Describing a Scatterplot

A scatterplot packs a lot into one picture, so one word can never capture it. Direction tells you whether the variables move together (positive) or opposite ways (negative) as you scan left to right. Form tells you the shape the pattern traces: a straight line, a curve, or no pattern at all. Strength tells you how tightly the points cluster around that form, from a thin, obedient band to a wide scatter cloud. And unusual points flag any observation that breaks away from the rest, either by sitting far from the pattern (an outlier) or by exerting unusual pull on where a fitted line would go (potentially influential).

To read these off a graph, start wide: does the cloud trend up, down, or show no trend? That is direction. Then step back further and ask what shape the trend takes: straight or curved? That is form. Next, judge how close the points sit to that shape: tight hugging means strong, loose scatter means weak. Finally scan for any point sitting apart from the crowd, and describe where it sits relative to the rest.

This topic is the entry point to the whole unit. Once you can describe a scatterplot in words, correlation gives strength and direction a number (but only for linear form), and the least-squares line only makes sense to fit when the form is actually straight. Residual plots later come back to check whether the form you assumed was really linear, so the habit of checking form here pays off every time you fit a line down the road.