For K-Nearest Neighbors (KNN) regression, a value $K$ and a prediction point $x_0$ are first chosen. The algorithm estimates the response value $f(x_0)$ by averaging the training observations closest to $x_0$. The process is as follows: 1. Calculate the distance (typically Euclidean) between $x_0$ and all other training observations. 2. Identify the $K$ training observations closest to $x_0$, denoted by the set $N_0$. 3. Average the response values of these $K$ observations to predict the output for $x_0$. Formally, the equation for this process is: $\hat{f}(x_0) = \frac{1}{K} \sum_{x_i \in N_0}y_i$