What range of values indicates a very strong correlation in Pearson's correlation coefficient?

A very strong correlation in Pearson's correlation coefficient is indicated by values ranging from 0.90 to 1 or -0.90 to -1. This measurement reflects the strength and direction of a linear relationship between two variables. When the correlation coefficient approaches 1 or -1, it signifies a strong positive or negative linear relationship, respectively. For example, a coefficient of 0.95 suggests that as one variable increases, the other variable also increases in a very consistent manner. Similarly, a coefficient of -0.95 indicates that as one variable increases, the other decreases consistently.

In contrast, values closer to 0 indicate weak correlations, while values between 0.70 to 0.89 or -0.70 to -0.89 represent a moderate correlation, not a very strong one. Thus, understanding the range of values helps in accurately interpreting the strength of relationships in data analysis involving Pearson's correlation coefficient.