In a scatter plot of two quantitative variables, what does a strong positive linear relationship look like?

• A. Points form a random cloud; correlation near 0
• B. Points cluster around a vertical line; correlation near -1
• C. Points cluster around an upward-sloping line; correlation close to +1
• D. Points lie along a horizontal line; correlation near -1

Answer: (C)

A strong positive linear relationship means the two variables rise together in a fairly perfect straight-line pattern. In a scatter plot, you’d see points tightly clustered around an upward-sloping line, so as one variable increases, the other tends to increase as well. The strength of that relationship is reflected by a correlation coefficient near +1, indicating both a clear direction (positive) and a tight fit to a line (strong).

If you saw a random cloud of points, there would be no clear upward or downward pattern, and the correlation would be near 0. If the data clustered around a vertical line, that wouldn’t represent a meaningful linear relationship between the two horizontal and vertical scales. A horizontal line would imply little change in the second variable as the first changes, also yielding near 0 correlation. A strong negative relationship would show a downward-sloping line with a correlation near -1, meaning one variable increases as the other decreases.