Consider the points (1,3) and (4,4). Find the equation of the line through the origin that the Sum y=mx "best fits" these two points. By best fits, it means of the vertical distances between these points and the line is minized. In the picture bebuy to find the slope m trying to find you are the sum of the lengths of the dotted lines are minized. (Hint: It is actually easier and minize the square equivalent to of the vertical distances.) such that juge of the sums.

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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the
Sum
Consider the points (1,3) and (4,4). Find the
equation of the line y = mx through the origin that
" best fits" these two points. By best fits, it means
of the vertical distances between there.
and the line is minized. In the picture bebuy
the slope
the sum of the lengths of the dotted lines are
minized. (Hint: It is actually easier
points
you are
such that
trying to find
and
equivalent
minize
the
of the
do
of the vertical distances.)
square
3
y
1
M
sums
y=mx
Jespost
Note: This problem is
what is called
a
simplified version of
the line of best fit for a set
data points. The actual lines of pest fit of
a set of points does not have to go through the
origin (like in our example). This requirement
implemented to make the problem simplex
for otherwise we st would have to find the
slope and the ynkeperpt.
we
Transcribed Image Text:the Sum Consider the points (1,3) and (4,4). Find the equation of the line y = mx through the origin that " best fits" these two points. By best fits, it means of the vertical distances between there. and the line is minized. In the picture bebuy the slope the sum of the lengths of the dotted lines are minized. (Hint: It is actually easier points you are such that trying to find and equivalent minize the of the do of the vertical distances.) square 3 y 1 M sums y=mx Jespost Note: This problem is what is called a simplified version of the line of best fit for a set data points. The actual lines of pest fit of a set of points does not have to go through the origin (like in our example). This requirement implemented to make the problem simplex for otherwise we st would have to find the slope and the ynkeperpt. we
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In step 3, why dont we find derivative of (3m-1) / sqrt (1+m^2) instead? 

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How do we get (1-3m)/ sqrt (1+m^2)

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