B) Rank Difference
C) Data set size
D) Degree of freedom
FAQs
Q1. क्या correlation का मतलब causation होता है?
👉 नहीं, correlation सिर्फ संबंध बताता है, कारण-परिणाम नहीं।
Q2. Karl Pearson’s r और Spearman’s ρ में अंतर?
👉 Pearson → Quantitative data, linear relation
👉 Spearman → Rank/order data, monotonic relation
Q3. r = 0.74 का मतलब?
👉 Strong Positive Correlation
Completed Topic: What is Correlation
Next Topic: 3.2 Regression (Concept + Equations + Solved Examples)
Also Read Classification of Data in Statistics