Correlation Coefficient

Statistics · Axiom Academy

LESSON Correlation Coefficient Understanding Pearson's Correlation Coefficient and Linear Relationships Correlation measures how two variables move together. When one variable increases, does the other tend to increase, decrease, or show no pattern? r = 1: Perfect positive correlation r = -1: Perfect negative correlation 2. Pearson's Correlation Formula The correlation coefficient is calculated using the deviations of each data point from their respective means. x i , y i are individual data points x̄, ȳ are the means of x and y The numerator measures how x and y vary together The denominator standardizes the result to [-1, 1] The correlation coefficient always falls between -1 and 1. Let's visualize what different values mean. 4. Interpreting Correlation Values Understanding what different correlation values tell us about the relationship between variables. 5. Key Properties of Correlation Important characteristics and limitations of Pearson's correlation coefficient. Dimensionless: r has no units and is not affected by changes in scale or units Symmetric: The correlation between X and Y equals the correlation between Y and X Linear relationships only: r measures linear association, not all types of relationships Sensitive to outliers: Extreme values can significantly influence the correlation Not causation: Correlation does not imply that one variable causes changes in the other Standardized: Always bounded between -1 and 1, making comparisons easy

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