Plot (graphics)

Introduction
A plot is a graphical technique for representing a data set, usually as a graph showing the relationship between two or more variables.

Creating Plots
The plot can be drawn by hand or by a computer. In the past, sometimes mechanical or electronic plotters were used. In learning resources creating a plot can be regarded as a relevant step in understanding data or understanding how parameters of a mathematical function determine the plot.

Visual Represention
Graphs are a visual representation of the relationship between variables, which are very useful for humans who can then quickly derive an understanding which may not have come from lists of values.

Extracting Data from Plots
Given a scale or ruler, graphs can also be used to read off the value of an unknown variable plotted as a function of a known one, but this can also be done with data presented in tabular form.

Applications of Plots
Graphs of functions are used in mathematics, sciences, engineering, technology, finance, and other areas.

Spatial Data
A digital elevation model can be regarded as mapping $$g$$ for points $$(x,y) \in \mathbb{R}^2$$ to the elevation $$g(x,y)=z$$ of the point. The result is a 3D plot.



Overview
Plots play an important role in statistics and data analysis. The procedures here can broadly be split into two parts:
 * quantitative and
 * graphical.

Quantitative Techniques
Quantitative techniques are a set of statistical procedures that yield numeric or tabular output. Examples of quantitative techniques include: These and similar techniques are all valuable and are mainstream in terms of classical analysis.
 * hypothesis testing
 * analysis of variance
 * point estimates and confidence intervals
 * least squares regression

Graphical Techniques
There are also many statistical tools generally referred to as graphical techniques. These include:
 * scatter plots
 * spectrum plots
 * histograms
 * probability plots
 * residual plots
 * box plots, and
 * block plots

Use-Cases of Graphical Techniques
Graphical procedures such as plots are a short path to gaining insight into a data set in terms of testing assumptions, model selection, model validation, estimator selection, relationship identification, factor effect determination, outlier detection. Statistical graphics give insight into aspects of the underlying structure of the data.

Solve Mathematical Equations Graphically
Graphs can also be used to solve some mathematical equations, typically by finding where two plots intersect.

Types of plots
The following learning resources focus on different type of plots.

Learning Activity
Walk over the type of plots and identify a individual use-case in your specific domain.


 * Biplot : These are a type of graph used in statistics. A biplot allows information on both samples and variables of a data matrix to be displayed graphically. Samples are displayed as points while variables are displayed either as vectors, linear axes or nonlinear trajectories. In the case of categorical variables, category level points may be used to represent the levels of a categorical variable. A generalised biplot displays information on both continuous and categorical variables.
 * Bland–Altman plot : In analytical chemistry and biostatistics this plot is a method of data plotting used in analysing the agreement between two different assays. It is identical to a Tukey mean-difference plot, which is what it is still known as in other fields, but was popularised in medical statistics by Bland and Altman.
 * Bode plots are used in control theory.
 * Box plot : In descriptive statistics, a boxplot, also known as a box-and-whisker diagram or plot, is a convenient way of graphically depicting groups of numerical data through their five-number summaries (the smallest observation, lower quartile (Q1), median (Q2), upper quartile (Q3), and largest observation). A boxplot may also indicate which observations, if any, might be considered outliers.
 * Carpet plot : A two-dimensional plot that illustrates the interaction between two and three independent variables and one to three dependent variables.
 * Comet plot : A two- or three-dimensional animated plot in which the data points are traced on the screen.
 * Contour plot : A two-dimensional plot which shows the one-dimensional curves, called contour lines on which the plotted quantity q is a constant. Optionally, the plotted values can be color-coded.
 * Dalitz plot : This a scatterplot often used in particle physics to represent the relative frequency of various (kinematically distinct) manners in which the products of certain (otherwise similar) three-body decays may move apart

Plots for specific quantities

 * Arrhenius plot : This plot compares the logarithm of a reaction rate ($$\ln(k)$$, ordinate axis) plotted against inverse temperature ($$1/T$$, abscissa). Arrhenius plots are often used to analyze the effect of temperature on the rates of chemical reactions.
 * Dot plot (bioinformatics) : This plot compares two biological sequences and is a graphical method that allows the identification of regions of close similarity between them. It is a kind of recurrence plot.
 * Lineweaver–Burk plot : This plot compares the reciprocals of reaction rate and substrate concentration. It is used to represent and determine enzyme kinetics.

Examples
Types of graphs and their uses vary very widely. A few typical examples are:
 * Simple graph: Supply and demand curves, simple graphs used in economics to relate supply and demand to price. The graphs can be used together to determine the economic equilibrium (essentially, to solve an equation).
 * Simple graph used for reading values: the bell-shaped normal or Gaussian probability distribution, from which, for example, the probability of a man's height being in a specified range can be derived, given data for the adult male population.
 * Very complex graph: the psychrometric chart, relating temperature, pressure, humidity, and other quantities.
 * Non-rectangular coordinates: the above all use two-dimensional rectangular coordinates; an example of a graph using polar coordinates, sometimes in three dimensions, is the antenna radiation pattern chart, which represents the power radiated in all directions by an antenna of specified type.

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