The correlation coefficient, \( r \), is a number between \( -\infty \) and \( \infty \) -10 and 10 0 and \( \infty \) 0 and 1 -1 and 1 0 and 10 0 and 100

The correlation coefficient, \( r \), ranges from -1 to 1, allowing us to understand both the strength and direction of a linear relationship between two variables. A value of -1 indicates a perfect negative correlation, where as one variable increases, the other decreases, while a value of 1 indicates a perfect positive correlation, meaning both variables increase together. A value of 0 suggests no correlation at all. When interpreting \( r \), it’s crucial to recognize common mistakes. Many assume that correlation implies causation, but that's a dangerous leap! Just because two variables are correlated doesn’t mean one causes the other. Also, look out for outliers, as they can skew your correlation coefficient significantly, yielding misleading conclusions!