Describing a Scatterplot

How do we describe the relationship between two quantitative variables using a scatterplot? We describe the overall pattern and deviations from that pattern.

This is the same way we describe the distribution of one quantitative variable using a dotplot or a histogram. To describe the overall pattern of the distribution of one quantitative variable, we describe the shape, center, and spread. We also describe deviations from the pattern (outliers).

Similarly, in a scatterplot, we describe the overall pattern with descriptions of direction, form, and strength. Deviations from the pattern are still called outliers.

Graph the distribution of two quantitative variables in a scatterplot.

Direction

The direction of the relationship can be positive, negative, or neither:

Scatterplot showing positive relationship Scatterplot showing negative relationship Scatterplot showing neither positive nor negative relationship

A positive (or increasing) relationship means that an increase in one of the variables is associated with an increase in the other.

A negative (or decreasing) relationship means that an increase in one of the variables is associated with a decrease in the other.

Not all relationships can be classified as either positive or negative.

Form

The form of the relationship is its general shape. To identify the form, describe the shape of the data in the scatterplot. In practice, forms that we commonly use have mathematical equations. We look at a few of these equations in this course. For now, we simply describe the shape of the pattern in the scatterplot. Here are a couple of forms that are quite common:

Linear form: The data points appear scattered about a line. We use a line to summarize the pattern in the data. We study the equation for a line in this module.

Scatterplot with linear form

Curved form: The data points appear scattered about a smooth curve. We use a curve to summarize the pattern in the data.

Scatterplot with curvilinear form

Strength

The strength of the relationship is a description of how closely the data follow the form of the relationship. Let’s look, for example, at the following two scatterplots displaying positive, linear relationships:

Scatterplot showing strongly related data Scatterplot showing weakly related data

In a strong linear relationship the data points closely follow the linear pattern. In a weaker linear relationship the data points also follow a linear pattern, but the points are not as close to the line. The data is more scattered about the line.

Labeling a relationship as strong or weak is not very precise. We develop a more precise way to measure the strength of a relationship soon.

Outliers

Outliers are points that deviate from the pattern of the relationship. In the scatterplot below, there is one outlier.

Scatterplot showing outlier

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