Using the Fit Spline command, 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.
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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.
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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.
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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.
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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.
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Sum of squared distances from each point to the fitted spline. It is the unexplained error (residual) after fitting the spline model.
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Enables you to change the λ value, either by entering a number, or by moving the slider.
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The Kernel Smoother command produces a curve formed by repeatedly finding a locally weighted fit of a simple curve (a line or a quadratic) at sampled points in the domain. The many local fits (128 in total) are combined to produce the smooth curve over the entire domain. This method is also called Loess or Lowess, which was originally an acronym for Locally Weighted Scatterplot Smoother. See Cleveland (1979).
The Local Smoother report contains the R-Square for the smoother fit and the Sum of Squares Error. You can use these values to compare the smoother fit to other fits, or to compare different smoother fits to each other.
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Sum of squared distances from each point to the fitted smoother. It is the unexplained error (residual) after fitting the smoother model.
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Specify how to weight the data in the neighborhood of each local fit. Loess uses tri-cube. The weight function determines the influence that each xi and yi has on the fitting of the line. The influence decreases as xi increases in distance from x and finally becomes zero.
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The Fit Each Value command fits a value to each unique X value. The fitted values are the means of the response for each unique X value.