Piecewise Linear Fitting for Two Sets of Discrete Data

Perform piecewise linear fitting on two sets of discrete data to achieve more accurate fitting results. Piecewise linear fitting is a method that segments the data into multiple intervals and applies linear regression within each segment. This approach is particularly useful when data exhibits distinct "staircase" or "curved" patterns. Implementation typically involves using algorithms like dynamic programming or optimization techniques to identify optimal breakpoints where the data behavior changes. Key functions may include segment identification using error minimization criteria (e.g., sum of squared residuals) and linear regression calculations for each segment using least squares method. By employing piecewise linear fitting, we can more precisely characterize the relationship between datasets, leading to better data interpretation. The fitting results will be visualized to provide an intuitive representation of the relationship between the two datasets, which can be achieved through plotting libraries that display both original data points and fitted line segments with different slopes for each interval.