Module 3: Examining Relationships: Quantitative Data
Module 3: Examining Relationships: Quantitative Data
Scatterplots (2 of 5)
Scatterplots (2 of 5)
Learning OUTCOMES
- Use a scatterplot to display the relationship between two quantitative variables. Describe the overall pattern (form, direction, and strength) and striking deviations from the pattern.
Interpreting the 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 described the distribution of one quantitative variable using a dotplot or a histogram in Summarizing Data Graphically and Numerically. 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).
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.
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.
Curvilinear form: The data points appear scattered about a smooth curve. We use a curve to summarize the pattern in the data. We study some specific types of curvilinear forms with their equations in Modules 4 and 12.
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:
In the left scatterplot, the data points closely follow the linear pattern. This is an example of a strong linear relationship. In the scatterplot on the right, 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. This is an example of a weaker linear relationship.Labeling a relationship as strong or weak is not very precise. We develop a more precise way to measure the strength of a relationship shortly.
Outliers are points that deviate from the pattern of the relationship. In the scatterplot below, there is one outlier.
Try It
Fill in the letter of the description that matches each scatterplot.
Descriptions:
A: X = month (January = 1), Y = rainfall (inches) in Napa, CA in 2010 (Note: Napa has rain in the winter months and months with little to no rainfall in summer.)
B: X = month (January = 1), Y = average temperature in Boston MA in 2010 (Note: Boston has cold winters and hot summers.)
C: X = year (in five-ye