Search⌘ K
AI Features
Home
Courses
Linear Algebra for Data Science Using Python

Least Squared Error Solution

Explore how to calculate and interpret the least squared error solution in linear regression problems. Learn to minimize the sum of squared errors of a linear system using vectorized notation and matrix operations. Gain hands-on experience applying these concepts with Python functions like pseudo-inverse and least squares solving to approximate solutions, even for inconsistent systems.

We'll cover the following...

Squared error

Squared distance is also known as squared error. Consider a linear equation in wiw_i's:

w1a1+w2a2+...+wnan=bw_1a_1+w_2a_2+...+w_na_n=b

The squared error (squared distance) on a given point, (w^1,w^2,...,w^n)(\hat w_1,\hat w_2,...,\hat w_n), is defined as:

SE(w^1,w^2,...,w^n)=(w^1a1+w^2a2+...+w^nan−b)2SE(\hat w_1,\hat w_2,...,\hat w_n)=(\hat w_1a_1+\hat w_2a_2+...+\hat w_na_n-b)^2 ...