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It is possible to have multiple independent variables or multiple dependent variables. For instance, in multivariable calculus, one often encounters functions of the form z = f(x,y), where z is a dependent variable and x and y are independent variables. [8] Functions with multiple outputs are often referred to as vector-valued functions.
A cooling curve is a line graph that represents the change of phase of matter, typically from a gas to a solid or a liquid to a solid. The independent variable (X-axis) is time and the dependent variable (Y-axis) is temperature. [1] Below is an example of a cooling curve used in castings. The initial point of the graph is the starting ...
A scatter plot, also called a scatterplot, scatter graph, scatter chart, scattergram, or scatter diagram, [2] 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.
For example, in the notation f(x, y, z), the three variables may be all independent and the notation represents a function of three variables. On the other hand, if y and z depend on x (are dependent variables) then the notation represents a function of the single independent variable x. [20]
Parametric equation. The butterfly curve can be defined by parametric equations of x and y. In mathematics, a parametric equation defines a group of quantities as functions of one or more independent variables called parameters. [1] Parametric equations are commonly used to express the coordinates of the points that make up a geometric object ...
The product of the x and y values of each point on the curve equals the constant of proportionality (k). Since neither x nor y can equal zero (because k is non-zero), the graph never crosses either axis. Direct and inverse proportion contrast as follows: in direct proportion the variables increase or decrease together.
In most mathematical contexts, the independent variable is placed on the horizontal axis and the dependent variable on the vertical axis. For example, if f(x) is plotted against x, conventionally x is plotted horizontally and the value of the function is plotted vertically. This placement is often, but not always, reversed in economic graphs.
The case shown, with deviations measured perpendicularly, arises when errors in x and y have equal variances. In applied statistics, total least squares is a type of errors-in-variables regression, a least squares data modeling technique in which observational errors on both dependent and independent variables are taken into account.