In the unitary linear regression model, the degree of freedom of the sum of squares of total deviation is n- 1, and then the degree of freedom of the sum of squares of regression is determined by the number of x, so the degree of freedom is 1, and the sum of squares of residuals is the sum of squares of total deviation minus the sum of squares of regression is n-2.

When regression equation or regression line is used to describe the statistical relationship between variables, what are the experimental value yi and the predicted value of regression line respectively? Not exactly the same. The greater the ESS, the better the fitting of multivariate linear regression lines to the observed values of samples.

Extended data:

The regression sum of squares is ESS, the difference between TSS and residual sum of squares, ESS= TSS-RSS.

When estimating the variance of the population, the sum of squares of deviations is used. As long as the sum of the squares of the deviations of the number n- 1 is determined, the variance is also determined; Because after determining the mean value, if the value of n- 1 is known, then the value of the nth number is also determined. Here, the average value is equivalent to a restrictive condition. With this restriction, the degree of freedom for estimating population variance is n- 1.

The degree of freedom in structural mechanics, or dynamic uncertainty, refers to the number of unknown node variables on effective structural nodes when analyzing structural systems. It is called "effective" because any point on the structural member should have the opportunity to have degrees of freedom. We only choose the node displacements that are useful for analyzing the whole structure to discuss, and it is called "unknown" because we usually reduce the number of degrees of freedom as much as possible for the convenience of solving, so we deduct the known displacements.

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