LOESS Smoothing Regression

LOESS smoothing regression estimates a smooth curve by fitting weighted local regressions in a moving neighbourhood of each point, with tricube weights and optional robustness iterations.

LOESS는 각 점 주변의 이웃 자료에 가중 국소회귀를 반복 적합해 매끄러운 추세 곡선을 그리는 비모수 평활 방법입니다.

I don't know what shape the relationship between two variables has; how can I draw a data-driven trend line?

두 변수 관계가 어떤 모양인지 모를 때 자료에서 추세선을 그리려면 어떻게 하나요?

LOESS fits a small weighted regression around each value of the predictor, using the nearest fraction of the data (the span), and joins the local fits into a smooth curve. It is mainly an exploratory tool for seeing the shape of a relationship, and it gives no single slope or p value.

When to use LOESS Smoothing Regression

• You want to see the shape of a relationship before choosing a parametric model
• The relationship may change direction more than once
• Outliers are present and a robust smoother is helpful

When to use something else

• You need coefficients, tests or confidence intervals for a curve; use natural cubic spline regression instead
• There are several predictors to adjust for at once; use generalized additive models (GAM) instead

Assumptions and requirements

• The mean of the outcome is a smooth function of the predictor
• The span is suitable for the amount of data and curvature
• Observations are independent
• A single predictor (the first feature) is smoothed with local linear fits

What the analysis reports

• Fitted curve evaluated over the range of the predictor
• Span and number of robustness iterations
• Variance explained by the smoother and by a straight line
• Residual standard error

How to report it

A LOESS smoother (span = [value]) showed that [outcome] rose with [predictor] up to about [value] and then levelled off; the smoother explained [value]% of the variance compared with [value]% for a straight line.

Related methods

• Natural Cubic Spline Regression
• Generalized Additive Models (GAM)
• Polynomial Regression

Run LOESS Smoothing Regression on Quorant