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A scatter plot, also called a scatterplot, scatter graph, scatter chart, scattergram, or scatter diagram, is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data. If the points are coded (color/shape/size), one additional variable can be displayed. The data are 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.Utts, Jessica M. Seeing Through Statistics 3rd Edition, Thomson Brooks/Cole, 2005, pp 166-167.
While Edmund Halley created a bivariate plot of temperature and pressure in 1686, he omitted the specific data points used to demonstrate the relationship. Friendly and Denis claim his visualization was different from an actual scatter plot. Friendly and Denis attribute the first scatter plot to John Herschel. In 1833, Herschel plotted the angle between the central star in the constellation Virgo and Gamma Virginis over time to find how the angle changes over time, not through calculation but with freehand drawing and human judgment.
Sir Francis Galton extended and popularized the scatter plot and many other statistical tools to pursue a scientific basis for eugenics. When, in 1886, Galton published a scatter plot and correlation ellipse of the height of parents and children, he extended Herschel's mere plotting of data points by binning and averaging adjacent cells to create a smoother visualization. Karl Pearson, R. A. Fischer, and other statisticians and eugenicists built on Galton's work and formalized correlations and significance testing.
A scatter plot can suggest various kinds of correlations between variables with a certain confidence interval. For example, weight and height would be on the -axis, and height would be on the -axis. Correlations may be positive (rising), negative (falling), or null (uncorrelated). If the dots' pattern slopes from lower left to upper right, it indicates a positive correlation between the variables being studied. If the pattern of dots slopes from upper left to lower right, it indicates a negative correlation. A line of Curve fitting (alternatively called 'trendline') can be drawn to study the relationship 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. No universal best-fit procedure is guaranteed to generate a correct solution for arbitrary relationships. A scatter plot is also very useful when we wish to see how two comparable data sets agree to show nonlinear relationships between variables. The ability to do this can be enhanced by adding a smooth line such as Local regression.William Cleveland (1993). 9780963488404, At & T Bell Laboratories Published by Hobart Press. . ISBN 9780963488404 Furthermore, if the data are represented by a mixture model of simple relationships, these relationships will be visually evident as superimposed patterns.
The scatter diagram is one of the seven basic tools of quality control.
Scatter charts can be built in the form of bubble chart, marker, or/and .
A person with a lung capacity of who held their breath for 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 will help to determine what kind of relationship there might be between the two variables.
A generalized scatter plot matrix offers a range of displays of paired combinations of categorical and quantitative variables. A mosaic plot, fluctuation diagram, or faceted bar chart may be used to display two categorical variables. Other plots are used for one categorical and one quantitative variables.
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