If the correlation coefficient r equals 0, what does that indicate about the relationship between two data sets?

If the correlation coefficient r equals 0, what does that indicate about the relationship between two data sets?

• A. There is a strong positive correlation.
• B. There is no relationship between the data sets.
• C. There is a strong negative correlation.
• D. The data sets are proportional.

Answer: (D)

The main idea being tested is what the correlation coefficient tells us about how two data sets relate linearly. When r is 0, there is no linear relationship between the two sets—the points on a scatterplot don’t line up along any straight line. That doesn’t mean there’s no relationship at all; there could be a nonlinear pattern where y depends on x in a curved way (like a parabola or a sine wave), which a straight line wouldn’t capture. Proportionality means a constant ratio y = kx, which creates a straight line through the origin and would give r near ±1, not 0. So r = 0 reflects the absence of a linear association, not necessarily the absence of any relationship.

The main idea being tested is what the correlation coefficient tells us about how two data sets relate linearly. When r is 0, there is no linear relationship between the two sets—the points on a scatterplot don’t line up along any straight line. That doesn’t mean there’s no relationship at all; there could be a nonlinear pattern where y depends on x in a curved way (like a parabola or a sine wave), which a straight line wouldn’t capture.

Proportionality means a constant ratio y = kx, which creates a straight line through the origin and would give r near ±1, not 0. So r = 0 reflects the absence of a linear association, not necessarily the absence of any relationship.