Empirical relationship
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In science
Science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...

, an empirical relationship is one based solely on observation rather than theory. An empirical relationship requires only confirmatory data irrespective of theoretical basis. Sometimes theoretical explanations for what were initially empirical relationships are found, in which case the relationships are no longer considered empirical. Other times the empirical relationships are merely approximations, often equivalent to the first few terms of the Taylor series
Taylor series
In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point....

of the "real" answer (though in practice these approximations may be so accurate it is difficult to tell they're approximations). Still other times the relationships may later be found to only hold under certain specific conditions, reducing them to special cases of more general relationships.

Historically the discovery of empirical relationships has been important as a stepping stone to the discovery of theoretical relationships. And on occasion, what was thought to be an empirical factor is later deemed to be a fundamental physical constant
Physical constant
A physical constant is a physical quantity that is generally believed to be both universal in nature and constant in time. It can be contrasted with a mathematical constant, which is a fixed numerical value but does not directly involve any physical measurement.There are many physical constants in...

.

An empirical equation is simply a mathematical statement of one or more empirical relationships in the form of an equation
Equation
An equation is a mathematical statement that asserts the equality of two expressions. In modern notation, this is written by placing the expressions on either side of an equals sign , for examplex + 3 = 5\,asserts that x+3 is equal to 5...

.

• Moore's law
Moore's Law
Moore's law describes a long-term trend in the history of computing hardware: the number of transistors that can be placed inexpensively on an integrated circuit doubles approximately every two years....

• Phenomenology (science)
Phenomenology (science)
The term phenomenology in science is used to describe a body of knowledge that relates empirical observations of phenomena to each other, in a way that is consistent with fundamental theory, but is not directly derived from theory. For example, we find the following definition in the Concise...

• Power law
Power law
A power law is a special kind of mathematical relationship between two quantities. When the frequency of an event varies as a power of some attribute of that event , the frequency is said to follow a power law. For instance, the number of cities having a certain population size is found to vary...

• Empiricism
Empiricism
Empiricism is a theory of knowledge that asserts that knowledge comes only or primarily via sensory experience. One of several views of epistemology, the study of human knowledge, along with rationalism, idealism and historicism, empiricism emphasizes the role of experience and evidence,...

• Empirical
Empirical
The word empirical denotes information gained by means of observation or experimentation. Empirical data are data produced by an experiment or observation....

• Heuristic argument
Heuristic argument
A heuristic argument is an argument that reasons from the value of a method or principle that has been shown by experimental investigation to be a useful aid in learning, discovery and problem-solving. A widely-used and important example of a heuristic argument is Occam's Razor....