Scatterplots & Correlation Coefficients: Learn It 3

  • Create scatterplots for bivariate data and answer questions from the graph.
  • Describe the trend of bivariate data.
  • Calculate the correlation coefficient and explain what it means.

Relationship of Bivariate Data

Scatterplots can be used to identify shapes and patterns.

Linear

The relationship between two variables is said to be linear when the points on the scatterplot resemble a straight line. The following scatterplot could be described as being linear.

A linear scatter plot showing vote totals for a reform party candidate. An outlier is circled.
Figure 1. A scatterplot showing a mostly linear relationship between Perot votes in 1996 and Buchanan votes in 2000 across Florida counties, with one clear outlier circled.

The circled point in the upper right-hand corner of the scatterplot represents an outlier (Palm Beach). Outliers appear as departures from the general trend. Scatterplots can be used to identify outliers or extreme observations in the bivariate data.

Non-linear

Scatterplots are also useful for identifying non-linear relationships. The data points can appear scattered about a smooth curve or have no patterns at all. The following scatterplot could be described as being non-linear.

A non-linear scatterplot of fuel efficiency vs steady driving speed.
Figure 2. A scatterplot showing a non-linear relationship between driving speed and fuel efficiency, where fuel efficiency increases up to a point and then decreases, forming a curved pattern.