Robust Locally-Weighted Regression

Robust Locally-Weighted Regression (LOWESS)

  • LOWESS is an outlier resistant, robust locally weighted regression and scatter smoothing, in which the fitted value of xk is the value of a polynomial fit to the data using weighted least squares, where the weight for (xi, yi) is large if xi is close to xk and small if xi is far from xk.
  • Using the order of polynomial as d=12, provides adequate smoothed points and flexibility for capturing information from the data.
Robust LOWESS Fit Compared to Standard Regression
  • LOWESS curve can display the relationships that are not visible in a standard linear regression analysis. It is another way of depicting the "local" relationship between a response variable and a predictor variable over parts of their ranges, which may differ from a "global" relationship determined using a standard linear regression.

An Example of Standard Linear Regression and the Corresponding 95% CI Band

Standard Linear Regression

Robust LOWESS Fit to the Same Data and the Corresponding Weighted 95% CI

Robust LOWESS Fit