Simple Linear Regression (SLR) is a method that determines the best-fitting line through data points by minimizing the least-squares projection error. Unlike the Least Squares Solution (LSS) that selects the closest output vector on a fixed line, SLR involves choosing the line itself, thus defining a space of reachable outputs. This approach involves a search over different possible orientations of the line, comparing projection errors to find the orientation that results in the smallest error. By rotating the line and observing changes in projection distance, SLR effectively identifies the optimal line orientation to model the data. This matters because it provides a foundational understanding of how linear regression models are constructed to best fit data, which is crucial for accurate predictions and analyses.
