What are degrees of freedom?

In econometrics, the degrees of freedom are the number of observations in a sample minus the number of restrictions which are placed upon them. If you were take a number of observations in a sample (n) then the amount of degrees of freedom you have in this sample are the amount of observations which are free to vary.

Take an example where we have 200 observations (N) and four variables with one constant. In the case of this model itself, the actual model has 4 degrees of freedom because the model has 4 independent variables within which the data is ‘free’ to vary. 1 degree of freedom out of the 200 observations is lost due to the present of the constant or intercept. Obviously, because the constant is fixed, it cannot vary. The remaining degrees of freedom equal to 195 are associated with the remainder which is the residual. Therefore, we have 200 observations with 199 degrees of freedom after you take 1 away for the presence of the constant. Hence, why we often observe the degrees of freedom presented as N-1.

As a general rule, the lower the degrees of freedom, the less reliable the estimates will be and vice versa.

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