Exploring Association — Quiz

Question 2 • Geometry with Statistics

Which is the best representation of a nonlinear association?

Answer

Image with description A scatterplot is shown on a first quadrant coordinate plane. The x axis ranges from 0 to 6 in increments of 1. The y axis ranges from 0 to 4 in increments of 1. There is a point at (0 point 7 comma 2 point 2). There is a point at (1 point 3 comma 1 point 4). There is a point at (1 point 5 comma 1 point 6). There is a point at (1 point 7 comma 1 point 7). There is a point at (1 point 8 comma 2). There is a point at (2 comma 2 point 3). There is a point at (2 point 3 comma 2 point 4). There is a point at (2 point 4 comma 2 point 5). There is a point at (2 point 5 comma 2 point 3). There is a point at (2 point 7 comma 2). There is a point at (3 comma 2 point 4). There is a point at (3 point 1 comma 3 point 5). There is a point at (3 point 3 comma 2 point 6). There is a point at (3 point 6 comma 2 point 4). There is a point at (3 point 8 comma 2 point 7). There is a point at (3 point 9 comma 2 point 6). There is a point at (4 point 1 comma 2 point 8). There is a point at (4 point 5 comma 2 point 7).

Image with description A scatterplot is shown on a first quadrant coordinate plane. The x axis ranges from 0 to 6 in increments of 1. The y axis ranges from 0 to 5 in increments of 1. There is a point at (1 point 2 comma 1 point 1). There is a point at (1 point 3 comma 1 point 4). There is a point at (1 point 6 comma 1 point 6). There is a point at (1 point 7 comma 1 point 7). There is a point at (1 point 8 comma 2). There is a point at (1 comma 2 point 3). There is a point at (2 point 3 comma 2 point 6). There is a point at (2 point 4 comma 2 point 5). There is a point at (2 point 5 comma 2 point 3). There is a point at (2 point 7 comma 2). There is a point at (3 comma 1 point 8). There is a point at (3 point 1 comma 2). There is a point at (3 point 3 comma 2). There is a point at (3 point 3 comma 2 point 3). There is a point at (3 point 6 comma 3 point 4). There is a point at (3 point 8 comma 2 point 7). There is a point at (3 point 9 comma 2 point 6). There is a point at (4 point 1 comma 2 point 8). There is a point at (4 point 5 comma 3).

Image with description A scatterplot is shown on a first quadrant coordinate plane. The x axis ranges from 0 to 6 in increments of 1. The y axis ranges from 0 to 4 in increments of 1. There is a point at (1 point 2 comma 1 point 3). There is a point at (1 point 3 comma 1 point 4). There is a point at (1 point 5 comma 1 point 6). There is a point at (1 point 7 comma 1 point 7). There is a point at (1 point 8 comma 2). There is a point at (2 comma 2 point 3). There is a point at (2 point 3 comma 2 point 4). 2 point 5 comma 2 point 5). There is a point at (2 point 6 comma 2 point 2). There is a point at (2 point 7 comma 2). There is a point at (3 comma 2 point 4). There is a point at (3 point 1 comma 2 point 5). There is a point at (3 point 3 comma 2 point 6). There is a point at (3 point 6 comma 2 point 4). There is a point at (3 point 8 comma 2 point 7). There is a point at (3 point 9 comma 4 point 6). There is a point at (4 point 1 comma 2 point 8). There is a point at (4 point 5 comma 3).

Image with description A scatterplot is shown on a first quadrant coordinate plane. The x axis ranges from 0 to 6 in increments of 1. The y axis ranges from 0 to 4 in increments of 1. There is a point at (0 point 5 comma 1 point 2). There is a point at (1 point 3 comma 2 point 4). There is a point at (1 point 5 comma 2). There is a point at (1 point 7 comma 2 point 3). There is a point at (1 point 8 comma 1 point 7). There is a point at (2 comma 1 point 7). There is a point at (2 point 3 comma 1 point 5). There is a point at (2 point 4 comma 1 point 5). There is a point at (2 point 5 comma 1 point 3). There is a point at (2 point 7 comma 1 point 2). There is a point at (3 comma 1 point 5). There is a point at (3 point 1 comma 1 point 3). There is a point at (3 point 3 comma 1 point 6). There is a point at (3 point 6 comma 1). There is a point at (3 point 8 comma 0 point 7). There is a point at (3 point 9 comma 0 point 8). There is a point at (4 point 1 comma 4 point 5). There is a point at (4 point 5 comma 4 point 2).

Explanation

A nonlinear association is one where the points do not follow an approximately straight-line trend. In D, the y-values rise at first, then generally fall as x increases, and finally rise sharply near x = 4.1 and 4.5. That changing direction makes D the best representation of a nonlinear association.

AI-written and checked against the verified answer.