When fitting a trend to an odd number of years, why is $x$ measured from the middle year?

It makes the slope

b

zeroCorrect answerYour answerIt makes

\sum x = 0

, so

a = \frac{\sum y}{n}

and

b = \frac{\sum xy}{\sum x^{2}}

Correct answerYour answerIt makes every

y

value equal to its trend valueCorrect answerYour answerIt is required for the trend to riseCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

The normal equations are $\sum y = na + b\sum x$ and $\sum xy = a\sum x + b\sum x^{2}$ .
With $\sum x = 0$ they separate: $a = \frac{\sum y}{n}$ , $b = \frac{\sum xy}{\sum x^{2}}$ .

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When fitting a trend to an odd number of years, why is xxx measured from the middle year?