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Say you have a bunch of data points (x;, Y;), i = 1,., n and wish to draw the line of best fit through them. The given points do not all fall on the same straight line but you can find the gradient mand intercept b such the line best 'fits' the given points (see figure). (х, у) d; (X1, Yı) • тх, + b Figure Now let d; = Y; – (mx; + b) be the vertical deviation of (;, Y;) from the line. To obtain the best fit line, we want to minimize Prove that the line of best fit is obtained when x; + bn = i=1 m Yi i=1 and т i=1 i=1 DO NOT USE LAGRANGE MULTIPLIERS FOR THIS PROBLEM.

Say you have a bunch of data points (x;, Y;), i = 1,., n and wish to draw the line of best fit through them. The given points do not all fall on the same straight line but you can find the gradient mand intercept b such the line best 'fits' the given points (see figure). (х, у) d; (X1, Yı) • тх, + b Figure Now let d; = Y; – (mx; + b) be the vertical deviation of (;, Y;) from the line. To obtain the best fit line, we want to minimize Prove that the line of best fit is obtained when x; + bn = i=1 m Yi i=1 and т i=1 i=1 DO NOT USE LAGRANGE MULTIPLIERS FOR THIS PROBLEM.

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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Say you have a bunch of data points (x;, Yi) , i = 1,..., n and wish to draw the line of best fit through them. The given points do not all fall on the same straight line but you can find the gradient mand intercept b such the line best 'fits' the given points (see figure). yA (X;, Y;) d{? (X1, Yı) • • тх, + b X Figure Now let d; = y; – (mx; + b) be the vertical deviation of (x;, y;) from the line. To obtain the best fit line, we want to minimize п i=1 Prove that the line of best fit is obtained when m X; + bn Yi i=1 and n Ea² +b т Xi i=1 DO NOT USE LAGRANGE MULTIPLIERS FOR THIS PROBLEM.
Transcribed Image Text:Say you have a bunch of data points (x;, Yi) , i = 1,..., n and wish to draw the line of best fit through them. The given points do not all fall on the same straight line but you can find the gradient mand intercept b such the line best 'fits' the given points (see figure). yA (X;, Y;) d{? (X1, Yı) • • тх, + b X Figure Now let d; = y; – (mx; + b) be the vertical deviation of (x;, y;) from the line. To obtain the best fit line, we want to minimize п i=1 Prove that the line of best fit is obtained when m X; + bn Yi i=1 and n Ea² +b т Xi i=1 DO NOT USE LAGRANGE MULTIPLIERS FOR THIS PROBLEM.
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