Linear Functions and Modeling

Linear Modeling

Scatterplots

Data can be represented in two variables using a scatterplot.

A scatterplot is a data display consisting of the graph of a set of ordered pairs. A scatterplot shows data for two variables and helps to indicate whether there is a relationship between those variables. The data points of a scatterplot, unlike those of a line graph, are not connected by line segments.

A scatterplot can be used in the real world to analyze data to make informed decisions about a situation. For example, a forester might use a scatterplot to determine how fast maple trees in a reforested area are growing based on their age. Before plotting the data on a scatterplot, a table can be created to organize the data, which represent ordered pairs. Plotting the data on to a scatterplot can then reveal the relationship between the xx- and yy-values of the data set.

Maple Tree Age and Height

Age (years) Height (meters)
2 1.5
2 1.6
3 1.75
3 2.1
4 1.55
4 1.75
4 1.95
5 2
5 2.15
5 2.4
5 2.7
6 2.25
6 3.1
7 2.6
8 2.5
8 2.75
8 3.05
9 3.2

Using a table can help organize data before plotting points on a scatterplot. For instance, a forester might use a table to record the age and height of maple trees in a reforested area.

Scatterplot of Maple Tree Age and Height

Scatterplots can help with visualizing patterns that indicate relationships between xx- and yy-values in a data set. For example, in a scatterplot showing the age and height of maple trees in a reforested area, clusters of points, their area of concentration, and their general direction reveal that the height of maple trees increases, represented by yy-values, as their age increases, represented by xx-values.