What can we say about the relationship between a correlation r and the slope b of the least-squares line for the same set of data?
A) r is always larger than b.
B) r and b always have the same sign (+ or -).
C) b is always larger than r.
D) b and r are measured in the same units.
E) Both "b is always larger than r" and "b and r are measured in the same units" are correct.

Question

Quizplus · Accepted Answer

The slope and the correlation measure two different things. The slope measures the change in the response variable for a one-unit increase in the explanatory variable, while the correlation measures the strength and direction of the linear relationship between the two variables. The sign of the slope and the correlation cannot be always the same because the slope can be positive or negative, while the correlation can only be positive or negative. However, the sign will be always the same for a positive correlation and a positive slope or for a negative correlation and a negative slope.

What Can We Say About the Relationship Between a Correlation