Kernel Smoother

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. See Cleveland (1979).

Use this method to quickly see the relationship between variables and to help you determine the type of analysis or fit to perform.

For details about the options in the Local Smoother menu, see Fitting Menus.

Local Smoother Report

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. For more information, 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.

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.