Find the formula that gives the least squares error for the points (-2, -3), (1, -1), (3, 4).
A) $( - 2 \mathrm {~A} + \mathrm { B } + 3 ) ^ { 2 }$ + $( A + B + 1 ) ^ { 2 }$ + $( 3 A + B - 4 ) ^ { 2 }$
B) $( - 2 A + B + 1 ) ^ { 2 }$ + $( A + B + 3 ) ^ { 2 }$ + $( 3 A + B - 4 ) ^ { 2 }$
C) $( - 2 \mathrm {~A} + \mathrm { B } + 3 ) ^ { 2 }$ + $( A + B + 1 ) ^ { 2 }$ + $( A + B - 4 ) ^ { 2 }$
D) $( - A + B + 3 ) ^ { 2 }$ + $( A + B + 1 ) ^ { 2 }$ + $( A + B - 4 ) ^ { 2 }$

Question

Quizplus · Accepted Answer

The formula for the least squares error involves the sum of the squares of the differences between the actual y-values and the predicted y-values from the linear equation $y = Ax + B$. For each point $(x, y)$, the error term is $(Ax + B - y)^2$. Substituting the given points into this formula results in choice A.

Find the Formula That Gives the Least Squares Error for the Points