What is the range of values for the correlation coefficient?

The correlation coefficient, commonly denoted as ( r ), measures the strength and direction of a linear relationship between two variables. The value of the correlation coefficient is bounded between -1 and 1.

When the correlation coefficient is exactly 1, it indicates a perfect positive linear relationship, meaning that as one variable increases, the other variable also increases in a perfectly proportional manner. Conversely, a correlation coefficient of -1 signifies a perfect negative linear relationship, where an increase in one variable corresponds to a decrease in the other variable in a perfectly proportional manner. A correlation coefficient of 0 indicates no linear relationship between the variables.

These bounds (-1 to 1) are crucial for interpreting the strength and direction of relationships in statistical analysis. Values outside this range do not exist for the correlation coefficient, reinforcing the importance of understanding its limits in data analysis.