Numerical experiments on a personal computer are used to illustrate the degrees of freedom concept. Random errors from a known distribution are added to a known model, for example,y(x) = α + β ·x, and the least squares fit to the model + error data is computed. The least squares fit produces a new model,y(x) =a+b · x. By definition the sum of squared deviations between the least squares fit model and the data is always less than the sum of squared deviations between the original model and the data. When this process is repeated thousands of times on the computer, using different random errors each time, a pattern emerges. On average the difference between the two sums of squared deviations approaches an integer multiple of the error distribution variance. Furthermore, this integer equals the number of regression parameters in the model. For instance, this is the origin of the two degrees of freedom associated with a linear model. Using the computer it is easy to verify this property for regression models with more than two parameters and for different error distributions. The previous degree of freedom property depends only on the variance of the error distribution and use of the least squares method; it does not depend on the detailed shape of the distribution. However, when the normal error distribution with mean = 0 and variance = 1 is used, a connection to another use of the degrees of freedom terminology is found. For a model withMparameters, the normalized frequency distribution of the difference between the two sets of squared deviations is calculated, using 2,000 computer trials, and shown to match the chi-square distribution withMdegrees of freedom.