Local Averaging

Assume that we have an independent variable $X$ and a dependent variable $Y$. The local averaging consists in finding some nearby data points around a specific data point $A(x, y)$, and calculating the average of $y$ values from the data point $A$ to the nearby data points.

The averaged $y$ serves as the predicted $\hat{y}$ for the $x$ in $A$. The local averaging method do the same with all data points in the dataset. Then, all predicted $\hat{y}$ values are connected to form a local averaging curve.

Considerations:

• The method of choosing data points for local averaging is called k-nearest neighbor.
• Because in the ends there is not the same number of data points to be averaged, the curve tends to be flat on both ends.
• The curve can be distorted by the existence of outliers.