Degrees of freedom

Updated: Aug 20, 2021

The minimal number of independent characteristics, or variables, required to specify completely the state of the system at a given moment. If there exists a constraint or a set of constraints on these variables, other words, relationships among the variables, each such constraint reduces the number of degrees of freedom. Thus, the number of degrees of freedom equals the number of variables that completely specify the system less the numbeisr of constraints imposed on these variables. For example, the number of degrees of freedom for the least squares residuals from a linear regression model with K parameters estimated from a sample of N observations equals (N-K), since in minimizing the sum of squared residuals K first-order conditions are imposed on N data points.

Reference: Oxford Press Dictonary of Economics, 5th edt.

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