Curve Fitting with Parametric Regression Analysis

Uses

• Is a straight line the model that is best suited to describe our data? Or is there something to be gained by including curves in our equation? Curves are represented by adding a higher order polynomial term to the equation. The fit of the model (i.e., the SS_M) will certainly increase with each additional polynomial term, however, it is not clear whether the new equation is significantly better? Remember we loose one df for each term added to our equation, so our MS_M model term in the numerator for the F-statistic may or may not increase.

How is this done

• calculate F = (SS_M for higher degree model - SS_M for lower degree model) / (MS_E for higher degree model)
• compare to F-Tables with numerator df = 1 and denominator df = residual df of the higher degree model

Things to consider

• you can always run this analysis with raw data, standardized (i.e, z-transform), centered (i.e., subtract mean) or on ranked data to make sure they give you essentially similar results.