Statistics Definitions > Contour Plots

## What are Contour Plots?

Contour plots (sometimes called Level Plots) are a way to show a three-dimensional surface on a two-dimensional plane. It graphs two predictor variables X Y on the y-axis and a response variable Z as contours. These contours are sometimes called *z-slices* or *iso-response values*.

This type of graph is widely used in cartography, where contour lines on a topological map indicate elevations that are the same. Many other disciples use contour graphs including: astrology, meteorology, and physics. Contour lines commonly show altitude (like height of a geographical features), but they can also be used to show density, brightness, or electric potential.

**A contour plot is appropriate if you want to see how some value Z changes as a function of two inputs, X and Y:
z = f(x,y). **

## Types

The most common form is the** rectangular contour plot**, which is (as the name suggests) shaped like a rectangle.

**Polar contour plots are circular.**

**Ternary plots**are triangular and show a relationship between

*three*explanatory variables and a response variable. Most commonly, the third explanatory variable is a height value for an XYZ value in ternary space.

## Making a Contour Plot

The **response variables** are *extremely complicated* to calculate by hand, so they are usually generated by specialized software. SPSS cannot generate these plots, but there are several packages that can, including:

**MATLAB**: has several functions including*contourf*(for a filled 2-D plot) and*contour3*(for a 3D plot).**R**: can create a plot with the “filled.contour” command. See this R Documentation for details.**Excel**: can create a*very*basic chart called a surface chart.**JMP**: click**Graph**and then**Contour Plot**. Has a ton of options for levels, data points, colors etc.

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