Using the Fit Spline option, you can fit a smoothing spline that varies in smoothness (or flexibility) according to the lambda (λ) value. The lambda value is a tuning parameter in the spline formula. As the value of λ decreases, the error term of the spline model has more weight and the fit becomes more flexible and curved. As the value of λ increases, the fit becomes stiff (less curved), approaching a straight line.
Note the following information:
• The smoothing spline can help you see the expected value of the distribution of Y across X.
• The points closest to each piece of the fitted curve have the most influence on it. The influence increases as you lower the value of λ, producing a highly flexible curve.
• If you want to use a lambda value that is not listed on the menu, select Fit Spline > Other. If the scaling of the X variable changes, the fitted model also changes. To prevent this from happening, select the Standardize X option. Note that the fitted model remains the same for either the original X variable or the scaled X variable.
• You might find it helpful to try several λ values. You can use the Lambda slider beneath the Smoothing Spline report to experiment with different λ values. However, λ is not invariant to the scaling of the data. For example, the λ value for an X measured in inches, is not the same as the λ value for an X measured in centimeters.
For more information about the options in the Smoothing Spline Fit menu, see Fitting Menus. For statistical details about this fit, see Fit Spline.
The Smoothing Spline Fit report contains the R-Square for the spline fit and the Sum of Squares Error. You can use these values to compare the spline fit to other fits, or to compare different spline fits to each other.
R-Square
Measures the proportion of variation accounted for by the smoothing spline model. See Smoothing Fit Reports.
Sum of Squares Error
Sum of squared distances from each point to the fitted spline. It is the unexplained error (residual) after fitting the spline model.
Change Lambda
Enables you to change the λ value, either by entering a number, or by moving the slider.