Local Regression

Local regression is a nonparametric smoother used to model relationships between variables.

It is applied when the relationship between predictive variables and a dependent variable is unknown or complex. Local regression performs a separate least squares regression for each data point, considering the point itself and its nearest neighbours. The influence of each regression on a new data point is inversely related to the distance from the training point.

For example, in a dataset of economic indicators, local regression can produce a best-fit curve for the unemployment rate over the last 30 years, even if the relationship cannot be expressed with a simple mathematical function.

Local regression is advantageous for modeling complex relationships but can lead to overfitting if not used with sufficient training data. It is computationally intensive and requires careful tuning of hyperparameters like the smoothing parameter and polynomial degree. Despite these challenges, it provides flexible and accurate modeling for various applications.