Describe an association from a scatterplot

Describe an association

Describe a plotted association using three separate features. Read direction from left to right, form from the shape of the path and strength from the spread of the points around it

1. Look for a pattern first A consistent pattern from left to right indicates an association; no consistent pattern indicates no association \(\displaystyle \text{consistent pattern}\Rightarrow\text{association}\)
2. Read direction from left to right An upward trend is positive and a downward trend is negative \(\displaystyle \text{up from left to right}\Rightarrow\text{positive}\)
3. Separate form from direction A straight path is linear and a curved path is non-linear, regardless of whether it rises or falls \(\displaystyle \text{straight path}\Rightarrow\text{linear form}\)
4. Judge strength by clustering Strength depends on how closely the points follow a path, not on the path's steepness or height \(\displaystyle \text{small spread about a path}\Rightarrow\text{stronger association}\)

Worked example

A scatterplot contains the points (1, 1), (2, 5), (3, 2), (4, 7), (5, 4) and (6, 8). The points follow a rising straight pattern with noticeable spread. Describe the association

1. \(\displaystyle x:1\to6,\quad y:1\to8\)The response values generally rise as the explanatory values increase, so the direction is positive
2. \(\displaystyle \text{straight path}\Rightarrow\text{linear form}\)The stated path is approximately straight, so the form is linear
3. \(\displaystyle \text{noticeable spread}\Rightarrow\text{moderate strength}\)The points have some but not large departures from the path, so the strength is moderate
4. \(\displaystyle \text{moderate positive linear association}\)The three features together give the complete description

Common mistakes

Difficulty levels

Questions about this topic

In this chapter