Four features, or it is not a description

A scatterplot shows two quantitative variables measured on the same individuals, one point per individual. The explanatory variable, the one used to explain or predict, goes on the horizontal axis; the response variable goes on the vertical axis.

Eight students report their weekly study hours and their exam scores. Hours is the explanatory variable and score the response, because the question is whether studying predicts performance. Swapping the axes produces a different plot and a different regression line later, so the choice is made deliberately and stated.

Not every pair has a natural direction. Height and arm span on the same people can go on either axis, and the plot is then simply a display of association. When the study does name a direction, following it keeps the analysis aligned with the question being asked.

A complete description covers all four, in context:

1. Form: linear, curved, or no clear pattern. Justified by how the points fall, not by whether a line can be drawn.
2. Direction: positive (as one variable increases the other tends to increase) or negative.
3. Strength: how tightly the points cluster around the pattern. Strong, moderate, or weak.
4. Unusual features: outliers, clusters, gaps, or any point that departs from the pattern.

For the study data: "the association between weekly study hours and exam score is positive, linear, and strong, with no apparent outliers; students who study more tend to score higher." Every clause names a variable, which is what makes it a description of these data rather than a template.

"It is positive" is the answer that loses three of the four marks. So is a description that never mentions hours or scores, since two variables with the same plot could be anything.

The justification for calling a form linear has to come from the points. A line can be drawn through any cloud, and drawing one proves nothing.

The tell for a curved pattern is that the points bend systematically: low at both ends and high in the middle, or rising steeply then flattening. Such a plot can still produce a large correlation, which is why the plot settles form and the correlation coefficient does not. Topic 5.4's residual plot makes the same point with more resolution.

Strength and form are separate judgments too. A tightly clustered curve is a strong nonlinear association; a loosely scattered straight band is a weak linear one. Reporting "strong" without saying strong what leaves the reader to guess which.

Three kinds of departure are worth calling out:

1. Outliers in the pattern: points far from the overall trend, even if neither of their coordinates is extreme.
2. Extreme x-values: points far to the left or right, which get outsized influence on a fitted line, as Topic 5.5 shows.
3. Clusters and gaps: two separate clouds may mean two subgroups, and a single description of the combined plot can then describe neither.

An unusual point is investigated, not removed. It may be a recording error, in which case it can be corrected, or a real observation, in which case it belongs in the analysis and usually in the description as well.