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Given n data points (x1, y1), ... (Xn, Yn), the linear least- squares fit is the linear function f(x) = mx +b that minimizes the sum of the squares (Figure E (m, b) = Ev; - f(x}))² j=l Show that the minimum value of E occurs for m and b satisfying the two equations Σ+ bn= Σy j=l Ex3+b£xj = £ m j=l j=l j=1 (Xµ, Yn) y= mx + b (X2, y2) (x1, y1) FIGURE The linear least-squares fit minimizes the sum of the squares of the vertical distances from the data points to the line.

Given n data points (x1, y1), ... (Xn, Yn), the linear least- squares fit is the linear function f(x) = mx +b that minimizes the sum of the squares (Figure E (m, b) = Ev; - f(x}))² j=l Show that the minimum value of E occurs for m and b satisfying the two equations Σ+ bn= Σy j=l Ex3+b£xj = £ m j=l j=l j=1 (Xµ, Yn) y= mx + b (X2, y2) (x1, y1) FIGURE The linear least-squares fit minimizes the sum of the squares of the vertical distances from the data points to the line.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Given n data points (x1, y1), ... (Xn, Yn), the linear least- squares fit is the linear function f(x) = mx +b that minimizes the sum of the squares (Figure E (m, b) = Ev; - f(x}))² j=l Show that the minimum value of E occurs for m and b satisfying the two equations Σ+ bn= Σy j=l Ex3+b£xj = £ m j=l j=l j=1 (Xµ, Yn) y= mx + b (X2, y2) (x1, y1) FIGURE The linear least-squares fit minimizes the sum of the squares of the vertical distances from the data points to the line.
Transcribed Image Text:Given n data points (x1, y1), ... (Xn, Yn), the linear least- squares fit is the linear function f(x) = mx +b that minimizes the sum of the squares (Figure E (m, b) = Ev; - f(x}))² j=l Show that the minimum value of E occurs for m and b satisfying the two equations Σ+ bn= Σy j=l Ex3+b£xj = £ m j=l j=l j=1 (Xµ, Yn) y= mx + b (X2, y2) (x1, y1) FIGURE The linear least-squares fit minimizes the sum of the squares of the vertical distances from the data points to the line.
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