# Scatterplots & Trends

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Different trends in scatter plots. Increasing, Decreasing, No-Trend, and another example of an Increasing trend.

A scatter plot is a type of display using Cartesian coordinates to display values for two variables for a set of data. The data is displayed as a collection of points, each having the value of one variable determining the position on the horizontal axis and the value of the other variable determining the position on the vertical axis. A scatter plot is also called a scatter chart, scatter diagram and scatter graph.

## Overview

A scatterplot showing a decreasing relationship.
The same scatterplot as above, with a trend-line or best-fit line drawn.

A scatter plot only specifies variables or independent variables when a variable exists that is under the control of the experimenter. If a parameter exists that is systematically incremented and/or decremented by the experimenter, it is called the control parameter or independent variable and is customarily plotted along the horizontal axis. The measured or dependent variable is customarily plotted along the vertical axis. If no dependent variable exists, either type of variable can be plotted on either axis and a scatter plot will illustrate only the degree of correlation between two variables.

A scatter plot can suggest various kinds of correlations between variables with a certain confidence level. Correlations may be positive (rising), negative (falling), or null (uncorrelated). If the pattern of dots slopes from lower left to upper right, it suggests a positive correlation between the variables being studied. If the pattern of dots slopes from upper left to lower right, it suggests a negative correlation. A line of best fit (alternatively called 'trendline') can be drawn in order to study the correlation between the variables. An equation for the correlation between the variables can be determined by established best-fit procedures. For a linear correlation, the best-fit procedure is known as linear regression and is guaranteed to generate a correct solution in a finite time. Unfortunately, no universal best-fit procedure is guaranteed to generate a correct solution for arbitrary relationships.

One of the most powerful aspects of a scatter plot, however, is its ability to show nonlinear relationships between variables. Furthermore, if the data is represented by a mixture model of simple relationships, these relationships will be visually evident as superimposed patterns.

For example, to display values for "lung capacity" (first variable) and how long that person could hold his breath (second variable), a researcher would choose a group of people to study, then measure each one's lung capacity (first variable) and how long that person could hold his breath (second variable). The researcher would then plot the data in a scatter plot, assigning "lung capacity" to the horizontal axis, and "time holding breath" to the vertical axis. A person with a lung capacity of 400 cc who held his breath for 21.7 seconds would be represented by a single dot on the scatter plot at the point (400, 21.7) in the Cartesian coordinates. The scatter plot of all the people in the study would enable the researcher to obtain a visual comparison of the two variables in the data set, and help to determine what kind of relationship there might be between the two variables.