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Scatter plot

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A scatter plot is a mathematical diagram used to display values for two variables within a set of data. It is also known as a scattergram, scatter graph, or scatter diagram. These plots use Cartesian coordinates to position individual data points on a grid. Each point represents a single observation from the data set. The position of a point on the horizontal axis is determined by one variable. The position on the vertical axis is determined by the other variable.

oldfaithful3
oldfaithful3

To understand how these plots work, you must look at the relationship between variables. In many experiments, one variable is the control parameter, also called the independent variable. This is the value that an experimenter changes or increments systematically. The independent variable is customarily plotted along the horizontal axis. The second variable is the dependent variable, which is the measured result. This variable is customarily plotted along the vertical axis. If no dependent variable exists, the variables can be placed on either axis. In such cases, the plot shows the degree of correlation between the two values.

Speed of cars and distance to stop
Speed of cars and distance to stop

Scatter plots reveal different types of correlations between variables. A positive correlation occurs if the pattern of dots slopes from the lower left to the upper right. This suggests that as one variable increases, the other also tends to increase. A negative correlation occurs if the pattern slopes from the upper left to the lower right. This indicates that as one value rises, the other value falls. If the dots appear as a random cloud, there is a null correlation, meaning the variables are uncorrelated. Researchers often draw a line of best fit, or trendline, to study these relationships. For linear correlations, a procedure called linear regression is used to find this line.

Matriz de gráficos de dispersão
Matriz de gráficos de dispersão

Beyond simple dots, scatter plots can become much more complex. You can add a third variable by coding the points with different colors, shapes, or sizes. This allows for the visualization of multivariate data, which involves more than two variables. In some advanced cases, a 3D scatter plot is used to show multiple scalar variables. These variables are combined to form coordinates in a phase space. For example, a researcher might study the link between lung capacity and breath-holding time. They would plot lung capacity on the horizontal axis and time on the vertical axis. A person with a capacity of 400 holding their breath for 21.7 seconds would be a single dot at the coordinates (400, 21.7).

The history of these diagrams involves several important scientific figures. In 1686, Edmund Halley created a bivariate plot of temperature and pressure. However, he did not include the specific data points, so many consider his work different from a true scatter plot. Most historians attribute the first actual scatter plot to John Herschel in 1833. Herschel plotted the angle of the star Gamma Virginis in the constellation Virgo over time. He used freehand drawing and human judgment rather than complex calculations to find the pattern. Later, Sir Francis Galton extended these tools to study the heights of parents and children. In 1886, Galton published a scatter plot that included a correlation ellipse. He made the data smoother by binning and averaging adjacent cells. This work was further formalized by statisticians such as Karl Pearson and R. A. Fischer.

Scatter plots are highly significant in modern science and industry. They are recognized as one of the seven basic tools of quality control. They help scientists see nonlinear relationships by adding smooth lines like LOESS. If a data set is a mixture of different simple relationships, those patterns will appear superimposed on the plot. This makes it easy to see if different groups exist within the same data. For instance, the Old Faithful Geyser in Yellowstone National Park shows two distinct types of eruptions. One type involves a short wait and a short duration, while the other involves a long wait and a long duration.

oldfaithful3
oldfaithful3

When dealing with a large number of variables, scientists use a scatter plot matrix. This is a single view that shows all pairwise scatter plots of the variables in a grid format. If you have several variables, the matrix will have rows and columns for each one. A plot located at the intersection of a specific row and column shows the relationship between those two specific variables. This allows a researcher to see how every possible pair of dimensions relates at once. This method is essential for understanding complex systems where many different factors are at play.

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File:Speed of cars and distance to stop.png
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File:Matriz de gráficos de dispersão.svg
Matriz de gráficos de dispersão.svg
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