SOLUTION: Using the least-squares method, what is the equation of the line of best fit for the data below? Data Points (2,3) (1,0) (1,2) (4,2) A. y= 7/4 B. y= 11/12

Algebra ->  Finance -> SOLUTION: Using the least-squares method, what is the equation of the line of best fit for the data below? Data Points (2,3) (1,0) (1,2) (4,2) A. y= 7/4 B. y= 11/12       Log On


   

Question 1119725: Using the least-squares method, what is the equation of the line of best fit for the data below?

Data Points
(2,3) (1,0)
(1,2) (4,2)
A. y= 7/4


B. y= 11/12


C. y= (1/3x) + (13/12)
D. y= (1/4x) + (5/6)
Answer by math_helper(2461) About Me  (Show Source):
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C.
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The work out:
The desired line is y=mx+b
Let E = error function for each data point

We take the square of the differences between y (=mx+b) and y%5Bi%5D:
E =


Simplifies to:
E = +22m%5E2+%2B+16mb+-+32m+%2B+%284b%5E2-14b%2B17%29+

Partial derivatives WRT m and b give 2 equations in two unknowns:
dE/db = 16m + 8b - 14 (treat m like a constant while taking dE/db)
dE/dm = 44m + 16b - 32 (treat b like a constant while taking dE/dm)


Solve
(1) 16m + 8b - 14 = 0
(2) 44m +16b - 32 = 0
to get m=1/3, b=13/12 —> y = (1/3)x + 13/12