Given n data points (x 1 , y 1 ), . . . , (x n ,

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Given n data points (x₁, y₁), . . . , (x_n, y_n), the linear least-squares fit is the linear function

that minimizes the sum of the squares (Figure 26): E(m, b) = ; - f(x;))2 j=1 f(x) = mx + b Show that the

or M m+=; j=1 j=1 j=1 M m x; +bn= j=1 j=1

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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Question Posted: Jan 17, 2024 03:00 AM

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Given n data points (x 1 , y 1 ), . . . , (x n ,

Question:

that minimizes the sum of the squares (Figure 26): E(m, b) = ; - f(x;))2 j=1 f(x) = mx + b Show that the minimum value of E occurs for m and b satisfying the two equations m x; + bn = V; j=1 m j=1 y -- + j=1 j=1 (X2, 32) (1,VD) (Xn, Vn) y = mx + b X

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Calculus

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