What is a high value for a correlation coefficient?

A correlation coefficient is a statistical measure that describes the strength and direction of a relationship between two variables. The value of the correlation coefficient ranges from -1 to 1. A value of 1 indicates a perfect positive correlation between the two variables, meaning that as one variable increases, the other variable also increases in a perfectly linear manner. This represents a strong relationship where changes in one variable are reliably associated with changes in the other.

On the other hand, a value of -1 indicates a perfect negative correlation, which means that as one variable increases, the other decreases in a perfectly linear manner. Values closer to 0 indicate a weaker relationship between the variables, where the changes in one do not consistently associate with changes in the other. Therefore, a correlation coefficient of 1 demonstrates the highest possible value and signifies a perfect linear relationship, making it the correct answer.