Correlation

Statistics · Axiom Academy

Understanding the Relationship Between Variables Correlation measures the strength and direction of the linear relationship between two quantitative variables. Strength: How closely the points follow a linear pattern Direction: Whether the relationship is positive or negative Linear: Correlation specifically measures straight-line relationships The correlation coefficient, denoted by r , ranges from -1 to +1, where values closer to -1 or +1 indicate stronger linear relationships. 2 Positive vs Negative Correlation The direction of correlation tells us whether the variables move together in the same direction or opposite directions. As one variable increases, the other tends to increase Example: Study hours and test scores As one variable increases, the other tends to decrease Example: Car age and resale value The strength of correlation indicates how tightly the data points cluster around a linear pattern. Strong: |r| > 0.7 — Points cluster tightly around a line Moderate: 0.3 < |r| < 0.7 — Clear pattern but with more scatter Weak: |r| < 0.3 — Points are widely scattered No Correlation: r ≈ 0 — No linear pattern Note: These are general guidelines. The interpretation can vary depending on the context and field of study. 4 Visualizing Correlation with Scatterplots A scatterplot is the best way to visualize the relationship between two quantitative variables. Each point represents one observation. The x-axis represents the independent (explanatory) variable

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