Interpreting Correlation Coefficient?

📌 CONCEPT: The correlation coefficient measures the strength and direction of the linear relationship between two variables.

In this case, the strong positive correlation between exercise and BMI suggests that as exercise increases, BMI also tends to increase. Similarly, the weak negative correlation between income and daily expenditure on food indicates that as income increases, daily expenditure on food tends to decrease.

📐 RULE / FORMULA: The correlation coefficient (r) is calculated using the formula r = (Σ [(xi - x̄)(yi - ȳ)]) / (√[Σ(xi - x̄)²] * √[Σ(yi - ȳ)²]), where xi and yi are individual data points, x̄ and ȳ are the mean values, and Σ denotes the sum.

💡 WORKED EXAMPLE: Suppose a study found that a person's exercise (in hours) and BMI (in kg/m²) are related as follows: (2, 22), (4, 24), (6, 26), and (8, 28). If the correlation coefficient is 0.8, we can say that there is a strong positive correlation between exercise and BMI.

⚠️ COMMON MISTAKE: Students often confuse correlation with causation. A strong correlation between two variables does not necessarily mean that one variable causes the other. There could be a third variable or other factors at play.