Explain the meaning of functional relationships and correlation relationships

The existence of a functional relationship between the random variable x and y indicates that there is a binary function f, such that f(x,y)=0, of course, you can also understand that there is a function f, such that y=f(x);

If there is a correlation between the two, it means that the correlation coefficient of the two is not 0, that is, the covariance is not equal to 0.

There is no necessary connection between these two concepts, and there is a functional relationship that exists in relation to each other, and a functional relationship that exists is not necessarily related.

1.Assuming that x and z are independently and equally distributed, and the variance exists and is greater than 0, so that y=x+z, then there is no functional relationship between y and x (mainly because z and x are independent, if you have some understanding of measure theory, you can try to prove it, otherwise you can only admit it), but we can calculate that the correlation coefficient between x and y is the property of the variance covariance combined with the definition of the correlation coefficient). Therefore, there may not be a functional relationship between the correlations.

2.Assuming x is a normal distribution with an expectation of 0 and y = x 2, there is a functional relationship between the two. But due to.

e(xy)=e(x 3)=0, and (ex)(ey)=0*ey=0

Therefore, the covariance of the two is 0, that is, the two are not related. Therefore, there is a functional relationship that may not be correlated.

Fully correlated to have function expressions.

First, the nature is different.

1. Correlation is a non-deterministic interdependence of objective phenomena, that is, each value of the independent variable, the dependent variable is non-deterministic due to the influence of random factors.

2. When one or several variables take a certain value, and another variable has a definite value corresponding to it, this relationship is called a deterministic functional relationship, which is recorded as y=f(x), where x is called the independent variable and y is called the dependent variable.

Second, the dependent variables are different.

2. Functional relationship: If the value of the dependent variable is definite and unique, the relationship between the two variables is called the functional relationship.

The correlation relationship is a random relationship in which the numerical changes of two phenomena are not completely determined, and it is an incompletely certain dependence. The difference between correlation and functional relationship is as follows: (1) Functional relationship means that the relationship between variables is definite, while the relationship between two variables of correlation is uncertain.

It can be changed within a certain range; (2) The dependence between the functionally related variables can be expressed by a certain equation y=f(x), and the dependent variable can be extrapolated given an independent variable, while the correlation cannot be expressed by a certain equation. Functional relations are special cases of correlation relations, that is, functional relations are complete correlations, and correlation relations are incomplete correlations. Information**.

Answer, support me.

It means that there is a relationship between two quantities, but the specific relationship is not clear.

A functional relation, on the other hand, is a definite relationship between two quantities that can be described mathematically.

Functional relationship: The value of y is uniquely determined by x, then y and x are called functional relations, for example, a teacup is 5 yuan, and the relationship between the number of money y and the number of x is y 5x, which is a functional relationship.

Correlation: There is some relationship between one variable and another variable, but it is also related to some other factors, such as height x and weight t, weight t and height x have a certain relationship, but it is also related to other factors, t and x are correlated.

1) Functional relationship means that the relationship between variables is definite, while the relationship between two variables is uncertain. It can be changed within a certain range; Zao's.

2) The dependence between the functionally related variables can be expressed by a certain equation y=f(x), and the dependent variable can be deduced by giving the independent variable, while the correlation cannot be expressed by a certain equation. Functional relations are special cases of correlation, i.e., functional relations are complete correlations, and correlations are incomplete functional relations. The stool is cleared.

The functional relationship is the relationship between deterministic phenomena, that is, after the number of one phenomenon is determined, the number of another phenomenon is also completely determined, and the leakage is manifested as a strict functional relationship.

For practical problems, it is very important to clarify the relationship between various quantities and quantities, and establish the correct functional relationship. When establishing a functional relationship, it is necessary to first determine the independent variable and the dependent variable in the problem, and then list the equations according to the relationship between them to derive the functional relationship.

It is not possible to express a correlation with an exact functional expression. According to the expression of the query function, the correlation cannot be expressed by an exact function expression, but through the analysis of a large number of observation data, it can be found that there are certain statistical laws between them, and the function relationship can usually be accurately represented by mathematical formulas, while the correlation cannot be accurately marked by mathematical formulas.

The function cavity relationship reflects that there is a clear and strict quantitative dependence between phenomena, and for each value of the independent variable, the dependent variable has a definite value corresponding to the cavity. This relationship can be reflected in a numerical expression or in an economic formula of quantitative equivalence.

There is indeed an objective quantitative internal relationship between phenomena, which is manifested in the quantitative change of one phenomenon and the corresponding quantitative change of another phenomenon.

The quantitative dependence between phenomena is not definite and has a certain randomness. It is manifested in the fact that given a value of an independent variable, the dependent variable will have a number of values corresponding to it, and there is a certain fluctuation between these values, and the dependent variable always changes around the average of these values and follows a certain law.