Interpreting Correlation Coefficient?

📌 CONCEPT: A correlation coefficient is a statistical measure that describes the relationship between two variables, indicating the strength and direction of the linear relationship between them.

📐 RULE / FORMULA: The correlation coefficient (r) ranges from -1 to 1, where 1 represents a perfect positive linear relationship, -1 represents a perfect negative linear relationship, and 0 indicates no linear relationship. The absolute value of r indicates the strength of the relationship, with higher values indicating a stronger relationship.

💡 WORKED EXAMPLE: Suppose we have a dataset of hours spent studying (x) and marks obtained (y). If we calculate the correlation coefficient and get a value of 0.8, it means that there is a strong positive linear relationship between hours spent studying and marks obtained. For instance, if a student studies for 10 hours, they are likely to obtain high marks (y). Similarly, if a student watches TV for 10 hours, they are likely to obtain low marks (y).

⚠️ COMMON MISTAKE: Students often mistake a high correlation coefficient for a causal relationship, but it only indicates a strong association between the variables. It does not imply that one variable causes the other.