Scatter plot 1

Scatter plot

Scatter plot

One of the Seven Basic Tools of QualityFirst described by Francis Galton

Purpose To identify the type of relationship (if any) between two variables

Waiting time between eruptions and the duration of the eruptionfor the Old Faithful Geyser in Yellowstone National Park,

Wyoming, USA. This chart suggests there are generally two"types" of eruptions: short-wait-short-duration, and

long-wait-long-duration.

A scatter plot or scattergraph is a type of mathematicaldiagram using Cartesian coordinates to display values fortwo variables for a set of data.

The data is displayed as a collection of points, eachhaving the value of one variable determining the positionon the horizontal axis and the value of the other variabledetermining the position on the vertical axis.[2] This kindof plot is also called a scatter chart, scatter diagram andscatter graph.

Overview

A scatter plot is used when a variable exists that is underthe control of the experimenter. If a parameter exists thatis systematically incremented and/or decremented by theother, it is called the control parameter or independentvariable and is customarily plotted along the horizontalaxis. The measured or dependent variable is customarilyplotted along the vertical axis. If no dependent variableexists, either type of variable can be plotted on either axisand a scatter plot will illustrate only the degree of correlation (not causation) between two variables.

A scatter plot can suggest various kinds of correlations between variables with a certain confidence interval.Correlations may be positive (rising), negative (falling), or null (uncorrelated). If the pattern of dots slopes fromlower left to upper right, it suggests a positive correlation

Scatter plot 2

A 3D scatter plot allows for the visualization of multivariate dataof up to four dimensions. The Scatter plot takes multiple scalarvariables and uses them for different axes in phase space. The

different variables are combined to form coordinates in the phasespace and they are displayed using glyphs and colored using

another scalar variable.[1]

between the variables being studied. If the pattern of dotsslopes from upper left to lower right, it suggests anegative correlation. A line of best fit (alternatively called'trendline') can be drawn in order to study the correlationbetween the variables. An equation for the correlationbetween the variables can be determined by establishedbest-fit procedures. For a linear correlation, the best-fitprocedure is known as linear regression and is guaranteedto generate a correct solution in a finite time.Unfortunately, no universal best-fit procedure isguaranteed to generate a correct solution for arbitraryrelationships. A scatter plot is also very useful whenwe wish to see how two comparable data sets agreewith each other. In this case, an identity line, i.e., ay=x line, or an 1:1 line, is often drawn as a reference.The more the two data sets agree, the more thescatters tend to concentrate in the vicinity of theidentity line; if the two data sets are numericallyidentical, the scatters fall on the identity line exactly.

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 amixture model of simple relationships, these relationships will be visually evident as superimposed patterns.The scatter diagram is one of the basic tools of quality control.[3]

ExampleFor example, to display values for "lung capacity" (first variable) and how long that person could hold his breath, aresearcher would choose a group of people to study, then measure each one's lung capacity (first variable) and howlong 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 ml who held his breath for 21.7 seconds would be represented by a single doton the scatter plot at the point (400, 21.7) in the Cartesian coordinates. The scatter plot of all the people in the studywould enable the researcher to obtain a visual comparison of the two variables in the data set, and will help todetermine what kind of relationship there might be between the two variables.

References[1] Visualizations that have been created with VisIt (https:/ / wci. llnl. gov/ codes/ visit/ gallery. html). at wci.llnl.gov. Last updated: November 8,

2007.[2] Utts, Jessica M. Seeing Through Statistics 3rd Edition, Thomson Brooks/Cole, 2005, pp 166-167. ISBN 0-534-39402-7[3] Nancy R. Tague (2004). "Seven Basic Quality Tools" (http:/ / www. asq. org/ learn-about-quality/ seven-basic-quality-tools/ overview/

overview. html). The Quality Toolbox. Milwaukee, Wisconsin: American Society for Quality. p. 15. . Retrieved 2010-02-05.

External links• What is a scatterplot? (http:/ / www. psychwiki. com/ wiki/ What_is_a_scatterplot?)• Correlation scatter-plot matrix - for ordered-categorical data (http:/ / www. r-statistics. com/ 2010/ 04/

correlation-scatter-plot-matrix-for-ordered-categorical-data/ ) - Explanation and R code

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Article Sources and ContributorsScatter plot  Source: http://en.wikipedia.org/w/index.php?oldid=414568862  Contributors: Acroterion, Ad1024, Alansohn, Alexius08, AndrewHowse, AugPi, Bento00, Bjoram11@yahoo.co.in,BoomerAB, CaAl, CardinalDan, Catalin Bogdan, Chris24, Claygate, Conscious, Cosmicfroggy, Courcelles, Crissov, Cryptic, Curtixlr8, Cyclopia, DVdm, Da monster under your bed,DanielPenfield, Den fjättrade ankan, Dimitrees, DoubleBlue, Downtown dan seattle, Dude1818, Epbr123, Epim, Eskimospy, Faithlessthewonderboy, Fangfufu, FelixKaiser, Funandtrvl, G716,Giftlite, Glenn macgougan, Gogo Dodo, Hgberman, Hooperbloob, Hu12, Hut 8.5, Ishikawa Minoru, Itai, JForget, Kadoo, Karnesky, Lambiam, Llygadebrill, Loodog, Mack2, Marianika,Martarius, Mathstat, McSly, Mdd, Melcombe, Mendaliv, Metacomet, Michael Hardy, Michael Snow, Micropw, Mitch Ames, Mmmmmmmmmm korn, Moorsmur, Nezzadar, Nigelovich,NightwolfAA2k5, Nishkid64, Nwstephens, Oleg Alexandrov, OnePt618, Orphan Wiki, Ph.eyes, Philip Trueman, Piotrus, Qwfp, RabidZombie, Rathinavelpec, Reyk, RodC, Roland Longbow,Ryk, Sbwoodside, ScaldingHotSoup, Snigbrook, Steinsky, Stevertigo, Sturm55, SueHay, TKD, Talgalili, Tedernst, VinceBowdren, VisFan, Watersidedoc, Whosasking, 152 anonymous edits

Image Sources, Licenses and ContributorsImage:Scatter diagram for quality characteristic XXX.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Scatter_diagram_for_quality_characteristic_XXX.svg  License: GNU FreeDocumentation License  Contributors: User:DanielPenfieldImage:oldfaithful3.png  Source: http://en.wikipedia.org/w/index.php?title=File:Oldfaithful3.png  License: Public Domain  Contributors: Anynobody, Maksim, Mdd, Nandhp, Oleg Alexandrov,WikipediaMaster, 6 anonymous editsImage:Scatter plot.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Scatter_plot.jpg  License: Public Domain  Contributors: UCRL

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