What can the value of the coefficient of correlation (r) be equal to?

The coefficient of correlation, denoted as r, measures the strength and direction of a linear relationship between two variables. It can take on values ranging from -1 to 1. When considering the choices provided, it is important to recognize that the relationship between r and the coefficient of determination, r², is significant.

The coefficient of determination represents the proportion of the variance in the dependent variable that is predictable from the independent variable(s). It is calculated by squaring the correlation coefficient. Because r² essentially derives from r, it follows that if r is high (either positive or negative), r² will also be high, reflecting a strong linear relationship. This makes the relationship clear: while r can indicate direction and strength, r² quantifies how much of the variability can be explained.

The other choices do not align with this context. The slope represents the change in the dependent variable for a unit change in the independent variable, and is distinct from the correlation coefficient. The intercept refers to the value of the dependent variable when the independent variable is zero, which has no relation to the correlation. Lastly, the error term pertains to the difference between observed and predicted values, adding another layer that is unrelated to the straightforward correlation coefficient and its squared value.