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 kernel smoother fit and the Sum of Squares Error. You can use these values to compare the kernel smoother fit to other fits, or to compare different kernel smoother fits to each other.
 R-Square Sum of Squares Error Sum of squared distances from each point to the fitted kernel smoother. It is the unexplained error (residual) after fitting the kernel smoother model. Local Fit (lambda) Select the polynomial degree for each local fit. Quadratic polynomials can track local bumpiness more smoothly. Lambda is the degree of certain polynomials that are fitted by the method. Lambda can be 1 or 2. Weight Function 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. Smoothness (alpha) Controls how many points are part of each local fit. Use the slider or type in a value directly. Alpha is a smoothing parameter. It can be any positive number, but typical values are 1/4 to 1. As alpha increases, the curve becomes smoother. Robustness Reweights the points to deemphasize points that are farther from the fitted curve. Specify the number of times to repeat the process (number of passes). The goal is to converge the curve and automatically filter out outliers by giving them small weights.
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