Pearson correlation measures the strength of linear relationship between two continuous variables.
⚠Both datasets must have the same number of values. Outliers can significantly affect correlation.
What is Pearson Correlation?
Pearson correlation coefficient (r) quantifies the linear relationship between two variables X and Y. It ranges from -1 to +1, where positive values indicate positive correlation and negative values indicate negative correlation.
Positive Correlation
r > 0: As X increases, Y tends to increase (e.g., height & weight)
Negative Correlation
r < 0: As X increases, Y tends to decrease (e.g., temperature & coat sales)
No Correlation
r ≈ 0: No linear relationship (e.g., shoe size & IQ)
Perfect Correlation
|r| = 1: All points lie on a straight line
💡 Example: X = [1,2,3,4,5], Y = [2,4,5,4,5]. x̄=3, ȳ=4. Σ(x-x̄)(y-ȳ)=6. r = 6/√(10×2) ≈ 0.9487.
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Frequently Asked Questions
What is Pearson correlation coefficient?▼
Pearson r measures linear relationship between two variables. Range: -1 to +1. +1 = perfect positive correlation, -1 = perfect negative correlation, 0 = no linear relationship.
What does correlation tell us?▼
Correlation indicates strength and direction of linear association. It does NOT imply causation. High correlation could be due to third variable or coincidence.
Use when both variables are normally distributed, relationship is linear, and data is paired. For non-linear or ordinal data, use Spearman rank correlation instead.
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