SSE and MSE

Sum of squared errors (SSE) is actually the weighted sum of squared errors if the heteroscedastic errors option is not equal to constant variance. The mean squared error (MSE) is the SSE divided by the degrees of freedom for the errors for the constrained model, which is n-2(k+1).

The minimum SSE for a k-joinpoint model is calculated using Lerman's grid-search method (1980) based on Kim et al's standard parametrization (Equation 1). The corresponding values for (τ₁,...,τ_k) and (β₀,β₁, δ₁,...,δ_k) are the estimates of joinpoints and regression coefficients, respectively.