What does a correlation coefficient r close to ±1 signify about a data set?

What does a correlation coefficient r close to ±1 signify about a data set?

• A. No linear relationship
• B. Weak linear relationship
• C. A strong linear relationship with direction indicated by sign
• D. A perfect non-linear relationship

Answer: (C)

The key idea is that the correlation coefficient measures how strongly two variables relate along a straight-line pattern and in what direction that pattern goes. When r is near +1 or near −1, the data points lie very close to a straight line, indicating a strong linear relationship. The sign tells the direction: a positive sign means the variables rise together, while a negative sign means one tends to decrease as the other increases. This reflects a tight linear association, though not necessarily a perfect one unless r is exactly ±1. If the relationship is curved rather than linear, r won’t be near ±1 even if there’s a noticeable association.

The key idea is that the correlation coefficient measures how strongly two variables relate along a straight-line pattern and in what direction that pattern goes. When r is near +1 or near −1, the data points lie very close to a straight line, indicating a strong linear relationship. The sign tells the direction: a positive sign means the variables rise together, while a negative sign means one tends to decrease as the other increases. This reflects a tight linear association, though not necessarily a perfect one unless r is exactly ±1. If the relationship is curved rather than linear, r won’t be near ±1 even if there’s a noticeable association.