In statistics, the correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. The value of r always lies between −1 and +1. A value of r closer to ±1 (either +1 or −1) indicates a stronger correlation, while r closer to 0 indicates a weaker or no correlation.
Correlation coefficient r always lies between −1 and +1.
r closer to ±1 = stronger correlation; r closer to 0 = weaker/no correlation.
r = +1: perfect positive; r = −1: perfect negative; r = 0: no correlation.
To compare strength: use |r| (absolute value). Higher |r| = stronger correlation.
Positive r: both variables move together. Negative r: one rises as other falls.
NCERT Class 11 Economics — Statistics for Economics (Correlation chapter).
Correlation Coefficient (r): • Symbol: r (Pearson's r) or ρ (Spearman's rho) • Range: −1 ≤ r ≤ +1 • Formula (Pearson's): r = [Σ(x−x̄)(y−ȳ)] / √[Σ(x−x̄)² × Σ(y−ȳ)²]
Which value of r shows stronger correlation? → The value of r closer to +1 or −1 shows STRONGER correlation. → The value of r closer to 0 shows WEAKER correlation.
Interpretation Table:
| Value of r | Type | Strength |
|---|---|---|
| r = +1 | Perfect positive correlation | Strongest (positive) |
| 0.8 ≤ r < 1 | Strong positive correlation | Strong |
| 0.5 ≤ r < 0.8 | Moderate positive correlation | Moderate |
| 0 < r < 0.5 | Weak positive correlation | Weak |
| r = 0 | No correlation | None |
| −0.5 < r < 0 | Weak negative correlation | Weak |
| −0.8 < r ≤ −0.5 | Moderate negative correlation | Moderate |
| −1 < r ≤ −0.8 | Strong negative correlation | Strong |
| r = −1 | Perfect negative correlation | Strongest (negative) |
Comparing Two Values: • Is r = 0.9 or r = 0.4 a stronger correlation? → r = 0.9 (closer to +1) • Is r = −0.8 or r = +0.3 a stronger correlation? → r = −0.8 (|−0.8| = 0.8 > 0.3)
Key Rule: Compare |r| (absolute value). Higher |r| = stronger correlation.
Positive vs Negative Correlation: • Positive (r > 0): both variables increase together (e.g., height and weight) • Negative (r < 0): one increases while other decreases (e.g., price and demand) • Zero (r = 0): no linear relationship
Example: Given r values: 0.6, −0.9, 0.2, −0.3 Ranked by strength (highest to lowest): −0.9, 0.6, −0.3, 0.2 (Compare absolute values: 0.9 > 0.6 > 0.3 > 0.2)
NCERT: Class 11 Economics — Statistics for Economics (Correlation) Also: Class 12 Maths (Probability and Statistics)
r = 0.9 indicates a stronger correlation. The closer the value of r is to ±1, the stronger the correlation. r = 0.9 is much closer to +1 than r = 0.4. To compare, use the absolute value: |0.9| = 0.9 > |0.4| = 0.4. So r = 0.9 shows a strong positive correlation, while r = 0.4 shows a weak positive correlation.
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