§ Sum of quadratic errors

• Consider the function $(x - a)^2 + (x - b)^2$
• Minimum error is at $2(x - a) + 2(x - b)$, or at (a + b)/2.
• As we move away towards either end-point, the error always increases !
• So the "reduction in error" by moving towards b from (a + b)/2 is ALWAYS DOMINATED by the "increase in error" by moving towards a from (a + b)/2.