Goodness-of-Fit Statistics

TableCurve 2D uses four common goodness of fit statistics. In the following descriptions, SSM is the sum of squares about the mean, SSE is the sum of squared errors (residuals), n is the total number of data values, and m is the number of coefficients in the model. DOF, the degree of freedom, is n-m.

Coefficient of Determination (r-squared)

r² = 1 - SSE/SSM

Degree of Freedom Adjusted Coefficient of Determination

DOF r² = (1 - SSE*(n-1))/(SSM*(DOF-1))

Fit Standard Error (Root MSE)

StdErr = sqrt(SSE/DOF)

F-statistic

F-stat = ((SSM-SSE)/(m-1))/(SSE/DOF)

As a fit becomes more ideal, the r² values approach 1.0 (0 represent a complete lack of fit), the standard error decreases toward zero, and the F-statistic goes toward infinity.