The Kernel Smoother option 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. The Kernel Smoother option implements the approach of Cleveland (1979) with a small adjustment for cases of near-perfect fits; the 6 * q50 argument in Cleveland’s biweight function is replaced by max(6 * q50, 2 * q90), where q50 and q90 are the 50th and 90th percentiles, respectively.
Use this method to quickly see the relationship between variables and to help you determine the type of analysis or fit to perform.
For more information about the options in the Local Smoother menu, see Fitting Menus.
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.
R-Square
Measures the proportion of variation accounted for by the smoother model. See Smoothing Fit Reports.
Sum of Squares Error
Sum of squared distances from each point to the fitted smoother. It is the unexplained error (residual) after fitting the 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 0, 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.
Sampling Delta
Controls the amount of sampling that is used in the fitting process. By default, the sampling delta is zero, which means that none of the points are skipped. As the sampling delta increases, points within delta of the last sample point are skipped in the fitting process. You can use this option to reduce the number of points used when the data are dense.
Robustness
Re-weights the points to de-emphasize 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.