EL ENG 126 Lecture Notes - Lecture 15: Hidden Markov Model, Multivariate Normal Distribution, Independent And Identically Distributed Random Variables
14 Dec 2017
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Document Summary
The goal of linear regression is to create a line that represents the relationship between two random variables. Consider having the random variables x and y. Given a number of points n , each with the form (xi, yi), we want to minimize the squared error. E[x a by]2 where (x, y) are uniformly chosen within the set {(xn, yn), n = 1, . For this reason, we can obtain the llse (linear least squares estimator) without any datapoints, if we know the joint distribution of x and y. The linear least squares estimator x is given by. X = l[x|y] = a + by where a and b minimize e[x a by]2. Then, we want to prove two things: e[ x] = 0, e[ xy] = 0. By having proved both those facts, we say that x is orthogonal to all linear functions of y. Thus, by the pythagorean theorem, we can say that.
