1/4/2024 0 Comments Piecewise graph![]() The most awesome part of this simple algorithm is that it allows you easily understand your data by solving multiple linear regressions, so if you have data that doesn’t fit a single line, piecewise linear regression can help you. Piecewise linear regression takes the best aspects of linear regression and solves complex problems that we wouldn’t be able to solve with a simple linear regression. ![]() We can see the PWLF result in the graph above. The most amazing thing about it is that you can still analyze each segment as a normal linear regression, calculate the same statistics as a linear regression, etc. Now with the break points known, we can fit our data. ![]() Variation of temperature (K) with height (m) and PWLF. Below we have the system of equations that construct our problem: The idea behind piecewise linear regression is that if the data follows different linear trends over different regions of the data, as shown before, then we should model the regression function in “pieces”. Piecewise Linear Regression: Solution of Our Problems However, if you need interpretability to deeply understand the problem, piecewise linear regression is your buddy. So if you don't care so much about interpretability, you can stop reading here. The problem of polynomial regression is that you lose the interpretability of the model when adding the polynomial terms (quadratic, cubic, etc). Above I plotted a 3rd order polynomial regression fitting the data. When I was brainstorming the problem, one of the question I asked myself was: why don’t I try to fit a polynomial regression? It’s simple and we can find implementations all over the internet. Variation of temperature (K) with height (m) and 3rd order polynomial regression
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