Kernel Regression

• Python
• R
• SPSS
• SAS
• Stata

from statsmodels.nonparametric.kernel_regression import KernelReg
model = KernelReg(y, X, var_type='c')

library(np)
model <- npreg(y ~ x, data=df)

# Kernel_Regression implementation for spss
* Requires custom extension commands or R/Python integration.

# Kernel_Regression implementation for sas
PROC KDE;
  UNIVAR x / OUT=output;
RUN;

# Kernel_Regression implementation for stata
lpoly y x, kernel(epanechnikov) degree(1) bw(0.5)

A dataset suitable for Kernel Regression analysis with non-linear relationship

• R Code
• Analysis Results

# Generate synthetic data for Kernel Regression
set.seed(123)

# Create non-linear relationship
x <- seq(0, 10, length.out=100)
y <- sin(x) + rnorm(100, sd=0.3)

df <- data.frame(x=x, y=y)

# Plot raw data
plot(x, y, main="Non-linear Relationship", pch=19)

# Perform kernel regression
library(np)
model <- npreg(y ~ x, data=df, bws=0.5)

# Plot fitted curve
x_grid <- seq(min(x), max(x), length.out=200)
pred <- predict(model, newdata=data.frame(x=x_grid))
lines(x_grid, pred, col="red", lwd=2)

# Cross-validate bandwidth selection
bw_cv <- npregbw(y ~ x, data=df)
print(bw_cv)

# Refit with optimal bandwidth
model_opt <- npreg(bw_cv)
pred_opt <- predict(model_opt, newdata=data.frame(x=x_grid))
lines(x_grid, pred_opt, col="blue", lwd=2, lty=2)

legend("topright", legend=c("Data", "Fixed BW", "CV BW"), 
       col=c("black", "red", "blue"), pch=c(19, NA, NA), 
       lty=c(NA, 1, 2), lwd=2)

> # Cross-validate bandwidth selection
> bw_cv <- npregbw(y ~ x, data=df)
> print(bw_cv)

Regression Data (100 observations, 1 variable(s)):

Bandwidth Selection Method: cv.ls

x: 0.456 (selected bandwidth)

> summary(model_opt)

Regression Data: 100 training points, in 1 variable(s)
                        x
Bandwidth(s): 0.456

Kernel Regression Estimator: Local-Constant
Bandwidth Type: Fixed

Residual standard error: 0.287
R-squared: 0.892

Continuous Kernel Type: Second-Order Gaussian
No. Continuous Explanatory Vars.: 1

Need help interpreting the results of your Kernel Regression analysis? Our comprehensive interpretation guide explains:

• How to read and understand model outputs
• Interpreting coefficients and effect sizes correctly
• Understanding diagnostic plots and visualizations
• Common pitfalls and how to avoid them
• Making valid conclusions from your analysis