Statistically, the degree of freedom refers to the number of independent or freely changeable data in the sample when the parameters of the population are estimated by the statistics of the sample, which is called the degree of freedom of statistics. Generally speaking, the degree of freedom is equal to the number of independent variables minus their derivatives. For example, the definition of variance is the sample minus the average (the derivative determined by the sample), so for n random samples, its degree of freedom is N- 1.

Mathematically, the degree of freedom is the dimension of a random vector, that is, the minimum number of unit vectors required for a vector to be completely described. For example, the displacement from the computer screen to the kitchen can be used as a three-dimensional vector.

So the degree of freedom of this displacement vector is 3. The degree of freedom is usually related to the sum of squares of these vectors and the parameters in chi-square distribution. .

The application of extended data statistical freedom is as follows:

The degree of freedom of statistical model is equal to the number of independent variables that can be taken freely. For example, in the regression equation, if * * * has a parameter to be estimated, it contains an independent variable (the independent variable corresponding to the intercept is constant). Therefore, the degree of freedom of the regression equation is.

In the individual population, the average value is. When you know an individual, the rest of the individuals can't change at will. Why is population variance calculated by division instead of division? Variance is the expected value of the square of the difference between the actual value and the expected value, so when the overall mean or other statistical parameters are known, variance should be divided, which is an unbiased estimation of variance.

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Baidu encyclopedia-degree of freedom