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

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) (Show Source): You can put this solution on YOUR website!
C.
===================
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 :
E =

Simplifies to:
E =

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

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