In the Bivariate platform, use the Flexible > Kernel Smoother option to fit a locally weighted least squares model to the data. The smoother is formed by repeatedly finding a locally weighted model (mean, linear or quadratic) at sampled points in the domain. The many local fits (512 in total) are combined to produce the smooth curve over the entire domain. This method is also called LOWESS (locally weighted scatterplot smoothing). 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. For more information about the options in the Local Smoother menu, see Bivariate Fit Options.
The Local Smoother report contains the following columns:
R-Square
Measures the proportion of variation accounted for by the smoother model. See Statistical Details for the Smoothing Fit Report.
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)
Enables you to specify the polynomial degree, or lambda, for each local fit.
Weight Function
Enables you to specify the weight function. The LOWESS model uses tri-cube weighting. The weight function determines the influence that each xi and yi has on the fitting of the model.
Smoothness (alpha)
Enables you to specify how many points are considered for each local fit either by entering a value, or by moving the slider. Alpha is a smoothing parameter between 0 and 1. As alpha increases, the curve becomes smoother.
Sampling Delta
Enables you to specify the sampling rate 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
Enables you to specify the robustness of the fitting routine. Each iteration re-weights the points to de-emphasize points that are farther from the fitted curve.