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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]
Two regression lines (red) bound the range of linear regression possibilities. The shallow slope is obtained when the independent variable (or predictor) is on the x-axis. The steeper slope is obtained when the independent variable is on the y-axis. By convention, with the independent variable on the x-axis, the shallower slope is obtained.
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.
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.