Finding the Best Fit Linear Regression with 3+ Points

With three or more data points, it's virtually impossible to find a line that passes through them all—meaning your Mean Squared Error (MSE) won't be zero.

So, how do we find the "Best Fit" line? We search for the w0(intercept) and w1(slope) that minimize the total squared error. The resulting loss function L(w_0, w_1) forms a convex bowl shape in 3D space!

The red point at the bottom of the bowl is the optimal solution, giving us the minimum MSE. We find this point mathematically by taking partial derivatives of the loss function with respect to w0 and w1 and setting them to zero. This is the core principle of minimizing errors in linear regression!

https://youtu.be/TbrQlUgJiyY
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All animations in this video were made with ManimGL and ManimCE, an open-source animation library built in Python. You can find more information about the project here: https://github.com/3b1b/manim, https://github.com/manimCommunity/manim
manimCE: https://www.manim.community/

#MachineLearning #MSE #SSE #LinearRegression #AI #manim#MLIntuition

Видео Finding the Best Fit Linear Regression with 3+ Points канала AIHighschool