What Are Empirical Formulas?

In scientific experiments and production practices, it is often necessary to start from a set of experimental data and seek an approximate expression y = (x) for the function y = f (x). This approximate expression is called an empirical formula.

The empirical formula is a type of function numerical approximation formula, which refers to the formula of the fitted curve obtained from the known data by the method of least squares. It is an approximate expression of a function inferred from the experimental results. The changing law of the phenomenon.

In order to establish an empirical formula that is both simple and practical and reflects the nature of the phenomenon, always outline the function's general image, select the type of function, and then use the image method, point selection method, average method, and least square method to determine the function. The parameter to be determined is the empirical constant to obtain the fitted curve and empirical formula. For example, the empirical formula is taken as an n-dimensional space straight line:

Where n coefficients

It is the empirical constant to be determined. ^[1]

Establish mathematical expressions of the relationships between variables based on measured data and historical data of related variables (usually known as empirical formulas). Use probability statistics theory to determine the validity of the mathematical expressions established and how to use the obtained empirical formulas to perform Predictive analysis.

Its main contents are: establishing mathematical expressions (usually known as empirical formulas) of the relationships between variables based on measured data and historical data of related variables, using probability statistics theory to determine the validity of established mathematical expressions and how to use the obtained The empirical formula goes to predictive analysis from literature sources.

The regression analysis method not only provides a general way to establish mathematical expressions (also often referred to as empirical formulas) of the correlation between variables, but also analyzes the effectiveness of the established empirical formulas through calculations so that they can be effectively used in Manage forecasting and control.

Most of the graphs encountered in the physics experiments of solving the parameters of the graph are ordinary curves (see the table below), so most of these graphs can be represented by an equation. The equations that are opposite to the experimental graph are generally called empirical formulas.

When studying the relationship between variables, often choose variables according to the stated goals, collect data, establish realistic regression equations, test the significance of the regression equations, and use regression analysis to find the relationship between the variables. The relational formula is not deterministic, but approximate. This kind of function usually called empirical formula is called a regression function.